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chapter
ii
Princeton Primers in Climate
David Archer, The Global Carbon Cycle
Geoffrey K. Vallis, Climate and the Oceans
Shawn J. Marshall, The Cryosphere
David Randall, Atmosphere, Clouds, and Climate
David Schimel, Climate and Ecosystems
Michael Bender, Paleoclimate
Andrew P. Ingersoll, Planetary Climates

iii
princeton university press Princeton & Oxford
Planetary Climates
Andrew P. Ingersoll

Copyright © 2013 by Princeton University Press
Published by Princeton University Press, 41 William Street, Princeton, New
Jersey 08540
In the United Kingdom: Princeton University Press, 6 Oxford Street, Wood-
stock, Oxfordshire OX20 1TW
press.princeton.edu
All Rights Reserved
ISBN 978-0-691-14504-4
ISBN (pbk.) 978-0-691-14505-1
Library of Congress Control Number: 2013939167
British Library Cataloging-in-Publication Data is available
This book has been composed in Minion Pro and Aviner LT Std
This book is printed on recycled paper
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
FPO
(FSC logo here)

Contents
1 Introduction: The Diversity of Planetary Climates 1
2 Venus: Atmospheric Evolution 7
3 Venus: Energy Transport and Winds 26
4 Mars: Long-Term Climate Change 74
5 Mars: The Present Era 92
6 Titan, Moons, and Small Planets 111
7 Jupiter the Gas Giant 136
8 Jupiter Winds and Weather 162
9 Saturn 202
10 Uranus, Neptune, and Exoplanets 223
11 Conclusion 240
Glossary 247
Notes 257
Further Reading 271
Index 273

1 Introduction:
The Diversity of
Planetary Climates
Climate is the average weather—long-term
properties of the atmosphere like temperature, wind,
cloudiness, and precipitation, and properties of the sur-
face like snow, glaciers, rivers, and oceans. Earth has a
wide range of climates, but the range among the planets
is much greater. Studying the climates of other planets
helps us understand the basic physical processes in a
larger context. One learns which factors are important in
setting the climate and how they interact.
Earth is the only planet with water in all three phases—
solid, liquid, and gas. Mars has plenty of water, but it’s al-
most all locked up in the polar caps as ice. There’s a small
amount of water vapor in its atmosphere but no stand-
ing bodies of liquid water. Venus has a small amount of
water vapor in its atmosphere, but the Venus surface is
hot enough to melt lead and is too hot for solid or
liquid
water. Thus by human standards, Venus is too hot and
Mars is too cold. The classic “habitable zone,” where
Earth resides and life evolved, lies in between.
Things get strange in the outer solar system. Titan, a
moon of Saturn, has rivers and lakes, but they’re made
of methane, which we know as natural gas. The giant

chapter 1
2
planets have no solid or liquid surfaces, so you would
need a balloon or an airplane to visit them. The climates
there range from terribly cold at the tops of the clouds
to scorching hot in the gaseous interiors, with warm,
wet, rainy layers in between. Some of the moons in the
outer solar system have oceans of liquid water beneath
their icy crusts. The solar system’s habitable zone could
be an archipelago that includes these icy moons, but the
crusts could be tens of kilometers thick. Their subsurface
oceans are beyond the scope of this book.
The diversity of planetary climates is huge, but the
basic ingredients are the same—the five elements H,
O, C, N, and S. A fundamental difference is the rela-
tive abundance of hydrogen and oxygen. In the inner
solar system—Earth, Mars, and Venus—the elements
are combined into compounds like oxygen (O2
), carbon
dioxide (CO2
), nitrogen (N2
), sulfur dioxide (SO2
), and
water (H2
O). In the outer solar system—Jupiter, Saturn,
Uranus, and Neptune—the elements are combined into
compounds like methane (CH4
), ammonia (NH3
), hy-
drogen sulfide (H2
S), and water. Saturn’s moon Titan has
an atmosphere of nitrogen and methane, and Jupiter’s
moon Io has an atmosphere of sulfur dioxide. The com-
position of a planetary atmosphere has a profound effect
on its climate, yet many of the processes that control the
composition are poorly understood.
The underlying physical processes are the same as
well. Temperature is a crucial variable, and it is largely
but not entirely controlled by distance to the Sun. The
temperature of the planet adjusts to maintain thermal

Diversit y of Pl anetary Climates
3
equilibrium—to keep the amount of outgoing infrared
radiation equal to the amount of absorbed sunlight.
Clouds and ice reflect sunlight, leading to cooler tem-
peratures, but clouds also block outgoing infrared radia-
tion, leading to warmer temperatures down below. Many
gases like water vapor, carbon dioxide, methane, am-
monia, and sulfur dioxide do the same. They are called
greenhouse gases, although an actual greenhouse traps
the warm air inside by blocking the wind outside. An
atmosphere has nothing outside, just space, so the green-
house gases trap heat by blocking the infrared radiation
to space. Venus has clouds of sulfuric acid and a massive
carbon dioxide atmosphere that together reflect 75% of
the incident sunlight. Yet enough sunlight reaches the
surface, and enough of the outgoing radiation is blocked,
to make the surface of Venus hotter than any other sur-
face in the solar system. Gases like nitrogen (N2
) and
oxygen (O2
) do not block infrared radiation and are not
significant contributors to the greenhouse effect.
The wind speeds on other planets defy intuition. At
high altitudes on Venus, the winds blow two or three
times faster than the jet streams of Earth, which blow
at hurricane force although they usually don’t touch the
ground. In fact, Earth has the slowest winds of any planet
in the solar system. Paradoxically, wind speed seems
to increase with distance from the Sun. Jupiter has jet
streams that blow three times faster than those on Earth,
and Neptune has jet streams that blow ten times faster.
The weather is otherworldly. At least it is unlike
what we are used to on Earth. Mars has two kinds of

chapter 1
4
clouds—water and carbon dioxide. And Jupiter has three
kinds—water, ammonia, and a compound of ammonia
and hydrogen sulfide. Mars has dust storms that occa-
sionally enshroud the planet. Jupiter and Saturn have
no oceans and no solid surfaces, but they have lightning
storms and rain clouds that dwarf the largest thunder-
storms on Earth. Saturn stores its energy for decades and
then erupts into a giant thunderstorm that sends out a
tail that wraps around the planet.
Many of these processes are not well understood.
Our Earth-based experience has proved inadequate to
prepare us for the climates we have discovered on other
planets. The planets have surprised us, and scientists
often emerge from a planetary encounter with more
questions than answers. But surprises tell us something
new, and new questions lead to new approaches and
greater understanding. If we knew what we would find
every time a spacecraft visited a planet, then we wouldn’t
be learning anything. In the chapters that follow, we will
see how much we know and don’t know about climate,
using the planets to provide a broader context than what
we experience on Earth.
We will visit the planets in order of distance from the
Sun, starting with Venus and ending with planets around
other stars. Most planets get one or two chapters. Usually
the first chapter is more descriptive—what the planet is
like and how it got that way. The second chapter is more
mechanistic—describing the physical processes that
control the present climate of that planet. The chapters
are augmented by sections called boxes, which contain

Diversit y of Pl anetary Climates
5
equations and constitute a brief textbook-type introduc-
tion to climate science.
Chapter 2 is about the greenhouse effect and climate
evolution, for which Venus is the prime example. Chap-
ter 3 is about basic physical processes like convection,
radiation, Hadley cells, and the accompanying winds,
with Venus as the laboratory. Mars illustrates the “faint
young Sun paradox,” in which evidence of ancient rivers
(chapter 4) contradicts results from astronomy that the
Sun’s output in the first billion years of the solar system
was 70% of its current value. Mars also allows us to talk
about the fundamental physical processes of conden-
sation and evaporation (chapter 5), since exchanges of
water vapor and CO2
between the atmosphere and polar
ice determine the climate of Mars. Titan allows us to
study a hydrologic cycle in which the working fluid is
not water (sections 6.1–6.3). Titan is an evolving atmo-
sphere, close to the lower size limit of objects that can
retain a sizeable atmosphere over geologic time (section
6.4). Below this limit, the atmospheres are tenuous and
transient (section 6.5).
Jupiter is almost a cooled-down piece of the Sun, but
the departures from solar composition tell a crucial story
about how the solar system formed (chapter 7). The giant
planetsarelaboratoriesforstudyingtheeffectofplanetary
rotation on climate (chapter 8), including the high-speed
jet streams and storms that last for centuries. Chapter 9 is
about Saturn, a close relative of
Jupiter, although the dif-
ferences are substantial and hard to understand. Uranus
spins on its side, which allows us to compare sunlight

chapter 1
6
and rotation for their effects on weather patterns (sec-
tion 10.1). Neptune has the
strongest winds of any planet
(section 10.2), and we speculate about why this might be.
The field of exoplanets—
planets around other stars (sec-
tion 10.3) is full of new discoveries, and we only give a
brief introduction to this rapidly expanding field.
This book was written for a variety of readers. One is an
undergraduate science major or a nonspecialist scientist
who knows little about planets or climate. This reader will
learn a lot about the planets and something about the fun-
damental physical processes that control climate. We go
fairly deep into the physical processes, but the emphasis is
on intuitive understanding. We touch on convection, ra-
diation, atmospheric escape, evaporation, condensation,
atmospheric chemistry, and the dynamics of rotating flu-
ids. There are good textbooks and popular science books
on planetary science1,2,3,4
and there are multiauthored
specialized books about individual planets.5,6,7,8,9
There
are also good textbooks on atmospheric science.10,11,12,13
Therefore another potential reader is a student of atmo-
spheric science who has learned the relevant equations
and wants to step back and think about the fundamental
processes in a broader planetary context. Finally, there
are the climate specialists and planetary specialists who
want to know about the mysteries and unsolved problems
in planetary climate. Such readers might solve some of
the many mysteries about planetary climates and thereby
help us understand climate in general.

2 Venus:
Atmospheric Evolution
2.1 Earth’s Sister Planet Gone Wrong
Until the beginning of the space age, Venus5
was
considered Earth’s sister planet. In terms of size, mass, and
distance from the Sun, it is the most Earth-like planet, and
people assumed it had an Earth-like climate—a humid at-
mosphere, liquid water, and warm temperatures beneath
its clouds, which were supposed to be made of condensed
water. This benign picture came apart in the 1960s when
radio telescopes14
peering through the clouds measured
brightness temperatures close to 700 K. Also in the 1960s,
the angular distribution of reflected sunlight
—the exis-
tence of a rainbow in the clouds—revealed that they were
made of sulfuric acid droplets.15
The Soviet Venera probes
showed that the atmosphere was a massive reservoir of
carbon dioxide, exceeding the reservoir of limestone
rocks on Earth. The U.S. Pioneer Venus radar images
showed a moderately cratered volcanic landscape with
no trace of plate tectonics.
We now know that Venus mostly has an Earth-like
inventory of volatiles—the basic ingredients of atmo-
spheres and oceans—but with one glaring exception,

chapter 2
8
and that is water. Earth’s ocean is three hundred times as
massive as its atmosphere. Water is more abundant than
all the other volatiles combined, including carbon diox-
ide, nitrogen, and oxygen. In contrast, Venus has only a
small amount of water, and it is all in the atmosphere.
Relative to the mass of the planet, the amount of water
on Venus is ~4 × 10−6
times the amount on Earth. This
raises some fundamental questions: Was Venus born dry,
and if so, how? Or, was Venus born with an Earth-like
inventory of water that it somehow lost? These ques-
tions are the theme of this chapter. In section 2.1 we re-
view the volatile inventories for the terrestrial planets.
In section 2.2 we discuss the possibility that Venus lost
a large amount of water, perhaps an ocean’s worth, over
geologic time. The evidence is found in the isotopes of
hydrogen
—the anomalously high deuterium to hydro-
gen ratio, which could come about when the lighter hy-
drogen escaped the planet’s gravity at a higher rate than
the heavier deuterium. Finally, in section 2.3 we discuss
how Venus might have lost its ocean while Earth held
on. The effect of extra sunlight on Venus is amplified
by feedback
—the warmer it gets, the more water vapor
enters the atmosphere, which makes it even warmer be-
cause water vapor is a potent greenhouse gas. Somewhere
between Earth and Venus, the theory goes, an Earth-like
planet cannot exist. Inside this critical zone, the oceans
boil away and are eventually lost to space.
Venus comes closer to the Earth than any other
planet—its orbit around the Sun is 72% the size of
Earth’s orbit. The planet itself is 95% the size of Earth,

