to

of

rstt of Toronto

Herbert Otto Frind Esq.

WAVES OF THE SEA

BY THE SAME AUTHOR.

The Panama Canal and its Makers*

With a Map and 63 Illustrations from the Author's
Photographs.

Large Crown Svo, cloth, 5s.

" It is a pleasure to have a book on the Panama Canal
by an English observer. Mr. Cornish is both qualified and
independent. He has produced an admirable description,
suited for the general reader, lucid, not overloaded with
technicalities, of the right length, yet comprehensive." —
Daily Chronicle.

" The author of this concise account of the history, the
progress, and the possibilities of a gigantic enterprise is to
be congratulated on the skilful manner in which he has
compressed an enormous amount of information and many
valuable opinions and observations into a very small space."
—Standard.

LONDOX: T. FISHER UNWIN.

WAVES OF THE SEA

AND OTHER WATER WAVES

BY

VAUGHAN CORNISH

Doctor of Science (Manchester Univ.), Fellow of the Royal

Geographical, Geological, and Chemical Societies of London

Member of the Japan Society

WITH 50 PHOTOGRAPHS TAKEN BY THE AUTHOR

T. FISHER UNWIN

LONDON: ADELPHI TERRACE

LEIPSIC: INSELSTRAS-SE 20

1910

(All rights reserved.}

TO

SIR CLEMENTS R. MARKHAM, K.C.B., F.R.S.
VICE-PRESIDENT AND PAST PRESIDENT

OF THE
ROYAL GEOGRAPHICAL SOCIETY

IN TOKEN OF

SINCERE REGARD AND VENERATION

I DEDICATE THIS BOOK

V. C.

PREFACE

MOST of us have felt the fascination of a wave.
The waves of the sea, which are the prototype of
all the phenomena which we now call waves, are
perhaps the most fascinating of all. Great as is
the beauty of their form, the mystery of their
motion is the greater charm. For while they move
they live and have a being, which, like our own,
is but momentarily associated with the matter of
which they are formed. The wave preserves its
individuality, its recognisable though not unchang-
ing form, its energy, partly active, partly in reserve,
whilst its material substance is constantly rejected
and renewed. Of all manifestations of the inor-
ganic world it is most like a living being. Yet
when we watch it to its end we find none of the
sad accompaniments of the exhaustion of life. It
is most beautiful at the last, as it culminates to its
fall and breaks in seething foam.

There are two aspects of sea waves which parti-
cularly attract our admiration. The first is that

8 PREFACE

of a storm at sea, the second is the surf which comes
in during calm weather upon a shore facing the
open ocean, the breakers booming like minute guns.
The first indicates the fury of the wind, but it is
the second which we almost instinctively recognise
as affording the best index of the greatness of the
expanse of water.

These things, and others of a like nature, I have
watched for many years, and I have set down in
this book what I have been able to add to former
knowledge.

I have written to inform the mind, not to stir the
imagination. The appearances are familiar and
recurrent, and I do not attempt to recall them by
much word-painting, but the precise observation
and measurement of waves, and the discovery of
the mode of their production, are matters of
difficulty, and to these I have given myself.

My investigations pn water waves have been
prosecuted during the last fifteen years. They have
been made in many parts of the world^ which I have
visited principally for the study of surface waves
of different kinds. The chief results as far ;as
they relate to water waves are contained in this
volume, which contains also a critical examination
of observations made by a number of seamen and
others upon the size and speed of ocean waves.

PREFACE 9

Most of Part III., relating to tidal bores and
other waves in rivers, was published in the
Geographical Journal and in Engineering in 1906,
but Parts I. and II., which relate to waves of the
sea, are new, and were written in 1909-10.

Side by side with the observations of water
waves, I have during the same period (i.e., since
1895) been investigating the progressive transverse
ridges which are produced in sand and snow by
the action of water or wind, and I have made
observations upon earthquakes and other wave-
phenomena which come within the province of
physical geography. These I intend to publish
later.

August, 1910. VAUGHAN CORNISH.

CONTENTS

PART I

ON THE SIZE AND SPEED OF DEEP-SEA WA VES
CHAPTER I

PAGE

Introduction — Waves on ponds — Waves on lakes — Coniston
Water — Lake of Geneva — Lake Superior — Waves in
semi-enclosed seas — Western Mediterranean — China
Sea .... 23

CHAPTER II

Observations of waves on the North Atlantic — Conclusion
as to height of North Atlantic waves — Waves on the
North Pacific — The effective length of fetch of strong
winds on the North Atlantic Ocean — The numerical
relation between the length of fetch of wind and
height of storm-waves — Waves on the South Atlantic
and Southern Indian Oceans — Waves on the South
Pacific Ocean — The discrepancy between wave-lengths
determined respectively by simultaneous and by suc-
cessive observation of wave-crests . . . 42