Venus: Atmospheric Evolution
9
and its surface gravity is 90% of Earth’s. The bulk den-
sities are nearly the same. The density of a terrestrial
planet tells us about the proportions of rock and metal
inside. The metal, mostly iron, is denser and resides in
the core. The rocks are oxidized metals, mostly silicon,
magnesium, and iron combined with oxygen, and have
densities one-third that of the metallic core. From the
bulk densities, one infers that the mass of rock relative
to the mass of metal is about 2.2 for Earth and about 3.0
for Venus. Thus Venus and Earth are rocky terrestrial
planets with similar amounts of metals locked away in
their metallic cores.
Given these similarities in size, distance from the Sun,
and bulk composition, one might expect the two planets
would have similar climates and similar inventories of
the lighter elements H, O, C, N, and S. These elements
are the main ingredients of atmospheres, oceans, and
ice sheets, which are the basic elements of climate. In
some ways this expectation is correct, but in other ways
it fails miserably. Venus has a small amount of water, all
in vapor form, a massive atmosphere of carbon dioxide,
and a surface temperature of ~730 K (457 °C , 855 °F).
Clouds of sulfuric acid enshroud the planet (fig. 2.1). The
pressure at the ground is 92 bars, or 92 times the Earth’s
sea-level pressure. Since pressure (force per unit area) is
the weight of overlying atmosphere (gravity g times mass
per unit area), the mass per unit area of the atmosphere
of Venus is about 100 times that of Earth when one takes
the lower gravity of Venus into account. Table 2.1 gives
the volatile inventories of Venus, Earth, and Mars.16,17

chapter 2
10
Earth actually has a lot of carbon dioxide, but it’s
not in the atmosphere. Instead it resides mostly in
limestone—calcium and magnesium sediments with
chemical formulas like CaCO3
and CaMg(CO3
)2
. These
carbonate compounds have accumulated over the life
of the Earth when igneous rocks (rocks formed from a
Figure 2.1. Venus whole disk in the ultraviolet. The clouds in the
image are made of sulfuric acid droplets and are ~65 km above the
planet’s surface.
(Source: http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery
-venus.html#clouds)

11
melt) containing calcium and magnesium have weath-
ered—ground down and dissolved—and then combined
with carbon dioxide in the oceans where they precipitate
out. Calcium is found in many kinds of igneous rock, but
a simple example is CaSiO3
. Dissolved in water, CO2
is a
weak acid, which helps to dissolve the rock. The net re-
sult is that the CaSiO3
combines with CO2
to make SiO2
(silica) and CaCO3
(calcium carbonate).
The silica precipitates out as quartz and as hydrated
silica (clay). The calcium carbonate precipitates out as
limestone. As CO2
is released from inside the Earth in
Table 2.1.
Mass of volatiles per mass of planet. Atm is the amount in the atmo-
sphere only. Total includes the amount in the crust, mantle, polar
ice, and oceans. Except for the numbers in parentheses, the table is
adapted from tables 4.2 and 4.4 of de Pater and Lissauer (2010).1
CO2
total for Earth is from carbonates in the crust and mantle given in
table IV of Donohue and Pollack (1983).16
The mantle value is highly
uncertain. H2
O total for Earth is for the oceans only. H2
O total for
Mars is from the volume of the polar caps given in table 10 of Smith
et al. (2001).38
CO2
total for Mars is the CO2
in the atmosphere plus
the CO2
ice in the polar caps reported by Phillips et al. (2011).34
Venus Earth Mars
H2
O atm 1.2 × 10−9
≤ 1.6 × 10−8
≤ 1.6 × 10−12
H2
O total 1.2 × 10−9
2.3 × 10−4
(3.5–5) × 10−6
CO2
atm 9.5 × 10−5
5.0 × 10−10
3.7 × 10−8
CO2
total 9.5 × 10−5
(5–15) × 10−5
(6–7) × 10−8
N2
atm 22 × 10−7
6.7 × 10−7
6.7 × 10−10
O2
atm 7 × 10−10
2.1 × 10−7
3.7 × 10−11
40
Ar atm 6 × 10−9
11 × 10−9
0.57 × 10−9

chapter 2
12
volcanoes and fumaroles (volcanic vents), and as silicate
rocks are weathered, the limestone accumulates. Biologi-
cal processes aid the precipitation. Some plankton and
other species use calcium carbonate in their shells, and
much of the limestone deposits on Earth are derived from
the shells of marine organisms. Other plankton species
use silica in their shells. When one adds up the lime-
stone deposits on Earth, the mass of CO2
sequestered is
60 to 180 times the total mass of Earth’s atmosphere. The
larger number includes estimates of carbonates that were
subducted into the mantle, and it is highly uncertain. In
any case the mass of CO2
in carbonate rocks on Earth
is comparable to—within a factor of two—the mass of
CO2
in the atmosphere of Venus. Formation of carbon-
ates depends on liquid water, so the fact that the CO2
on Venus is in the atmosphere and the CO2
on Earth is
in carbonate rocks is probably tied to the question of
why only Earth has oceans. That question hinges on the
greenhouse effect and climate, as we shall see.
Before discussing water, let us discuss two other gases
whose abundances are comparable on Earth and Venus.
The first is nitrogen (N2
), which makes up 3.5% of Venus’s
92-bar atmosphere and 78% of Earth’s 1-bar atmosphere.
These percentages refer to the numbers of molecules, not
their masses. The ratio of the atmospheric masses of ni-
trogen on Venus and Earth is 3.0, which means they are
comparable. The other gas is argon, which, on Earth at
least, is mostly 40
Ar. The number 40 refers to the mass of
the nucleus, which is controlled by the number of pro-
tons and neutrons. 40
Ar is produced from the decay of

13
radioactive potassium, 40
K. The amount of 40
Ar in a ter-
restrial planet atmosphere is a measure of the amount
of radioactive potassium in the crust and the degree
of outgassing—the extent to which the gaseous argon
is released from the rock and conveyed to the surface.
Relative to the planet’s mass, the ratio of the mass of 40
Ar
in the atmosphere of Venus to that of the Earth is ~0.5,
which means the amount of outgassing on the two plan-
ets is comparable as well.
The message from CO2
, N2
, and 40
Ar is that Venus
and Earth have comparable inventories of at least some
of the lighter elements and compounds, including those
that are important for climate. These are the volatile
compounds—those capable of existing as a gas or liquid
at ordinary planetary temperatures. We have been using
the word “comparable” to mean within a factor of 2 or
3. When it comes to water, however, Venus and Earth
are dramatically different. For the sake of this discussion,
we only consider the oceans and atmospheres, leaving
off possible water in the crust and mantle. The depth of
Earth’s oceans varies, but if one turned all the oceans
into vapor it would press down on the surface with a
pressure of 260 bars. In other words, the mass of Earth’s
oceans is 260 times the mass of the atmosphere. Venus
has no oceans. Water is present in the Venus atmosphere,
mostly as vapor but also as a component of the sulfuric
acid clouds, which are a compound of SO3
and water.
The total atmospheric water is 30 ppm (parts per mil-
lion). The mass of Venus water relative to the mass of
the planet is ~5 × 10−6
times the comparable number for

chapter 2
14
Earth. This is an astonishingly small ratio for two sister
planets.
2.2 Loss of Water
and Escape of Hydrogen
So why are the planets so different in this important re-
spect? Did they start out with comparable amounts of
water, until Venus lost all but a tiny fraction of its initial
inventory? Or was Venus born much drier than Earth,
even though in many other respects the two planets are
similar? A clue, or perhaps just an interesting fact, is
that the water on Venus is different from the water on
Earth. Although water is always two hydrogen atoms
and one oxygen atom, the distributions of the isotopes
of hydrogen and oxygen may differ. Oxygen has three
stable isotopes, 16
O, 17
O, and 18
O, and hydrogen has two,
H and D, where D stands for deuterium. The nucleus
of ordinary hydrogen H is a single proton; that of deu-
terium D is a proton and a neutron, and since protons
and neutrons have about the same mass, an atom of D is
twice as massive as an atom of H. Their chemistry is the
same, but their masses are different. This means that a
process whose rate depends on mass may fractionate the
hydrogen
—alter the D/H ratio from its initial value. In
most parts of the solar system the D/H ratio—the num-
ber of D atoms relative to the number of H atoms—is 10−4
within a factor of 2 in either direction.18
This number ap-
plies to Earth, the giant planets, comets, and probably to
the protosolar nebula out of which the Sun and planets

15
formed. Mars has a D/H ratio that is 7 times the Earth’s
ratio, indicating that some mass-dependent process has
driven off the H at a faster rate than it has driven off D.
However Venus has a D/H ratio that is at least 150 times
the Earth’s value19
(fig. 2.2). This number applies to the
water vapor in the lower atmosphere and to the hydro-
gen in the sulfuric acid clouds. Values up to 300 apply in
the upper atmosphere, where the atmosphere is merging
into space.20
The implication is that some process has al-
tered the D/H ratio on Venus, since the rest of the solar
system is so nearly uniform in this respect.
Protosolar
Semarkona and
Bishunpur
meteorites (OD)
HDO
Halley
Hyakutake
Protoices
HD
Galileo
HD
ISO
HD
ISO
HD*
HD* HD*
CH3D*
CH3D*
CH3D*
CH3D*
Hale Bopp
Jupiter Saturn Uranus Neptune Comets
Venus
Mars
Earth
D/H
10–5
10–4
10–3
10–2
Figure 2.2. Deuterium to hydrogen (D/H) ratio in solar system.
Asterisks are inferred from Earth-based observations. The high D/H
of Venus suggests that the planet has lost a large amount of water
during its lifetime.
(Adapted from fig. 4 of Bockelee-Morvan et al., 1998and supple-
mented with material from Donohue et al., 1997)18,19

chapter 2
16
One such process is atmospheric escape. The mole
cules of a gas obey a Maxwell-Boltzmann distribution
(box 2.1), which says that the fraction of molecules with
kinetic energy E is proportional to exp(−E/kB
T), where
kB
is a universal constant called Boltzmann’s constant.
This probability is the same for all molecules, regardless
of their mass. The light molecules have just as much ki-
netic energy as the heavy ones, which implies they are
moving faster. The gravitational binding energy—the en-
ergy needed to escape the planet—is GMm/R, where G is
the gravitational constant, M is the mass of the planet, m
is the mass of the molecule, and R is the planet’s radius
(box 2.2). Since GMm/R is the kinetic energy (1/2)mvesc
2
needed to escape, the escape velocity vesc
is (2GM/R)1/2
.
If a molecule reaches escape velocity at the top of the
atmosphere, where collisions with the molecules above
are unlikely, then it will escape. The probability of this
happening is greater for the lighter molecules, since their
gravitational binding energy is less. Equivalently, one
can say that the probability of reaching the escape veloc-
ity is greater for the lighter molecules because they are
moving faster.
Atmospheric escape can alter the D/H ratio of what
remains. An atom of H has a higher escape probability
than an atom of D because the mass of H is one-half
the mass of D. With H escaping faster, the D/H ratio of
the remainder builds up. If one starts with water with
hydrogen isotopic ratios like most other solar system
bodies, that is, D/H ~10−4
, the ratio will slowly increase
over time. The more water is lost, the larger the ratio

17
Box 2.1.
Distribution of Velocities in a Gas
The molecules of a gas follow a Maxwell-Boltzmann distribu-
tion of velocities. The probability of a molecule having its
x-component of velocity in the range from vx
to vx
+ dvx
is
( )
2 2
exp
f v dv
k T
m
k T
mv
dv
1/2 2
x x
B B
x
x
π
= d f
n p
Here m is the mass of the molecule, T is the absolute tempera-
ture, and kB
is Boltzmann’s constant, 1.38 × 10−23
J K−1
. Similar
distributions hold for the other two components of velocity.
The probabilities of the three components are independent, so
the joint probability is proportional to their product. Since ex-
ponents add when one takes the product of exponentials, the
joint probability is proportional to exp[−½ m (vx
2
+ vy
2
+ vz
2
)/
(kB
T)] = exp[−E/(kB
T)], where E is the kinetic energy of the
molecule. Each distribution is normalized such that the inte-
gral over the entire range of vx
from −∞ to +∞ is 1.0. The mean
speed, obtained by multiplying f(vx
) by vx
and integrating from
−∞ to +∞, is zero. The average of the square of the speed, ob-
tained by multiplying by vx
2
and integrating from −∞ to +∞, is
kB
T/m, so the typical speed associated with each component of
velocity is (kB
T/m)1/2
. The average kinetic energy, which is (1/2)
m times the average square of the speed, is kB
T/2 for each com-
ponent, so the average kinetic energy of the molecule is (3/2)
kB
T. The average kinetic energy is independent of the mass of
the molecule. For water vapor at 273 K, the value of (kB
T/m)1/2
is 355 m s−1
. The velocity of the molecules is comparable to the
speed of sound, which means their kinetic energy on a micro-
scopic scale is large. This is part of the internal energy of the
gas, which is what we sense when the gas is warm. If the mean
velocity of the molecules is zero, the gas will have no kinetic

chapter 2
18
becomes. Working backward from today’s D/H ratio to
infer how much water has been lost is uncertain because
one doesn’t know the fractionation factor—how much
advantage the H had relative to D in its rate of escape. If
the temperature of the upper atmosphere were low over
the age of the planet, the H would have had a large ad-
vantage, and a high D/H ratio would build up quickly.
On the other hand, if the temperature were high, the H
would have a smaller advantage, and it would take more
water lost to build up a high D/H. The minimum amount
of water lost from Venus is 150 times the current amount
in the atmosphere, since that corresponds to no loss of D
and only loss of H. That scenario is highly unlikely, so it
is probable that much more water was lost, perhaps even
an ocean’s worth.
The above process is called thermal escape or equiva-
lently Jeans escape. There are other escape processes,
like the solar wind stripping atoms from the upper at-
mosphere and ultraviolet photons causing molecules to
fly apart at speeds greater than the escape speed, and
they all have the potential of increasing the D/H ratio.
(Box 2.1 continued)
energy on a macroscopic scale. The other part of the internal
energy is associated with the molecule’s rotational and vibra-
tional degrees of freedom and is also independent of its mass.
For instance, a mole (6.02 × 1023
molecules) of hydrogen has
approximately the same amount of internal energy as a mole
of nitrogen or oxygen.

19
Box 2.2.
Escape of Planetary Atmospheres
The escape velocity vesc
is the velocity that an object needs to
escape the gravitational field of a planet. Equivalently, the ki-
netic energy Eesc
= (1/2)mvesc
2
is equal to the work done against
gravity, i.e., the integral of the gravity force with respect to
distance from the surface of the planet at radius R to a point
infinitely far away:
( / )
2
1
E GMm r dr
R
GMm
mv
2 2
esc esc
R
= = =
3
#
Here G is the gravitational constant, M is the mass of the
planet, m is the mass of the molecule, and vesc
is the escape ve-
locity. If the molecule’s kinetic energy is greater than Eesc
, it will
escape if it does not collide with other molecules. The above
equation says that vesc
= (2GM/R)1/2
. Notice that vesc
is indepen-
dent of the mass of the escaping particle. The escape velocity
from the surface of Earth is 11.2 km s−1
. The escape velocity is
less if the escaping particle has kinetic energy due to the plan-
et’s rotation or if the particle starts at some altitude above the
planet’s surface. For the terrestrial planets, only the molecules
in the high-energy tail of the velocity distribution have enough
energy to escape. The probability (box 2.1) of a molecule hav-
ing kinetic energy Eesc
is exp[−Eesc
/(kB
T)] = exp(−λesc
), where
λesc
= GMm/(RkB
T) is called the escape parameter. When λesc
is
large, e.g., when the mass of the molecule is large, the probabil-
ity of escape is small. Also, when the mass of the planet is large
and the radius is small, or when the temperature is small, then
the probability of escape is small as well. This type of escape—
from the high-energy tail of the velocity distribution, is called
thermal escape or Jeans escape after Sir James Jeans, who first
worked out the theory.

chapter 2
20
The large value of this ratio is telling us about the history
of water on Venus, since water is where the hydrogen
resides. Thermal escape does not remove intact water
molecules—they are too heavy—but it does remove the
atoms of D and H that are knocked off the water mole-
cules when they absorb ultraviolet light, a process called
photodissociation. The oxygen remains behind and
either accumulates in the atmosphere or else combines
with crustal materials to make oxides. For instance, iron
in igneous rocks typically exists in ferrous form, FeO,
but it can be oxidized to the ferric form, Fe2
O3
, thereby
removing one oxygen atom for every two atoms of iron.
Or unoxidized volcanic gases like CO, CH4
, H2
S, and H2
can combine with oxygen to make CO2
, SO2
, and H2
O.
Removal of oxygen from the atmosphere allows the hy-
drogen to escape, because otherwise the oxygen would
build up and recombine with the hydrogen to make
water. Whether Venus lost an entire ocean’s worth of
water by this process is unknown. What we do know is
that the D/H ratio on Venus is two orders of magnitude
higher than on almost every other object in the solar
system.
2.3 The Runaway Greenhouse
Why should Venus have lost all its water when Earth did
not? It could be that an Earth-like planet, with a liquid
water ocean, can only exist outside a certain distance
from the Sun. Venus could be inside this limit and Earth
could be outside. The argument hinges on the extreme

21
sensitivity of the climate to the amount of sunlight. The
sensitivity arises because water vapor is a potent green-
house gas and its abundance is controlled by cycles of
evaporation and precipitation. On Earth, these cycles
maintain the relative humidity—the amount of water
vapor the air does hold compared to the amount it
could hold—at an average value of about 50%. As the air
warms, it holds more water vapor. Venus, being closer
to the Sun, is naturally warmer. But that leads to more
water vapor in its atmosphere, and that makes it even
warmer, since water vapor is a potent greenhouse gas.
The intensity of sunlight is about twice as great at the
orbit of Venus compared to the orbit of Earth, and this
may be enough to have pushed Venus over the edge into
its current hellish state.
A personal anecdote is appropriate here. In the first
class I ever taught, I composed a homework problem with
a twist. I asked the students to compute the temperature
at the surface of a planet that absorbed a certain fraction
of the incident sunlight and whose atmosphere blocked
a certain fraction of the outgoing infrared radiation. The
blocking was due to greenhouse gases, and the point was
to illustrate the greenhouse effect. With enough simpli-
fying assumptions, it is a fairly easy problem, but I made
the amount of greenhouse gases depend on temperature.
The cycles of evaporation and precipitation would en-
sure that the atmosphere was 50% saturated with water
vapor, so higher temperatures meant more water vapor,
and more water vapor meant higher temperatures be-
cause water vapor is a potent greenhouse gas.

chapter 2
22
The homework problem didn’t work. The Earth
couldn’t exist in its present state, according to the assump-
tions given. I apologized to the class and dialed down the
sensitivity to the surface temperature as much as I could.
Then the Earth could exist but Venus couldn’t, at least
not with an atmosphere that was close to saturation. The
only way for Venus to exist was to make it so hot that the
air was no longer saturated, but that meant boiling away
the oceans. I wrote up the results and sent the paper off
to a reputable scientific journal, where it was rejected as
too speculative. So I added a lot of features to make it
more realistic, and I sent it off to another reputable jour-
nal. This time it was rejected because the added features
didn’t measure up to the standards of terrestrial meteo-
rology. I couldn’t meet those standards because I was try-
ing to guess what Venus was like four billion years ago, so
I stripped the model down to its essence and explained
that it was the concept I was after and not the quantitative
details. The third journal, which was also quite reputable,
accepted the paper, and it was published as “The Run-
away Greenhouse: A History of Water on Venus.”21
In engineering, feedback is a return of a portion of
the output of a device back to its input. If the device is
the climate of a planet and the output is temperature,
the inputs are the absorbed sunlight and the emitted in-
frared radiation. If either of these depends on tempera-
ture, then you have feedback. Negative feedback tends
to stabilize the system. Outgoing long-wave radiation is
an example: The warmer it gets, the more infrared ra-
diation is emitted, and this cools the planet back to its

23
equilibrium state. Positive feedback tends to destabilize
the system, and two examples come to mind. The first is
ice-albedo feedback, where the ability of the planet to ab-
sorb sunlight depends on the temperature. Albedo is the
fraction of the incident sunlight that gets reflected back
to space. The colder it gets, the more ice accumulates on
the ground, which causes more sunlight to be reflected.
This cools the Earth further and leads to large climate
excursions and possibly even to tipping points—regime
changes—where the system changes to a new stable state.
A cold, ice-covered Earth—called snowball Earth by the
geologists—would stay cold by reflecting the incoming
sunlight. There is geological evidence that such a regime
occurred several times in early Earth history.
The positive feedback that is most relevant for Venus
is due to water vapor. If one took an Earth-like planet
with a global ocean and moved it closer to the Sun, the
water-vapor content of the atmosphere would rise and
amplify the warming effect of the extra sunlight. At some
orbital position, probably between the orbits of Earth and
Venus, the climate system would run away. The planet
would have a massive water vapor atmosphere with a
surface pressure of 300 bars, most of it due to the weight
of water vapor, and the rest—the original nitrogen and
oxygen—accounting for an additional 1 bar. For a watery
planet moving in from Earth’s orbit, this transition is a
tipping point, a regime change. For a watery planet at the
orbit of Venus, it is the only possible state of the system.
What we have just described is called a runaway
greenhouse,21
to distinguish it from the modest terrestrial

chapter 2
24
greenhouse that keeps our planet warm and comfort-
able. Climate models22
have reproduced the runaway
greenhouse state for Venus, with surface temperatures
as high as 1400 K. If Venus started wet but immediately
went into a runaway greenhouse state, the water would
no longer be protected from photodissociation by ultra-
violet light from the Sun. Photodissociation occurs in
the stratosphere and above, where the ultraviolet pho-
tons first encounter the atmospheric gases. On Earth
these high-altitude layers are predominantly nitrogen
and oxygen. Water vapor is present in abundances of 1
or 2 parts per million. In particular, the oxygen forms a
radiation shield that protects Earth’s water from ultra-
violet light and prevents the chain of events that leads to
hydrogen escape and oxidation of crustal materials. On
a watery planet at the orbit of Venus, water vapor would
be the major constituent at all altitudes.21
Instead of 1 or
2 photons striking a water molecule out of one million
incident photons, almost all of the photons would do
so. This could lead to destruction of water and escape of
hydrogen over geologic time, and could account for the
absence of water on Venus today.
The near-zero abundance of water on Venus today
is on firm ground. The high D/H ratio is also on firm
ground. The existence of water vapor feedback is a
theoretical concept, but it is also on fairly firm ground.
However the whole history of water on Venus remains
uncertain. It is still possible that Venus was born dry,
although this contradicts the sister planet evidence, es-
pecially the similarities in the abundances of CO2
, N2
,

25
and 40
Ar. It is also possible that the high D/H reflects
relatively modern processes. Small reservoirs of hydro-
gen, like the present Venus atmosphere, are easier to alter
than large reservoirs like the Earth’s oceans. This doesn’t
necessarily imply that Venus was born dry, but it does
complicate the interpretation of the high D/H ratio.
Could a runaway greenhouse happen on Earth? The
incident sunlight is almost two times greater at Venus,
so a runaway greenhouse is more likely there. We could
increase the odds for Earth by plugging up the infrared
spectrum of our atmosphere with greenhouse gases.
Their heat-trapping effect—the radiative forcing—is
qualitatively the same as increasing the sunlight, but
we have a long way to go. The radiative forcing due to
human activities up to the present is in the 1% range.10
A factor of two seems safely out of reach, but we don’t
know where the tipping point lies. It is probably between
the orbits of Earth and Venus, since Earth has an ocean
and Venus does not. We don’t know exactly how Venus
got to be such a hellish place, but it is a lesson for Earth
nonetheless.