CHAPTER III

The wave-length of the swell which reaches the shore after
storms — The height of the swell at sea during storms
— The co-existence of waves of different lengths — The
give and take between air and water in the develop-
ment of waves . . . . . -85

11

12 CONTENTS

CHAPTER IV

PACK

The velocity of the wind at sea— The numerical relation
between velocity of wind and average height of waves
— The relation between the velocity of the wind and
the velocity of the waves — The connection between
the rate of progress of cyclones and the character of
the waves — The effect of squalls and gusts upon
waves — On wave-fronts in a veering wind, and on the
irregularity of the waves in the region of the Trade
winds — The observed profile of waves at sea — The
mountainous appearance of waves . . .107

PART II

ON THE ACTION OF SEA WAVES TO TRANS-
PORT SHINGLE, SAND, AND MUD

CHAPTER V

On the depth to which wave-agitation extends, and on the
transport of fine mud — The action of waves to drive
shingle shorewards — The effect of percolation to pro-
mote the building-up of beaches — The movement of
sand by waves — The undertow . . ... . 141

CHAPTER VI

On the actions which determine the 'longshore transport of
beach shingle — On the causes which give rise to an
arrangement of pebbles according to their sizes along
the Chesil Beach and certain other beaches — On the
production and maintenance of the Shambles sand-bank
near Portland — The formation of patches of shingle
upon a sandy beach by the action of breakers . .176

CONTENTS 13

PART III

ON STATIONARY AND PROGRESSIVE WAVES IN
RIVERS

CHAPTER VII

PAGE

The flood-wave of rivers — The roll- wave in the Tees — In
the Ure — In the Nikko torrent — On the advance of a
flood over dry ground . . . . .221

CHAPTER VIII

Tidal bores — Wave-length of the Severn bore — On the
want of concordance between height of tide and
height of bore, and on the conditions which deter-
mine the starting-point of the bore . . . 230

CHAPTER IX
Cinematographing the Severn bore . , . . 254

CHAPTER X

Stationary or standing waves — Cross-stream progressive

waves : observations in Niagara River . . . 265

CHAPTER XI

On streams which flow as a series of roll-waves — Observa-
tions on a conduit from Territet to Glion — Observations
on the conduit of the Griinnbach (Merlingen,Thunersee)
— Observations on the conduit of the Guntenbach
(Gunten, Thunersee) . . . , . 294

CHAPTER XII

The sounds of running water — The gushing motion of
cataracts — Conical structures produced by the break-
up of a waterfall — The wave-track of a ship . . 333

LIST OF ILLUSTRATIONS

PLATES.

WAVES MEETING AND CROSSING IN VERY SHALLOW WATER

Frontispiece

PAGE

A MODERATE GALE IN THE MEDITERRANEAN . . 37

From S.S. Orizaba. Height of camera 22 feet.

A STRONG GALE IN THE NORTH ATLANTIC . . -47

From S.S. Ivernia. Height of camera 40 feet.

HEAVY SWELL IN THE NORTH ATLANTIC '!" . Ji. $1

WAVES AND SWELL IN THE NORTH ATLANTIC ' .' ' . 57

UNDULATING HORIZON OF A ROUGH SEA . . 65

WEATHER IN THE NORTH ATLANTIC. ' . . . 11$

THE PROFILE OF BREAKING WAVES AT EASTBOURNE . 143

WAVES BREAKING ON A SHINGLE BEACH . . • J51

A WAVE BEFORE AND AFTER BREAKING . . .. 155

WAVE BURSTING AGAINST A VERTICAL WALL . . 159

BREAKER AND BORES ON A FLAT SHORR . . . .163

THE FRINGE OF FOAM LEFT BY THE BORE UPON A FLAT

SHORE . . . . . , ' . !67

15

16 LIST OF ILLUSTRATIONS

PAGE

WAVES APPROACHING ONE ANOTHER IN VERY SHALLOW

WATER . • • *73

WAVES SHOWN BY DISTORTED REFLECTION OF MASTS

(KINGSTON, JAMAICA) . 177

SHINGLE RIDGES . . • l8l

THE ENCROACHMENT OF SHINGLE (SLAUGHDEN, NEAR ALDE-

BURGH, SUFFOLK) » . . . .185

STONES ON THE BEACH NEAR CHESILTON AND THE GRA-
DATION OF STONES FROM BURTON BRADSTOCK TO
CHESILTON .* . . . . . 195

SHORE BETWEEN EAST END OF CHESIL BEACH AND
BLACKNOR POINT . . . . -195

SAND BROUGHT BACK AFTER A STORM AND SAND DRIFTED

ALONGSHORE . . . . . . 2OI

SHINGLE SORTED FROM SAND BY THE WASH OF A HEAVY

SWELL (BRANKSOME CHINE, NEAR BOURNEMOUTH) . 213

REMOVING SHINGLE AFTER A HEAVY SWELL, BEFORE THE
SAND IS BROUGHT BACK IN CALMER WEATHER . 215

CHEVRON-SHAPED PATCH OF SHINGLE FORMED BY THE
WASH OF THE SWELL ON A SANDY SHORE (BOSCOMBE) 217

THE COURSE OF THE RIVER SEVERN FROM GLOUCESTER

TO THE SEVERN TUNNEL . . . . 233

LIST OF ILLUSTRATIONS 17

PAGE

THE BORE ON THE SHALLOWS OF DENNY ROCK, AND AFTER

REACHING DEEPER WATER .... 237

THE NOOSE SANDBANK ..... 243

CINEMATOGRAPHS OF THE BORE APPROACHING STONEBENCH 2$$

CINEMATOGRAPHS OF THE BORE ON REACHING STONEBENCH 259

BORE VIEWED FROM BEHIND AFTER PASSING STONEBENCH 263

STATIONARY WAVES CAUSED BY A WEIR ON THE RIVER

AARE, SWITZERLAND ..... 269

BIRD'S-EYE VIEW OF WAVES IN WHIRLPOOL RAPIDS, NIAGARA 275

LEAPING WAVE, WHIRLPOOL RAPIDS, NIAGARA . . 279

WAVES IN WHIRLPOOL RAPIDS, NIAGARA . . y 285

WAVES IN A RAPID ON THE ST. LAWRENCE, TAKEN GOING

DOWN-STREAM IN A STEAMER .... 289

ROLL-WAVES IN THE GRUNNBACH CONDUIT, LOOKING UP-
STREAM ....*. . 303

ROLL-WAVE LEAPING THE OUTFALL OF THE GRUNNBACH

CONDUIT. .> ^ . ; , , . ,,^. M.« 307

ROLL-WAVES IN THE GRUNNBACH CONDUIT, LOOKING

DOWN-STREAM . . ,. . ., , » 315

OUTFALL OF THE GUNTENBACH AT THE WAVE-TROUGH, AND

(A FEW SECONDS LATER) AT THE WAVE-CREST . 321

2

18 LIST OF ILLUSTRATIONS

PAGE

THE GUNTENBACH WITH TWO ROLL- WAVES . • 32$

UPPER PART OF FALLS AT NIAGARA, SHOWING UNBROKEN

WATER ... • 331

NIAGARA FALLS, SHOWING FLEECY APPEARANCE PRODUCED

BY THE BREAKING OF THE FALLING WATER . - 335

THE BREAKING WATER OF NIAGARA FALLS, TAKEN FROM

S.S. MAID-OF-THE-MIST . . 339

FALLS OF THE TSCHINGELBACH, BURGLAUENEN , . 343

WATER ROCKETS PROJECTED UPWARDS FROM THE FOOT

OF THE HORSESHOE FALLS, NIAGARA . . . 347

WAVE-TRACK OF STEAMER ON THUNERSEE, SHOWING

THWART-SHIP AND DIVERGING WAVES . . • 351

WAVE-TRACK OF STEAMER ON CONISTON WATER, SHOWING
INTERFERENCE BANDS BETWEEN DIVERGING WAVES OF
THE BOW AND STERN SERIES . ' ; *V . 355

WAVE-TRACK OF STEAMER ON CONISTON WATER, SHOWING
INTERFERENCE BANDS AND DOUBLE-CRESTED DIVERG-
ING WAVES . . . . ... .361

WAVE-TRACK OF STEAMER ON LAKE LEMAN 363

WAVE-TRACK OF STEAMER ON LAKE LEMAN, SHOWING, ON
THE LEFT, THE INNER BOUNDARY OF GROUP OF
DIVERGING WAVES ,:. . ,, < . . . 365

LIST OF ILLUSTRATIONS 19

FIGURES IN THE TEXT.

PAGE

COMBINATION OF WAVE AND SWELL . . .98

A CYCLONIC SYSTEM . . . . . .122

VERTICAL AND HORIZONTAL CURRENTS OF WAVES . . 147

THE CHESIL BEACH .... . IQI

CHART SHOWING THE SHAMBLES SHOAL . . . 207

DIAGRAM OF VERTICAL AND HORIZONTAL COMPONENTS OF

THE TIDE NEAR PORTLAND .... 209

PART I

ON THE SIZE AND SPEED OF DEEP-
SEA WAVES

CHAPTER I

Introduction — Waves on ponds — Waves on lakes — Coniston
Water — Lake of Geneva — Lake Superior — Waves in semi-
enclosed seas — Western Mediterranean — China Sea.