3 Venus: Energy
Transport and Winds
3.1 Convection
To this point we have invoked the greenhouse

effect in fairly general terms, but it is time to discuss
the modern-day climate of Venus in greater detail. The
details matter if we want to compare Venus to Earth to
see how likely a runaway greenhouse is for our planet.
The essence of the atmospheric greenhouse is that the
gas is more transparent to sunlight than it is to infra-
red radiation. The sunlight that reaches the surface is
absorbed and turned into heat, but the infrared radia-
tion can’t carry it up to the levels where it is radiated to
space—the gas is too opaque. Instead, the surface heats
up until convection kicks in. Convection involves warm
air moving up and cold air moving down, leading to a
net transfer of energy upward. Convection only kicks
in where the lapse rate reaches a certain critical value,
where lapse rate is defined as the rate of temperature de-
crease with altitude. Once the critical point is reached,
however, convection is very efficient in transporting
heat upward. The atmosphere reaches a kind of radia-
tive-convective equilibrium, where sunlight deposits
heat at the surface and convection carries the heat up

Venus: Energy Transport and Winds
27
to the levels where the gas becomes transparent to in-
frared radiation, at which point the heat is radiated to
space. With its massive atmosphere, Venus radiates to
space at altitudes around 65 km. Earth radiates to space
at altitudes around 5 km. It’s like piling more blankets
on the bed. The thicker the pile, the warmer you are at
the bottom.
Most planets radiate to space from altitudes where
the pressure is several hundred mbar. This is the level
where the typical infrared photon stands an even chance
of passing through the layers above without absorption.
It’s the level you “see” when you peer into an atmosphere
with infrared eyes. You see the warm glow of the gases
at that level. If they are cold, you see very little glow; if
they are warm, the glow is greater. The pressure you see
depends on how transparent or opaque the gases are at
infrared wavelengths. Certain gases, like water vapor and
CO2
are good absorbers of infrared light, which means
you can’t see as deep when these gases are present. These
are the greenhouse gases—they block infrared light
and raise the altitude (lower the pressure) at which the
planet radiates to space. By raising the altitude, they are
increasing the thickness of the pile of blankets, and this
raises the surface temperature. Clouds also absorb infra-
red light. Venus has a uniform layer of high clouds and
an atmosphere of CO2
, whereas Earth has a ~50% cloud
cover and an atmosphere with small amounts of water
vapor and CO2
. Therefore one sees deeper into Earth’s at-
mosphere—to 500 mbar—than into Venus’s atmosphere,
where one sees only to ~100 mbar.

chapter 3
28
Box 3.1.
Gases in Hydrostatic Equilibrium
The equation of state of an ideal gas is often written PV = NkB
T,
where P is pressure, V is volume, N is the number of molecules,
kB
is Boltzmann’s constant (see box 2.1), and T is the absolute
temperature. One can divide by volume to get P = nkB
T, where
n = N/V is the number of molecules per unit volume. One can
multiply and divide by the mass m of the molecule and use the
definition of density r = mn to get
/
P k T m R T
B g
ρ ρ
= =
Here Rg
= kB
/m is the gas constant for that particular gas.
If there is a mixture of gases, then m = (Smi
ni
)/(Sni
) is the

average of the masses weighted by the number of molecules
of each type.
Hydrostatic equilibrium is when the pressure difference dP
between the bottom and top of a layer supports its weight. Let
z be the vertical coordinate. If dz is the thickness of the layer,
the mass per unit area is rdz and the weight per unit area is
rgdz. The force per unit area is dP, which is equal to −rgdz
when the layer is in hydrostatic equilibrium. The minus sign
signifies that the pressure increases as the height decreases.
Thus the equation for hydrostatic equilibrium is
/
dP dz g
ρ
= −
We can substitute for the density using the equation of state
r = P/(Rg
T) to get
1 1
P dz
dp
R T
g
H
g
= − = −
Here H = Rg
T/g = kB
T/(mg) is called the scale height. If temper-
ature and gravity were constant, pressure and density would

29
How high is the 100-mbar level on Venus? How thick
is the pile of blankets? The surface pressure on Venus is
92 bar—92 times the sea level pressure on Earth. If we
define a scale height (box 3.1) as the vertical distance
over which the pressure drops by a factor of e = 2.718 . . . ,
then there are ln(92/0.1) = 6.8 scale heights from the sur-
face to the 100 mbar level. On Earth there are ln(1/0.5) =
0.69 scale heights from the surface to the 500 mbar level.
Because the pressure range is so much greater for Venus
than for Earth, the height where the planets radiate to
space is much greater as well. The scale height is pro-
portional to temperature, and ranges from 6 to 9 km on
Earth and from 5 to 15 km on Venus. Venus radiates to
space from altitudes near 65 km. Earth radiates to space
from altitudes near 5 km.
Figure 3.1 shows the temperature of the Venus atmo-
sphere from the ground to an altitude of 80 km.23
It is a
vertical profile measured at one location on the planet,
but it is typical of the planet as a whole because the mas-
sive atmosphere, with its large heat-carrying capacity,
tends to reduce the horizontal variations. We will treat
this profile as an average for the planet, with the sunlight
vary as exp(−z/H), and H would be the vertical distance over
which the pressure decreases by a factor of e = 2.718 . . . More
generally, pressure varies as exp(−dz/H), but in all cases the
scale height is a useful measure of atmospheric thickness. For
the midtroposphere of Earth (T = 255 K, g = 9.8 m s−2
, and m =
0.029 kg per mole, one finds that H = 7.5 km.

chapter 3
30
averaged over night and day and over high and low lati-
tudes. On Venus, 75% of the incident sunlight is reflected
back to space, mostly by the sulfuric acid clouds and the
dense CO2
atmosphere. The remaining 25% is absorbed,
both in the atmosphere and at the surface. To maintain
thermal equilibrium, all of the absorbed energy must be
transported upward to the level where the photons can
escape to space.
Figure 3.1 shows the measured profiles and other
curves labeled adiabats. An adiabat is the pressure ver-
sus temperature relation for a parcel that moves with-
out exchanging heat with its surroundings (box 3.2).
Temperature (K)
200 300 400 500 600 700 800
Altitude
(km)
20
0
40
8.98 K/km
ADIABAT
Upper clouds
Middle clouds
Lower clouds
60
80
Figure 3.1. Venus temperature variation with altitude from the
Pioneer Venus large probe. The profile is nearly the same as a global
average. Contrasts from day to night and equator to pole are less than
±10 K. Altitudes where the temperature follows an adiabat are those
where convection is occurring. (Adapted from fig. 11 of Seiff, 1983)23

31
Box 3.2.
Adiabatic Lapse Rate and Stability
The lapse rate is the decrease of temperature with height.
The actual lapse rate compared to the adiabatic lapse rate
tells whether the atmosphere is stable to convection or not.
The adiabatic lapse rate follows from the first law of thermo
dynamics. For an ideal gas the change in internal energy is
Cv
dT. Therefore
C dT PdV dQ
v + =
Here Cv
is the specific heat at constant volume and dQ is the
added heat, which is zero for an adiabatic process. The volume
per unit mass is V, which is 1/r, so dV = (Rg
/P)dT – (Rg
T/P2
)
dP, which follows from the equation of state. Therefore
( ) ( )
/
C R dT R T P dP dQ
v g g
+ − =
The first term is the heat added per unit mass when dP = 0.
Thus Cv
+ Rg
is Cp
, the specific heat at constant pressure. The
second term is −(1/r)dP, which follows from the equation of
state, and (1/r)dP is −gdz, which follows from the equation for
hydrostatic equilibrium. Thus for an adiabatic process, i.e., for
dQ = 0, we have
,
C dT gdz
dz
dT
C
g
0 or
p
p
+ = = −
This equation gives the temperature change with respect to
height when an air parcel moves adiabatically in a hydrostatic
gas. The parcel cools as it goes up because it is expanding and
doing work on its surroundings. If dT/dz of the surroundings
is more positive than −g/Cp
, then the parcel, rising adiabati-
cally, will find the surroundings warmer than itself. The parcel
will be more dense than the surroundings and it will fall back.

chapter 3
32
The adiabats all have the same slope, such that dT/dz =
−g/Cp
, but they have different intercepts, that is, differ-
ent temperatures at a given pressure level. Here g is the
gravitational acceleration and Cp
is the specific heat of
the atmosphere. Thus there are warm adiabats and cold
adiabats. The decrease of temperature with altitude is
called the lapse rate, so g/Cp
is called the adiabatic lapse
rate. Convection is occurring where the lapse rate is
equal to the adiabatic value. Convection cannot occur
when the lapse rate is less than the adiabatic lapse rate,
such that temperature falls off more gradually than the
adiabat (dT/dz > −g/Cp
). Then a parcel displaced rapidly
upward will find itself colder than its surroundings. Its
lower temperature means higher density than the sur-
roundings, and the parcel will sink back to its original
level. Thus an atmosphere with a sub-adiabatic lapse rate
is stable, and convection will not occur.
On the other hand, if the atmospheric temperature
falls off more steeply than the adiabat (dT/dz < −g/Cp
),
In the opposite case, when dT/dz of the surroundings is more
negative than −g/Cp
, then the surroundings will be colder and
more dense than the parcel and it will continue to rise. In this
case the atmosphere is unstable, since a small displacement
tends to grow. The atmosphere is stable when dT/dz + g/Cp
is
positive, and it is unstable when dT/dz + g/Cp
is negative. This
derivation assumes there is no condensation, so g/Cp
is called
the dry adiabatic lapse rate.
(Box 3.2 continued)

33
a parcel displaced upward will find itself warmer and
less dense than the surroundings, and it will continue to
rise. Since it is warmer, it will carry extra energy with
it. Similarly, a sinking parcel will continue to sink and
it will carry a deficit of energy with it. Thus an atmo-
sphere with a super-adiabatic lapse rate, where dT/dz <
−g/Cp
, is unstable to convection. Convection implies an
upward transfer of energy, since hot air is rising and cold
air is sinking. The net effect of convection is to warm the
upper levels and cool the lower levels. This makes dT/
dz less negative—it reduces the unstable lapse rate and
brings it closer to the adiabat, at which point the convec-
tion shuts itself off. In practice, convection is so efficient
that the lapse rate never exceeds the adiabatic value by a
significant amount. When one sees the temperature pro-
file following an adiabat, one can infer that convection
is occurring and energy is being transported upward.
When the lapse rate is sub-adiabatic, one can infer that
convection is absent. According to figure 3.1, convection
is occurring below 25 km and within the clouds from 47
to 56 km.
3.2 Radiation
In this one-dimensional view of the Venus atmosphere,
the only other process that transports energy vertically is
electromagnetic radiation (box 3.3).
Acting together, radiation and convection largely
determine the temperature structure of the Venus at-
mosphere. In steady state, each layer of the atmosphere

chapter 3
34
Box 3.3.
Electromagnetic Radiation: Flux and Intensity
The radiant energy flux (irradiance), is the power per unit
area falling on a surface. An example is the flux of energy in
solar radiation. At 1 AU from the Sun the average flux is 1361
Wm−2
, and it varies by ±1 Wm−2
due to solar activity. This is
the power you would receive if you held a square meter per-
pendicular to the sunlight. As you move around in the solar
system, the flux varies as 1/r2
, where r is distance to the Sun.
One can regard this inverse-square dependence in two ways.
One way is that the same amount of radiant power passes
through each sphere of radius r surrounding the Sun. The
power per unit area on the sphere is inversely proportional
to the sphere’s area, which is 4pr2
. The other way is that the
power that you receive is proportional to the area of the Sun
in the sky. The Sun looks smaller as you move away from it.
It’s the angular area, measured in square radians, that counts.
This area, called solid angle, is p(R/r)2
, where R is the Sun’s ra-
dius. The inverse square dependence arises from the factor of
r2
in the denominator. Implicit in this argument is that there
is some intrinsic property of the Sun that is independent of r.
This intrinsic property is the intensity (also called radiance or
brightness) of the solar disk, and it is the flux per unit solid
angle in a narrow beam. The brightness of the solar disk is the
same wherever you are, but the solid angle varies as 1/r2
. An
example is a blank wall. The wall looks just as bright from a
large distance as it does from a small distance. The brightness
is an intrinsic property of the wall. Solid angle is measured in
square radians, or steradians, and is abbreviated sr. Just as the
total angular size of a circle is 2p (the circumference divided
by r), the total solid angle of a sphere is 4p (the sphere’s sur-
face area divided by r2
).

35
Flux is the integral of the intensity over all directions. For
example, a horizontal surface radiates into the upward hemi-
sphere, whose total solid angle is 2p. In spherical polar coor-
dinates, the element of solid angle is sinqdqdl where q is the
angle from the polar axis and l is longitude. Each element of
solid angle, times the intensity in that direction, multiplied by
the cosine of the angle with respect to vertical, contributes to
the vertical flux. For the special case of a surface whose in-
tensity I is the same in all directions, the flux F is p times the
intensity:
cos sin
F I d dl I
0
/2
0
2
θ θ θ π
= =
π
π
#
#
A snowfield is a good approximation. It has the same
brightness whether you look at it obliquely or straight down.
Another example is a small hole in a large furnace whose inner
walls are all at the same temperature. You see the same red-
hot glow (brightness) regardless of the angle, although the hole
looks smaller (as cosq) when you look at it obliquely. The red-
hot glow is called cavity radiation, or blackbody radiation, and
is described further in box 3.4.
adjusts its temperature until it is gaining as much energy
as it is losing. The gain may be from absorption of sun-
light, from absorption of infrared radiation emitted by
other parts of the atmosphere, or from warm parcels ris-
ing up from below, replacing cold parcels that sink down.
The loss may be from emission of infrared radiation or
from exchange of warm parcels for cold ones.
A useful approximation for treating radiative trans-
fer involves the concept of blackbody radiation (box
3.4). Blackbody radiation exists inside a closed cavity

chapter 3
36
Box 3.4.
Blackbody Radiation, the Planck Function
Inside an isothermal cavity, the radiation field comes into
equilibrium with the walls. A hole in the walls does not disturb
the light inside if the hole is small enough. Any light that goes
in through the hole gets lost inside and doesn’t find its way
out, so the hole is described as black. The light coming out of
the hole originates inside and is called blackbody radiation, or
cavity radiation. The intensity inside is a universal function of
wavelength and temperature called the Planck function, after
Max Planck who derived the exact shape of the function by
assuming that the energy of each optical mode could change
only in quantized steps proportional to the frequency of the
light. Frequency n is c/l, where l is the wavelength and c is
the velocity of the light. Planck’s discovery was the beginning
of quantum mechanics, and the constant of proportionality h,
Planck’s constant, is the fundamental constant of quantum me-
chanics. The Planck function depends on h, c, and Boltzmann’s
constant kB
, which is the fundamental constant of statistical
mechanics. For blackbody radiation, the intensity (power per
cross-sectional area per steradian) within a wavelength inter-
val from l to l + dl is
( )
2( )
1
, 69.504
B T d
h c
k T
e
w dw
w
hc
k T
T
3 2
4
1/
5
B
w
B
λ
λ
λ
=
−
= =
λ
−
Here λ is in meters, T is in Kelvins, and w is a dimensionless
variable proportional to wavelength. See figure 3.2 for a graph
of the function w–5
/(e1/w
– 1). The integral over w from 0 to ¥
is an integral over the entire spectrum of blackbody radiation.
After multiplying by π the result is
( )
2 ( )
1
F B T d
h c
k T
e
w dw
T
0
3 2
4
1/
5
4
0
BB
B
w
π λ
π
σ
= =
−
=
3 3
λ
−
# #

37
The factor of p was inserted to convert intensity into flux as-
suming the intensity is independent of direction, as it is for
blackbody radiation (box 3.3). Thus sT4
is the total flux, inte-
grated over all wavelengths, from a blackbody at temperature
T. It is the flux coming out of the small hole in the cavity. The
Stefan-Boltzmann constant s = 5.67 × 10−8
Wm−2
K−4
is a uni-
versal constant that depends only on h, kB
, and c. For a 273 K
blackbody, the flux is 315 Wm−2
.
Figure 3.2 shows the dimensionless Planck function w−5
/
(e1/w
– 1). The abscissa is the dimensionless wavelength w. The
peak of the dimensionless Planck function is at w = 0.2014,
so if T = 5800 K, then l at the peak is 0.50 microns (0.5 ×
10−6
m). These numbers provide a good fit to the Sun’s spec-
trum, which has total energy about equal to a 5800 K black-
body and a peak at l = 0.5 microns—in the green portion of
the spectrum.
whose walls are all at the same temperature, where the
radiation field has come into equilibrium with the walls.
Blackbody radiation also exists inside a thick isothermal
medium like a cloud or an absorbing gas. Remarkably,
many real substances behave like blackbodies even if you
take away half of the medium—the other half emits as if
it were still surrounded by opaque cloud or gas. Then the
outgoing heat flux (power per unit area) is σT4
, where
T is its absolute temperature, and s is a universal physi-
cal constant—the Stefan-Boltzmann constant. This uni-
versality applies to a perfectly absorbing (nonscattering)
medium, but most planetary substances come close to
this ideal at infrared wavelengths (box 3.5).

chapter 3
38
Box 3.5.
Blackbodies in the Solar System
It is remarkable that the Sun, which is pouring energy out
into space, should have the same distribution of radiation as
a closed cavity that is in thermal equilibrium with the walls.
The Sun behaves this way because the ions and electrons in the
Sun’s atmosphere are interacting with each other so frequently
that they remain in thermal equilibrium despite the exposure
to empty space. The Sun is a good blackbody, and its 5800 K
brightness temperature is roughly that of the ions and elec-
trons in the Sun’s atmosphere.
Blackbody radiation is relevant in planetary science be-
cause most planetary materials are good absorbers of infrared
light. In other words, they behave like blackbodies at infrared
wavelengths. Infrared is the relevant wavelength because that
is where the Planck function peaks at planetary temperatures.
For a temperature of 290 K, which is 1/20 of the Sun’s effec-
tive temperature, the peak is at a wavelength of 20 times the
peak of the solar spectrum, or 10 microns. This follows from
the definition of w (box 3.4), which says that l scales as 1/T for
the same value of w. Light at 10 microns is in the middle of the
thermal infrared, and that is where most planetary materials,
including rocks, sand, ice, liquid water, clouds, and gases, be-
have as blackbodies. The same materials reflect visible light, so
they are not such good absorbers at those wavelengths. Metals
are not good absorbers in the infrared, so they do not radiate
as blackbodies. On the other hand, metals are not important
elements of planetary climate.

39
The spectrum of blackbody radiation is given by the
Planck function Bl
(T), which is a function only of the
wavelength λ and the temperature T (box 3.4). The di-
mensionless form of the Planck function is shown in
figure 3.2. Blackbody radiation is thermal radiation,
which occurs when the energy of molecular motions
is turned into electromagnetic energy. Sunlight is ther-
mal radiation, as is the infrared radiation emitted by the
planets. The difference is that the particles in the Sun’s
atmosphere—atoms, ions, and electrons—are at an aver-
age temperature of 5800 K, and particles near the tops
w
0 0.2 0.4 0.6 0.8 1.0
B
(w)
0
20
25
10
15
5
Figure 3.2. Planck function in dimensionless units. The Planck func-
tion Bl
(T) gives the distribution of blackbody radiation with respect
to wavelength. The graph shows the universal function B(w) = w−5
/
(e1/w
− 1), where w is proportional to wavelength and temperature.
In dimensional units Bl
(T)dl is B(w)dw times a factor proportional
to T to the fourth power. See box 3.4 for a precise definition of
variables.

chapter 3
40
of the clouds on Earth and Venus are at temperatures of
~250 K. The characteristic wavelengths of blackbody ra-
diation are inversely proportional to the temperature of
the emitting body, so the wavelengths of solar radiation
are much shorter than the wavelengths of planetary radi-
ation. The maximum intensity of a blackbody at 5800 K
is in the middle of the visible range at 0.5 microns, or
0.5 × 10−6
meters. The maximum intensity of a blackbody
at 250 K is in the infrared range at a wavelength of 11.6
microns (box 3.4).
The probability of a photon traveling a certain dis-
tance decreases exponentially as the distance increases
(box 3.6). The probability is usually expressed in terms of
optical depth tl
, such that exp(−tl
) is the transmission
—
the probability of the photon going the distance. Opti-
cal depth is an integral over distance. The integrand
depends on the medium—its density r and the ability
of a unit mass to absorb light. The latter is called the ab-
sorption coefficient kl
, and it can be a strong function
of the wavelength l. One sees farther into the medium
at wavelengths where the absorption coefficient is low.
For a nonscattering medium, the intensity of radiation
is a weighted average of Bl
(T) from all the points along
the ray path from tl
= 0 to tl
>> 1 (box 3.7). The weight-
ing is proportional to exp(−tl
), the probability that the
photons can reach the observer without being absorbed.
As mentioned earlier, the measured temperature
profile on Venus follows a dry adiabat below 25 km
and within the clouds from 47 to 56 km (fig. 3.1). These

layers are places where the infrared radiation is unable to

41
Box 3.6.
Radiative Transfer
Consider a narrow beam of radiation propagating through a
planetary atmosphere. The light encounters a thin slab of gas
that is aligned perpendicular to the direction of propagation,
and the slab has thickness ds. A fraction of the intensity will be
absorbed, another fraction will be scattered, and the remaining
fraction will be transmitted through the slab. In addition, the
slab will emit thermal radiation, which will increase the inten-
sity exiting the slab. Scattering is a change in the direction of
the light without loss of energy. Emission is a conversion of in-
ternal energy of the medium into electromagnetic energy. The
extinction—the fraction that is either absorbed or scattered—is
called the optical thickness, which is written dtl
= kl
rds, where
r is the density of the gas and kl
is an intrinsic property of the
gas called the extinction coefficient. The subscript l indicates
that the extinction coefficient is a function of the wavelength of
the light. The difference between the intensity emerging from
the slab and the intensity incident on the other side is
dI I I d I dJ
out in
τ
= − = − +
λ λ λ λ λ λ
The first term on the right is the extinction. The second term
on the right has two parts. One is the light scattered into the
beam from other directions, and the other is thermal emission.
The scattered light depends on the incident radiation—the ra-
diation environment of the slab—and the thermal emission
does not. We derive the expression for dJl
by imagining the
slab at equilibrium inside an isothermal cavity. Then Il
= Bl
everywhere, and dIl
= 0, which means dJl
= dtl
Bl
. For the
special case of a gas that does not scatter radiation, dJl
is inde-
pendent of the radiation environment, so it remains the same
when we take the slab out of the isothermal cavity. Therefore

chapter 3
42
Box 3.7.
Solution of the Equation of Transfer
The equation of transfer is linear in the intensity and can be
solved for Il
(tl
) when Bl
(tl
) is given. Here tl
= kl
rds is a co-
ordinate that is zero at the observer and increases backward
along the ray path to a point where the optical depth is τλ
*
and
the intensity is Il
(tl
*
). Thus Il
(tl
*
) is the incident intensity en-
tering the slab from the other side. The slab may be optically
thin (tl
*
<< 1), optically thick (tl
*
>> 1),or anything in between.
The Planck function depends on tl
because temperature is a
function of position within the medium. The solution to the
equation of transfer is
(0) ( ) ( ) ( ) ( )
exp exp
I I B d
* *
0
*
τ τ τ τ τ
= − + −
λ λ λ λ λ λ λ
τλ
#
The exponential in the first term is the transmission—the
fraction of the incident light that reaches the observer. Since
( ),
dI d I B
d
dI
I B
or
τ
τ
= − − = − +
λ λ λ λ
λ
λ
λ λ
This is the equation of transfer for a nonscattering (pure ab-
sorbing) medium. Extinction and absorption are the same for
this case. The minus sign assumes that tl
increases in the di-
rection of the light beam, although we will make the opposite
assumption later. Radiative transfer in a purely absorbing me-
dium is simply the slab removing intensity dtl
Il
from the beam
and replacing it by dtl
Bl
where Bl
is the Planck function at the
temperature of the slab.
(Box 3.6 continued)

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*** START OF THE PROJECT GUTENBERG EBOOK CELTIC
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CELTIC FOLKLORE
J. RHŶS
HENRY FROWDE, M.A.
PUBLISHER TO THE UNIVERSITY OF OXFORD
LONDON, EDINBURGH, AND NEW YORK

CELTIC FOLKLORE
WELSH AND MANX
BY
JOHN RHŶS, M.A., D.Litt.
HON. LL.D. OF THE UNIVERSITY OF
EDINBURGH
PROFESSOR OF CELTIC
PRINCIPAL OF JESUS COLLEGE,
OXFORD
VOLUME II
OXFORD

AT THE CLARENDON PRESS
MDCCCCI
Oxford
PRINTED AT THE CLARENDON PRESS
BY HORACE HART, M.A.
PRINTER TO THE UNIVERSITY

Triumphs of the Water-world
Une des légendes les plus répandues en Bretagne est
celle d’une prétendue ville d’Is, qui, à une époque
inconnue, aurait été engloutie par la mer. On montre, à
divers endroits de la côte, l’emplacement de cette cité
fabuleuse, et les pécheurs vous en font d’étranges
récits. Les jours de tempête, assurent-ils, on voit, dans
les creux des vagues, le sommet des flèches de ses
églises; les jours de calme, on entend monter de
l’abîme le son de ses cloches, modulant l’hymne du
jour.—Renan.
More than once in the last chapter was the subject of submersions and
cataclysms brought before the reader, and it may be convenient to
enumerate here the most remarkable cases, and to add one or two to their
number, as well as to dwell at somewhat greater length on some instances
which may be said to have found their way into Welsh literature. He has
already been told of the outburst of the Glasfryn Lake (p. 367) and Ffynnon
Gywer (p. 376), of Ỻyn Ỻech Owen (p. 379) and the Crymlyn (p. 191),
also of the drowning of Cantre’r Gwaelod (p. 383); not to mention that one
of my informants had something to say (p. 219) of the submergence of Caer
Arianrhod, a rock now visible only at low water between Celynnog Fawr
and Dinas Dinỻe, on the coast of Arfon. But, to put it briefly, it is an ancient
belief in the Principality that its lakes generally have swallowed up
habitations of men, as in the case of Ỻyn Syfađon (p. 73) and the Pool of
Corwrion (p. 57). To these I now proceed to add other instances, to wit
those of Bala Lake, Kenfig Pool, Ỻynclys, and Helig ab Glannog’s territory
including Traeth Lafan.
Perhaps it is best to begin with historical events, namely those implied in
the encroachment of the sea and the sand on the coast of Glamorganshire,
from the Mumbles, in Gower, to the mouth of the Ogmore, below Bridgend.
It is believed that formerly the shores of Swansea Bay were from three to
five miles further out than the present strand, and the oyster dredgers point

to that part of the bay which they call the Green Grounds, while trawlers,
hovering over these sunken meadows of the Grove Island, declare that they
can sometimes see the foundations of the ancient homesteads overwhelmed
by a terrific storm which raged some three centuries ago. The old people
sometimes talk of an extensive forest called Coed Arian, ‘Silver Wood,’
stretching from the foreshore of the Mumbles to Kenfig Burrows, and there
is a tradition of a long-lost bridle path used by many generations of
Mansels, Mowbrays, and Talbots, from Penrice Castle to Margam Abbey.
All this is said to be corroborated by the fishing up every now and then in
Swansea Bay of stags’ antlers, elks’ horns, those of the wild ox, and wild
boars’ tusks, together with the remains of other ancient tenants of the
submerged forest. Various references in the registers of Swansea and
Aberavon mark successive stages in the advance of the desolation from the
latter part of the fifteenth century down. Among others a great sandstorm is
mentioned, which overwhelmed the borough of Cynffig or Kenfig, and
encroached on the coast generally: the series of catastrophes seems to have
culminated in an inundation caused by a terrible tidal wave in the early part
of the year 16071.
To return to Kenfig, what remains of that old town is near the sea, and it is
on all sides surrounded by hillocks of finely powdered sand and flanked by
ridges of the same fringing the coast. The ruins of several old buildings half
buried in the sand peep out of the ground, and in the immediate
neighbourhood is Kenfig Pool, which is said to have a circumference of
nearly two miles. When the pool formed itself I have not been able to
discover: from such accounts as have come in my way I should gather that
it is older than the growing spread of the sand, but the island now to be seen
in it is artificial and of modern make2. The story relating to the lake is given
as follows in the volume of the Iolo Manuscripts, p. 194, and the original,
from which I translate, is crisp, compressed, and, as I fancy, in Iolo’s own
words:—
‘A plebeian was in love with Earl Clare’s daughter: she would not have him
as he was not wealthy. He took to the highway, and watched the agent of the
lord of the dominion coming towards the castle from collecting his lord’s
money. He killed him, took the money, and produced the coin, and the lady

married him. A splendid banquet was held: the best men of the country were
invited, and they made as merry as possible. On the second night the
marriage was consummated, and when happiest one heard a voice: all ear
one listened and caught the words, “Vengeance comes, vengeance comes,
vengeance comes,” three times. One asked, “When?” “In the ninth
generation (âch),” said the voice. “No reason for us to fear,” said the
married pair; “we shall be under the mould long before.” They lived on,
however, and a goresgynnyđ, that is to say, a descendant of the sixth direct
generation, was born to them, also to the murdered man a goresgynnyđ,
who, seeing that the time fixed was come, visited Kenfig. This was a
discreet youth of gentle manners, and he looked at the city and its
splendour, and noted that nobody owned a furrow or a chamber there except
the offspring of the murderer: he and his wife were still living. At cockcrow
he heard a cry, “Vengeance is come, is come, is come.” It is asked, “On
whom?” and answered, “On him who murdered my father of the ninth âch.”
He rises in terror: he goes towards the city; but there is nothing to see save a
large lake with three chimney tops above the surface emitting smoke that
formed a stinking….3 On the face of the waters the gloves of the murdered
man float to the young man’s feet: he picks them up, and sees on them the
murdered man’s name and arms; and he hears at dawn of day the sound of
praise to God rendered by myriads joining in heavenly music. And so the
story ends.’
On this coast is another piece of water in point, namely Crymlyn, or
‘Crumlin Pool,’ now locally called the Bog. It appears also to have been
sometimes called Pwỻ Cynan, after the name of a son of Rhys ab Tewdwr,
who, in his flight after his father’s defeat on Hirwaen Wrgan, was drowned
in its waters4. It lies on Lord Jersey’s estate, at a distance of about one mile
east of the mouth of the Tawe, and about a quarter of a mile from high-
water mark, from which it is separated by a strip of ground known in the
neighbourhood as Crymlyn Burrows. The name Crymlyn means Crooked
Lake, which, I am told, describes the shape of this piece of water. When the
bog becomes a pool it encloses an island consisting of a little rocky hillock
showing no trace of piles, or walling, or any other handiwork of man5. The
story about this pool also is that it covers a town buried beneath its waters.

Mr. Wirt Sikes’ reference to it has already been mentioned, and I have it on
the evidence of a native of the immediate neighbourhood, that he has often
heard his father and grandfather talk about the submerged town. Add to this
that Cadrawd, to whom I have had already (pp. 23, 376) to acknowledge my
indebtedness, speaks in the columns of the South Wales Daily News for
February 15, 1899, of Crymlyn as follows:—
‘It was said by the old people that on the site of this bog once stood the old
town of Swansea, and that in clear and calm weather the chimneys and even
the church steeple could be seen at the bottom of the lake, and in the
loneliness of the night the bells were often heard ringing in the lake. It was
also said that should any person happen to stand with his face towards the
lake when the wind is blowing across the lake, and if any of the spray of
that water should touch his clothes, it would be only with the greatest
difficulty he could save himself from being attracted or sucked into the
water. The lake was at one time much larger than at present. The efforts
made to drain it have drawn a good deal of the water from it, but only to
convert it into a bog, which no one can venture to cross except in
exceptionally dry seasons or hard frost.’
On this I wish to remark in passing, that, while common sense would lead
one to suppose that the wind blowing across the water would help the man
facing it to get away whenever he chose, the reasoning here is of another
order, one characteristic in fact of the ways and means of sympathetic
magic. For specimens in point the reader may be conveniently referred to
page 360, where he may compare the words quoted from Mr. Hartland,
especially as to the use there mentioned of stones or pellets thrown from
one’s hands. In the case of Crymlyn, the wind blowing off the face of the
water into the onlooker’s face and carrying with it some of the water in the
form of spray which wets his clothes, howsoever little, was evidently
regarded as establishing a link of connexion between him and the body of
the water—or shall I say rather, between him and the divinity of the water?
—and that this link was believed to be so strong that it required the man’s
utmost effort to break it and escape being drawn in and drowned like
Cynan. The statement, supremely silly as it reads, is no modern invention;
for one finds that Nennius—or somebody else—reasoned in precisely the

same way, except that for a single onlooker he substitutes a whole army of
men and horses, and that he points the antithesis by distinctly stating, that if
they kept their backs turned to the fascinating flood they would be out of
danger. The conditions which he had in view were, doubtless, that the men
should face the water and have their clothing more or less wetted by the
spray from it. The passage (§ 69) to which I refer is in the Mirabilia, and
Geoffrey of Monmouth is found to repeat it in a somewhat better style of
Latin (ix. 7): the following is the Nennian version:—
Aliud miraculum est, id est Oper Linn Liguan. Ostium fluminis illius fluit in
Sabrina et quando Sabrina inundatur ad sissam, et mare inundatur similiter
in ostio supra dicti fluminis et in stagno ostii recipitur in modum voraginis
et mare non vadit sursum et est litus juxta flumen et quamdiu Sabrina
inundatur ad sissam, istud litus non tegitur et quando recedit mare et
Sabrina, tunc Stagnum Liuan eructat omne quod devoravit de mari et litus
istud tegitur et instar montis in una unda eructat et rumpit. Et si fuerit
exercitus totius regionis, in qua est, et direxerit faciem contra undam, et
exercitum trahit unda per vim humore repletis vestibus et equi similiter
trahuntur. Si autem exercitus terga versus fuerit contra eam, non nocet ei
unda.
‘There is another wonder, to wit Aber Ỻyn Ỻiwan. The water from the
mouth of that river flows into the Severn, and when the Severn is in flood
up to its banks, and when the sea is also in flood at the mouth of the above-
named river and is sucked in like a whirlpool into the pool of the Aber, the
sea does not go on rising: it leaves a margin of beach by the side of the
river, and all the time the Severn is in flood up to its bank, that beach is not
covered. And when the sea and the Severn ebb, then Ỻyn Ỻiwan brings up
all it had swallowed from the sea, and that beach is covered while Ỻyn
Ỻiwan discharges its contents in one mountain-like wave and vomits forth.
Now if the army of the whole district in which this wonder is, were to be
present with the men facing the wave, the force of it would, once their
clothes are drenched by the spray, draw them in, and their horses would
likewise be drawn. But if the men should have their backs turned towards
the water, the wave would not harm them6.’

One story about the formation of Bala Lake, or Ỻyn Tegid7 as it is called in
Welsh, has been given at p. 376: here is another which I translate from a
version in Hugh Humphreys’ Ỻyfr Gwybodaeth Gyffredinol (Carnarvon),
second series, vol. i, no. 2, p. 1. I may premise that the contributor, whose
name is not given, betrays a sort of literary ambition which has led him to
relate the story in a confused fashion; and among other things he uses the
word edifeirwch, ‘repentance,’ throughout, instead of dial, ‘vengeance.’
With that correction it runs somewhat as follows:—Tradition relates that
Bala Lake is but the watery tomb of the palaces of iniquity; and that some
old boatmen can on quiet moonlight nights in harvest see towers in ruins at
the bottom of its waters, and also hear at times a feeble voice saying, Dial a
đaw, dial a đaw, ‘Vengeance will come’; and another voice inquiring, Pa
bryd y daw, ‘When will it come?’ Then the first voice answers, Yn y drydeđ
genhedlaeth, ‘In the third generation.’ Those voices were but a recollection
over oblivion, for in one of those palaces lived in days of yore an
oppressive and cruel prince, corresponding to the well-known description of
one of whom it is said, ‘Whom he would he slew; and whom he would he
kept alive.’ The oppression and cruelty practised by him on the poor
farmers were notorious far and near. This prince, while enjoying the
morning breezes of summer in his garden, used frequently to hear a voice
saying, ‘Vengeance will come.’ But he always laughed the threat away with
reckless contempt. One night a poor harper from the neighbouring hills was
ordered to come to the prince’s palace. On his way the harper was told that
there was great rejoicing at the palace at the birth of the first child of the
prince’s son. When he had reached the palace the harper was astonished at
the number of the guests, including among them noble lords, princes, and
princesses: never before had he seen such splendour at any feast. When he
had begun playing the gentlemen and ladies dancing presented a superb
appearance. So the mirth and wine abounded, nor did he love playing for
them any more than they loved dancing to the music of his harp. But about
midnight, when there was an interval in the dancing, and the old harper had
been left alone in a corner, he suddenly heard a voice singing in a sort of a
whisper in his ear, ‘Vengeance, vengeance!’ He turned at once, and saw a
little bird hovering above him and beckoning him, as it were, to follow him.
He followed the bird as fast as he could, but after getting outside the palace

he began to hesitate. But the bird continued to invite him on, and to sing in
a plaintive and mournful voice the word ‘Vengeance, vengeance!’ The old
harper was afraid of refusing to follow, and so they went on over bogs and
through thickets, whilst the bird was all the time hovering in front of him
and leading him along the easiest and safest paths. But if he stopped for a
moment the same mournful note of ‘Vengeance, vengeance!’ would be sung
to him in a more and more plaintive and heartbreaking fashion. They had by
this time reached the top of the hill, a considerable distance from the palace.
As the old harper felt rather fatigued and weary, he ventured once more to
stop and rest, but he heard the bird’s warning voice no more. He listened,
but he heard nothing save the murmuring of the little burn hard by. He now
began to think how foolish he had been to allow himself to be led away
from the feast at the palace: he turned back in order to be there in time for
the next dance. As he wandered on the hill he lost his way, and found
himself forced to await the break of day. In the morning, as he turned his
eyes in the direction of the palace, he could see no trace of it: the whole
tract below was one calm, large lake, with his harp floating on the face of
the waters.
Next comes the story of Ỻynclys Pool in the neighbourhood of Oswestry.
That piece of water is said to be of extraordinary depth, and its name means
the ‘swallowed court.’ The village of Ỻynclys is called after it, and the
legend concerning the pool is preserved in verses printed among the
compositions of the local poet, John F. M. Dovaston, who published his
works in 1825. The first stanza runs thus:—
Clerk Willin he sat at king Alaric’s board,
And a cunning clerk was he;
For he’d lived in the land of Oxenford
With the sons of Grammarie.
How much exactly of the poem comes from Dovaston’s own muse, and
how much comes from the legend, I cannot tell. Take for instance the king’s
name, this I should say is not derived from the story; but as to the name of
the clerk, that possibly is, for the poet bases it on Croes-Willin, the Welsh
form of which has been given me as Croes-Wylan, that is Wylan’s Cross,

the name of the base of what is supposed to have been an old cross, a little
way out of Oswestry on the north side; and I have been told that there is a
farm in the same neighbourhood called Tre’ Wylan, ‘Wylan’s Stead.’ To
return to the legend, Alaric’s queen was endowed with youth and beauty,
but the king was not happy; and when he had lived with her nine years he
told Clerk Willin how he first met her when he was hunting ‘fair Blodwell’s
rocks among.’ He married her on the condition that she should be allowed
to leave him one night in every seven, and this she did without his once
knowing whither she went on the night of her absence. Clerk Willin
promised to restore peace to the king if he would resign the queen to him,
and a tithe annually of his cattle and of the wine in his cellar to him and the
monks of the White Minster. The king consented, and the wily clerk hurried
away with his book late at night to the rocks by the Giant’s Grave, where
there was an ogo’ or cave which was supposed to lead down to Faery.
While the queen was inside the cave, he began his spells and made it
irrevocable that she should be his, and that his fare should be what fed on
the king’s meadow and what flowed in his cellar. When the clerk’s potent
spells forced the queen to meet him to consummate his bargain with the
king, what should he behold but a grim ogress, who told him that their
spells had clashed. She explained to him how she had been the king’s wife
for thirty years, and how the king began to be tired of her wrinkles and old
age. Then, on condition of returning to the Ogo to be an ogress one night in
seven, she was given youth and beauty again, with which she attracted the
king anew. In fact, she had promised him happiness
Till within his hall the flag-reeds tall
And the long green rushes grow.
The ogress continued in words which made the clerk see how completely he
had been caught in his own net:
Then take thy bride to thy cloistered bed,
As by oath and spell decreed,
And nought be thy fare but the pike and the dare,
And the water in which they feed.

The clerk had succeeded in restoring peace at the king’s banqueting board,
but it was the peace of the dead;
For down went the king, and his palace and all,
And the waters now o’er it flow,
And already in his hall do the flag-reeds tall
And the long green rushes grow.
But the visitor will, Dovaston says, find Willin’s peace relieved by the
stories which the villagers have to tell of that wily clerk, of Croes-Willin,
and of ‘the cave called the Grim Ogo’; not to mention that when the lake is
clear, they will show you the towers of the palace below, the Ỻynclys,
which the Brython of ages gone by believed to be there.
We now come to a different story about this pool, namely, one which has
been preserved in Latin by the historian Humfrey Lhuyd, or Humphrey
Ỻwyd, to the following effect:—
‘After the description of Gwynedh, let vs now come to Powys, the seconde
kyngedome of VVales, which in the time of German Altisiodorensis [St.
Germanus of Auxerre], which preached sometime there, agaynst Pelagius
Heresie: was of power, as is gathered out of his life. The kynge wherof, as
is there read, bycause he refused to heare that good man: by the secret and
terrible iudgement of God, with his Palace, and all his householde: was
swallowed vp into the bowels of the Earth, in that place, whereas, not farre
from Oswastry, is now a standyng water, of an vnknowne depth, called
Lhunclys, that is to say: the deuouryng of the Palace. And there are many
Churches founde in the same Province, dedicated to the name of German8.’
I have not succeeded in finding the story in any of the lives of St.
Germanus, but Nennius, § 32, mentions a certain Benli, whom he describes
as rex iniquus atque tyrannus valde, who, after refusing to admit St.
Germanus and his following into his city, was destroyed with all his
courtiers, not by water, however, but by fire from heaven. But the name
Benli, in modern Welsh spelling Benỻi9, points to the Moel Famau range of
mountains, one of which is known as Moel Fenỻi, between Ruthin and

Mold, rather than to any place near Oswestry. In any case there is no reason
to suppose that this story with its Christian and ethical motive is anything
like so old as the substratum of Dovaston’s verses.
The only version known to me in the Welsh language of the Ỻynclys legend
is to be found printed in the Brython for 1863, p. 338, and it may be
summarized as follows:—The Ỻynclys family were notorious for their
riotous living, and at their feasts a voice used to be heard proclaiming,
‘Vengeance is coming, coming,’ but nobody took it much to heart.
However, one day a reckless maid asked the voice, ‘When?’ The prompt
reply was to the effect that it was in the sixth generation: the voice was
heard no more. So one night, when the sixth heir in descent from the time of
the warning last heard was giving a great drinking feast, and music had
been vigorously contributing to the entertainment of host and guest, the
harper went outside for a breath of air; but when he turned to come back, lo
and behold! the whole court had disappeared. Its place was occupied by a
quiet piece of water, on whose waves he saw his harp floating, nothing
more.
Here must, lastly, be added one more legend of submergence, namely, that
supposed to have taken place some time or other on the north coast of
Carnarvonshire. In the Brython for 1863, pp. 393–4, we have what purports
to be a quotation from Owen Jones’ Aberconwy a’i Chyffiniau, ‘Conway
and its Environs,’ a work which I have not been able to find. Here one reads
of a tract of country supposed to have once extended from the Gogarth10,
‘the Great Orme,’ to Bangor, and from Ỻanfair Fechan to Ynys Seiriol,
‘Priestholme or Puffin Island,’ and of its belonging to a wicked prince
named Helig ab Glannawc or Glannog11, from whom it was called Tyno
Helig, ‘Helig’s Hollow.’ Tradition, the writer says, fixes the spot where the
court stood about halfway between Penmaen Mawr and Pen y Gogarth, ‘the
Great Orme’s Head,’ over against Trwyn yr Wylfa; and the story relates that
here a calamity had been foretold four generations before it came, namely
as the vengeance of Heaven on Helig ab Glannog for his nefarious impiety.
As that ancient prince rode through his fertile heritage one day at the
approach of night, he heard the voice of an invisible follower warning him
that ‘Vengeance is coming, coming.’ The wicked old prince once asked

excitedly, ‘When?’ The answer was, ‘In the time of thy grandchildren,
great-grandchildren, and their children.’ Peradventure Helig calmed himself
with the thought, that, if such a thing came, it would not happen in his
lifetime. But on the occasion of a great feast held at the court, and when the
family down to the fifth generation were present taking part in the
festivities, one of the servants noticed, when visiting the mead cellar to
draw more drink, that water was forcing its way in. He had only time to
warn the harper of the danger he was in, when all the others, in the midst of
their intoxication, were overwhelmed by the flood.
These inundation legends have many points of similarity among
themselves: thus in those of Ỻynclys, Syfađon, Ỻyn Tegid, and Tyno Helig,
though they have a ring of austerity about them, the harper is a favoured
man, who always escapes when the banqueters are all involved in the
catastrophe. The story, moreover, usually treats the submerged habitations
as having sunk intact, so that the ancient spires and church towers may still
at times be seen: nay the chimes of their bells may be heard by those who
have ears for such music. In some cases there may have been, underlying
the legend, a trace of fact such as has been indicated to me by Mr. Owen M.
Edwards, of Lincoln College, in regard to Bala Lake. When the surface of
that water, he says, is covered with broken ice, and a south-westerly wind is
blowing, the mass of fragments is driven towards the north-eastern end near
the town of Bala; and he has observed that the friction produces a somewhat
metallic noise which a quick imagination may convert into something like a
distant ringing of bells. Perhaps the most remarkable instance remains to be
mentioned: I refer to Cantre’r Gwaelod, as the submerged country of
Gwyđno Garanhir is termed, see p. 382 above. To one portion of his fabled
realm the nearest actual centres of population are Aberdovey and Borth on
either side of the estuary of the Dovey. As bursar of Jesus College I had
business in 1892 in the Golden Valley of Herefordshire, and I stayed a day
or two at Dorstone enjoying the hospitality of the rectory, and learning
interesting facts from the rector, Mr. Prosser Powell, and from Mrs. Powell
in particular, as to the folklore of the parish, which is still in several respects
very Welsh. Mrs. Powell, however, did not confine herself to Dorstone or
the Dore Valley, for she told me as follows:—‘I was at Aberdovey in 1852,
and I distinctly remember that my childish imagination was much excited

by the legend of the city beneath the sea, and the bells which I was told
might be heard at night. I used to lie awake trying, but in vain, to catch the
echoes of the chime. I was only seven years old, and cannot remember who
told me the story, though I have never forgotten it.’ Mrs. Powell added that
she has since heard it said, that at a certain stage of the tide at the mouth of
the Dovey, the way in which the waves move the pebbles makes them
produce a sort of jingling noise which has been fancied to be the echo of
distant bells ringing.
These clues appeared too good to be dropped at once, and the result of
further inquiries led Mrs. Powell afterwards to refer me to The Monthly
Packet for the year 1859, where I found an article headed ‘Aberdovey
Legends,’ and signed M. B., the initials, Mrs. Powell thought, of Miss
Bramston of Winchester. The writer gives a sketch of the story of the
country overflowed by the neighbouring portion of Cardigan Bay,
mentioning, p. 645, that once on a time there were great cities on the banks
of the Dovey and the Disynni. ‘Cities with marble wharfs,’ she says, ‘busy
factories, and churches whose towers resounded with beautiful peals and
chimes of bells.’ She goes on to say that ‘Mausna is the name of the city on
the Dovey; its eastern suburb was at the sand-bank now called Borth, its
western stretched far out into the sea.’ What the name Mausna may be I
have no idea, unless it is the result of some confusion with that of the great
turbary behind Borth, namely Mochno, or Cors Fochno, ‘Bog of Mochno.’
The name Borth stands for Y Borth, ‘the Harbour,’ which, more adequately
described, was once Porth Wyđno, ‘Gwyđno’s Harbour.’ The writer,
however, goes on with the story of the wicked prince, who left open the
sluices of the sea-wall protecting his country and its capital: we read on as
follows:—‘But though the sea will not give back that fair city to light and
air, it is keeping it as a trust but for a time, and even now sometimes,
though very rarely, eyes gazing down through the green waters can see not
only the fluted glistering sand dotted here and there with shells and tufts of
waving sea-weed, but the wide streets and costly buildings of that now
silent city. Yet not always silent, for now and then will come chimes and
peals of bells, sometimes near, sometimes distant, sounding low and sweet
like a call to prayer, or as rejoicing for a victory. Even by day these tones
arise, but more often they are heard in the long twilight evenings, or by

night. English ears have sometimes heard these sounds even before they
knew the tale, and fancied that they must come from some church among
the hills, or on the other side of the water, but no such church is there to
give the call; the sound and its connexion is so pleasant, that one does not
care to break the spell by seeking for the origin of the legend, as in the idler
tales with which that neighbourhood abounds.’
The dream about ‘the wide streets and costly buildings of that now silent
city’ seems to have its counterpart on the western coast of Erin—
somewhere, let us say, off the cliffs of Moher12, in County Clare—witness
Gerald Griffin’s lines, to which a passing allusion has already been made, p.
205:—
A story I heard on the cliffs of the West,
That oft, through the breakers dividing,
A city is seen on the ocean’s wild breast,
In turreted majesty riding.
But brief is the glimpse of that phantom so bright:
Soon close the white waters to screen it.
The allusion to the submarine chimes would make it unpardonable to pass
by unnoticed the well-known Welsh air called Clychau Aberdyfi, ‘The Bells
of Aberdovey,’ which I have always suspected of taking its name from fairy
bells13. This popular tune is of unknown origin, and the words to which it is
usually sung make the bells say un, dau, tri, pedwar, pump, chwech, ‘one,
two, three, four, five, six’; and I have heard a charming Welsh vocalist
putting on saith, ‘seven,’ in her rendering of the song. This is not to be
wondered at, as her instincts must have rebelled against such a
commonplace number as six in a song redolent of old-world sentiment. But
our fairy bells ought to have stopped at five: this would seem to have been
forgotten when the melody and the present words were wedded together. At
any rate our stories seem to suggest that fairy counting did not go beyond
the fingering of one hand. The only Welsh fairy represented counting is
made to do it all by fives: she counts un, dau, tri, pedwar, pump; un, dau,
tri, pedwar, pump, as hard as her tongue can go. For on the number of times
she can repeat the five numerals at a single breath depends the number of

the live stock of each kind, which are to form her dowry: see p. 8 above,
and as to music in fairy tales, see pp. 202, 206, 292.
Now that a number of our inundation stories have been passed in review in
this and the previous chapter, some room may be given to the question of
their original form. They separate themselves, as it will have been seen, into
at least two groups: (1) those in which the cause of the catastrophe is
ethical, the punishment of the wicked and dissolute; and (2) those in which
no very distinct suggestion of the kind is made. It is needless to say that
everything points to the comparative lateness of the fully developed ethical
motive; and we are not forced to rest content with this theoretical
distinction, for in more than one of the instances we have the two kinds of
story. In the case of Ỻyn Tegid, the less known and presumably the older
story connects the formation of the lake with the neglect to keep the stone
door of the well shut, while the more popular story makes the catastrophe a
punishment for wicked and riotous living: compare pp. 377, 408, above. So
with the older story of Cantre’r Gwaelod, on which we found the later one
of the tipsy Seithennin as it were grafted, p. 395. The keeping of the well
shut in the former case, as also in that of Ffynnon Gywer, was a precaution,
but the neglect of it was not the cause of the ensuing misfortune. Even if we
had stories like the Irish ones, which make the sacred well burst forth in
pursuit of the intruder who has gazed into its depths, it would by no means
be of a piece with the punishment of riotous and lawless living. Our
comparison should rather be with the story of the Curse of Pantannas,
where a man incurred the wrath of the fairies by ploughing up ground
which they wished to retain as a green sward; but the threatened vengeance
for that act of culture did not come to pass for a century, till the time of one,
in fact, who is not charged with having done anything to deserve it. The
ethics of that legend are, it is clear, not easy to discover, and in our
inundation stories one may trace stages of development from a similarly
low level. The case may be represented thus: a divinity is offended by a
man, and for some reason or other the former wreaks his vengeance, not on
the offender, but on his descendants. This minimum granted, it is easy to
see, that in time the popular conscience would fail to rest satisfied with the
cruel idea of a jealous divinity visiting the iniquity of the fathers upon the
children. One may accordingly distinguish the following stages:—

1. The legend lays it down as a fact that the father was very wicked.
2. It makes his descendants also wicked like him.
3. It represents the same punishment overtaking father and sons, ancestor
and descendants.
4. The simplest way to secure this kind of equal justice was, no doubt, to let
the offending ancestors live on to see their descendants of the generation for
whose time the vengeance had been fixed, and to let them be swept away
with them in one and the same cataclysm, as in the Welsh versions of the
Syfađon and Kenfig legends, possibly also in those of Ỻyn Tegid and Tyno
Helig, which are not explicit on this point.
Let us for a moment examine the indications of the time to which the
vengeance is put off. In the case of the landed families of ancient Wales,
every member of them had his position and liabilities settled by his
pedigree, which had to be exactly recorded down to the eighth generation or
eighth lifetime in Gwyneđ, and to the seventh in Gwent and Dyfed. Those
generations were reckoned the limits of recognized family relationship
according to the Welsh Laws, and to keep any practical reckoning of the
kind, extending always back some two centuries, must have employed a
class of professional men14. In any case the ninth generation, called in
Welsh y nawfed âch, which is a term in use all over the Principality at the
present day, is treated as lying outside all recognized kinship. Thus if AB
wishes to say that he is no relation to CD, he will say that he is not related o
fewn y nawfed âch, ‘within the ninth degree,’ or hyd y nawfed âch, ‘up to
the ninth degree,’ it being understood that in the ninth degree and beyond it
no relationship is reckoned. Folklore stories, however, seem to suggest
another interpretation of the word âch, and fewer generations in the direct
line as indicated in the following table. For the sake of simplicity the
founder of the family is here assumed to have at least two sons, A and B,
and each succeeding generation to consist of one son only; and lastly the
women are omitted altogether:—
Tâd I (Father)

1
Brother A II B Mâb (Son)
2 2
i Cousin Aa III Ba Wyr (Grandson)
3 3
ii Cousin Ab IV Bb Gorwyr (Great-Grandson)
4 4
iii Cousin Ac V Bc Esgynnyđ (G.G.Grandson)
5 5
iv Cousin Ad VI Bd Goresgynnyđ (G.G.G.Grandson).
In reckoning the relationships between the collateral members of the family,
one counts not generations or begettings, not removes or degrees, but
ancestry or the number of ancestors, so that the father or founder of the
family only counts once. Thus his descendants Ad
and Bd
in the sixth
generation or lifetime, are fourth cousins separated from one another by
nine ancestors: that is, they are related in the ninth âch. In other words, Ad
has five ancestors and Bd
has also five, but as they have one ancestor in
common, the father of the family, they are not separated by 5 + 5 ancestors,
but by 5 + 5 - 1, that is by 9. Similarly, one being always subtracted, the
third cousins Ac
and Bc
are related in the seventh âch, and the second
cousin in the fifth âch: so with the others in odd numbers downwards, and
also with the relatives reckoned upwards to the seventh or eighth
generation, which would mean collaterals separated by eleven or thirteen
ancestors respectively. This reckoning, which is purely conjectural, is based
chiefly on the Kenfig story, which foretold the vengeance to come in the
ninth âch and otherwise in the time of the goresgynnyđ, that is to say in the
sixth lifetime. This works out all right if only by the ninth âch we
understand the generation or lifetime when the collaterals are separated by
nine ancestors, for that is no other than the sixth from the founder of the
family. The Welsh version of the Ỻynclys legend fixes on the same
generation, as it says yn oes wyrion, gorwyrion, esgynnyđ a goresgynnyđ,
‘in the lifetime of grandsons, great-grandsons, ascensors, and their

children,’ for these last’s time is the sixth generation. In the case of the
Syfađon legend the time of the vengeance is the ninth cenhedlaeth or
generation, which must be regarded as probably a careless way of
indicating the generation when the collaterals are separated by nine
ancestors, that is to say the sixth from the father of the family. It can hardly
have the other meaning, as the sinning ancestors are represented as then still
living. The case of the Tyno Helig legend is different, as we have the time
announced to the offending ancestor described as amser dy wyrion, dy
orwyrion, a dy esgynyđion, ‘the time of thy grandsons, thy great-grandsons,
and thy ascensors,’ which would be only the fifth generation with collaterals
separated only by seven ancestors, and not nine. But the probability is that
goresgynyđion has been here accidentally omitted, and that the generation
indicated originally was the same as in the others. This, however, will not
explain the Bala legend, which fixes the time for the third generation,
namely, immediately after the birth of the offending prince’s first grandson.
If, however, as I am inclined to suppose, the sixth generation with
collaterals severed by nine ancestors was the normal term in these stories, it
is easy to understand that the story-teller might wish to substitute a
generation nearer to the original offender, especially if he was himself to be
regarded as surviving to share in the threatened punishment: his living to
see the birth of his first grandson postulated no extraordinary longevity.
The question why fairy vengeance is so often represented deferred for a
long time can no longer be put off. Here three or four answers suggest
themselves:—
1. The story of the Curse of Pantannas relates how the offender was not the
person punished, but one of his descendants a hundred or more years after
his time, while the offender is represented escaping the fairies’ vengeance
because he entreated them very hard to let him go unpunished. All this
seems to me but a sort of protest against the inexorable character of the
little people, a protest, moreover, which was probably invented
comparatively late.
2. The next answer is the very antithesis of the Pantannas one; for it is, that
the fairies delay in order to involve all the more men and women in the

vengeance wreaked by them: I confess that I see no reason to entertain so
sinister an idea.
3. A better answer, perhaps, is that the fairies were not always in a position
to harm him who offended them. This may well have been the belief as
regards any one who had at his command the dreaded potency of magic.
Take for instance the Irish story of a king of Erin called Eochaid Airem,
who, with the aid of his magician or druid Dalán, defied the fairies, and dug
into the heart of their underground station, until, in fact, he got possession
of his queen, who had been carried thither by a fairy chief named Mider.
Eochaid, assisted by his druid and the powerful Ogams which the latter
wrote on rods of yew, was too formidable for the fairies, and their wrath
was not executed till the time of Eochaid’s unoffending grandson, Conaire
Mór, who fell a victim to it, as related in the epic story of Bruden Dáderga,
so called from the palace where Conaire was slain15.
4. Lastly, it may be said that the fairies being supposed deathless, there
would be no reason why they should hurry; and even in case the delay
meant a century or two, that makes no perceptible approach to the
extravagant scale of time common enough in our fairy tales, when, for
instance, they make a man who has whiled ages away in fairyland, deem it
only so many minutes16.
Whatever the causes may have been which gave our stories their form in
regard of the delay in the fairy revenge, it is clear that Welsh folklore could
not allow this delay to extend beyond the sixth generation with its
cousinship of nine ancestries, if, as I gather, it counted kinship no further.
Had one projected it on the seventh or the eighth generation, both of which
are contemplated in the Laws, it would not be folklore. It would more likely
be the lore of the landed gentry and of the powerful families whose
pedigrees and ramifications of kinship were minutely known to the
professional men on whom it was incumbent to keep themselves, and those
on whom they depended, well informed in such matters.
It remains for me to consider the non-ethical motive of the other stories,
such as those which ascribe negligence and the consequent inundation to

the woman who has the charge of the door or lid of the threatening well.
Her negligence is not the cause of the catastrophe, but it leaves the way
open for it. What then can have been regarded the cause? One may gather
something to the point from the Irish story where the divinity of the well is
offended because a woman has gazed into its depths, and here probably, as
already suggested (p. 392), we come across an ancient tabu directed against
women, which may have applied only to certain wells of peculiarly sacred
character. It serves, however, to suggest that the divinities of the water-
world were not disinclined to seize every opportunity of extending their
domain on the earth’s surface; and I am persuaded that this was once a
universal creed of some race or other in possession of these islands. Besides
the Irish legends already mentioned (pp. 382, 384) of the formation of
Lough Neagh, Lough Ree, and others, witness the legendary annals of early
Ireland, which, by the side of battles, the clearing of forests, and the
construction of causeways, mention the bursting forth of lakes and rivers;
that is to say, the formation or the coming into existence, or else the serious
expansion, of certain of the actual waters of the country. For the present
purpose the details given by The Four Masters are sufficient, and I have
hurriedly counted their instances as follows:—
Anno Mundi 2532, number of the lakes formed, 2.
,, ,,
2533,
,, ,, ,,
lakes
,,
1.
,, ,,
2535,
,, ,, ,,
lakes
,,
2.
,, ,,
2545,
,, ,, ,,
lakes
,,
1.
,, ,,
2546,
,, ,, ,,
lakes
,,
1.
,, ,,
2859,
,, ,, ,,
lakes
,,
2.
,, ,,
2860,
,, ,, ,,
lakes
,,
2.
,, ,,
3503,
,, ,, ,,
rivers
,,
21.

,, ,,
3506,
,, ,, ,,
lakes
,,
9.
,, ,,
3510,
,, ,, ,,
rivers
,,
5.
,, ,,
3520,
,, ,, ,,
rivers
,,
9.
,, ,,
3581,
,, ,, ,,
lakes
,,
9.
,, ,,
3656,
,, ,, ,,
rivers
,,
3.
,, ,,
3751,
,, ,, ,,
lakes
,,
1.
,, ,, ,, ,, ,, ,,
rivers
,,
3.
,, ,,
3790,
,, ,, ,,
lakes
,,
4.
,, ,,
4169,
,, ,, ,,
rivers
,,
5.
,, ,,
4694,
,, ,, ,,
lakes
,,
1.
This makes an aggregate of thirty-five lakes and forty-six rivers, that is to
say a total of eighty-one eruptions. But I ought, perhaps, to explain that
under the head of lakes I have included not only separate pieces of water,
but also six inlets of the sea, such as Strangford Lough and the like. Still
more to the point is it to mention that of the lakes two are said to have burst
forth at the digging of graves. Thus, A.M. 2535, The Four Masters have the
following: ‘Laighlinne, son of Parthalon, died in this year. When his grave
was dug, Loch Laighlinne sprang forth in Ui Mac Uais, and from him it is
named17.’ O’Donovan, the editor and translator of The Four Masters,
supposes it to be somewhere to the south-west of Tara, in Meath. Similarly,
A.M. 4694, they say of a certain Melghe Molbthach, ‘When his grave was
digging, Loch Melghe burst forth over the land in Cairbre, so that it was
named from him.’ This is said to be now called Lough Melvin, on the
confines of the counties of Donegal, Leitrim, and Fermanagh. These two
instances are mentioned by The Four Masters; and here is one given by

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Planetary Climates Course Book Andrew Ingersoll

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Planetary Climates Course Book Andrew Ingersoll