Introduction

MEASUREMENTS of waves at sea by means of the
eye are not susceptible of great accuracy ; but the
irregularity of the waves themselves is so con-
siderable, especially in their most important condi-
tion, which is during storms, that it is more useful
to measure many waves somewhat roughly than
to obtain (even if it be possible) the precise
measurement of a few. The advantage of the mere
number of observations does not, however, apply
when we pass from rough measurements by careful
observers to mere guessing at the dimensions of
waves as seen from on board ship . Measurements of
the height of waves, for instance, taken in the usual
way by finding the height above the ship's water-
line from which a neighbouring wave-crest just
intercepts the horizon, are believed to be accurate

24 WAVES OF THE SEA

to within i foot in 10 when made by a practised
observer. This was the estimate of the late
Lieutenant Paris, of the French Navy, for his obser-
vations, and the late Lord Kelvin informed me that
he relied upon his own measurements to the same
extent. When, however, an unpractised observer,
judging merely by the look of things from the deck
of a ship, guesses the height and length of waves, it
is possible for him to err much more widely than
he would on the land, where he stands on a firm
platform, with objects of known size in the neigh-
bourhood to afford a scale. The rolling of the
ship, in particular, alters the apparent direction of
the vertical so as to mislead the judgment as to
height. It is difficult to say how widely these
guesses may depart from fact, but I do not think
it unlikely that waves 20 feet high may, according
to the circumstances, be guessed by unpractised
or careless observers at anything from 10 to
30 feet. This is a range of error of 100 per cent,
as against the i o per cent, of the practised observer.
While, therefore, in dealing with the data before
me, I have been anxious to obtain numerous
records, I have been still more anxious not to
include any which might belong to the category
of misleading guesses. As far as possible, I have
relied upon figures in which the observer has ex-

AND OTHER WATER WAVES 25

plained his method of measurement, and detailed
the attendant circumstances of wind, weather, and
environment. This may have led to the rejection
for the purpose of this book of good measurements,
but the importance of all measurements or estimates
of the size of sea waves being accompanied by a
statement of the method of observation and the
attendant circumstances cannot be too strongly
emphasised.

The relation between the wave-length in deep
water and the period (or time which elapses
between the passage of a fixed point by two
succeeding wave-crests) has been calculated
mathematically, and verified by observation. I
have, therefore, in what follows applied the formula
thus obtained, viz. :

Wave length = 5^ x square of period,

to obtain the wave-length when only the period
has been measured. In all cases, however, the
reader is informed which observation was made,
that of length or period.

WAVES ON PONDS

As the sea is always heaving with the disturb-
ance due to former winds, the commencement of
the wave -making action of wind is best observed

26 WAVES OF THE SEA

on smaller sheets of water. In a rock pool, 20 feet
in diameter, under High Peak, Sidmouth, Devon,
I have measured waves of i inch wave-length at the
windward end, and 4£ inches at the leeward end,
the wind having the force of a gale. Thus if we
take the average length of the waves to be 2 J inches,
there was in this small pool a series of ninety
consecutive waves, the longest of which was i-6oth
of the length of the series.

On the Round Pond in Kensington Gardens,
London, 670 feet in diameter, the water on an
absolutely still day has a glassy surface, but any
breath of air sufficient to be felt upon the cheek
is enough to ruffle its surface and to do away with
the mirror -like reflection. It will then be seen
that the area of ruffled water has been instan-
taneously covered with an almost uniform pattern
of little waves about an inch in length from crest
to crest. As the minutes pass during which the
breeze continues, the height and length of the waves
to leeward increases, but those on the windward
edge of the ruffled water remain of the original size.
Soon the whole pond, except a few feet at the
windward end, is covered with waves travelling
before the wind whose size increases regularly from
the windward to the leeward shore. The maximum
size attained at the latter place depends to some

AND OTHER WATER WAVES 27

extent upon the strength of the wind, but even in
a whole gale (October 6, 1901) the little breakers
on the shelving lee shore followed one another at
intervals of only i second.1 The wave-length was
not measured, but appeared to be about 3 feet.
The whole of this effect was soon produced, being
a matter of minutes ; the height of the waves
quickly diminished when the wind lulled, and could
be seen to increase instantaneously when squalls
occurred, the height increasing by a considerable
fraction during a squall lasting four minutes.

If we take the greatest length of waves observed
in the Round Pond on the day referred to as 3 feet,
and adopt the simple mean of the shortest ( i inch)
and the longest (36 inch) wave as the average
wave-length for the pond during a gale, we find
that there is then a series of 436 consecutive waves,
of which the longest is 1-2 2 3rd of the length of the
series, or of the length of fetch of the wind, or of
the length of run of the waves.

On the Serpentine Water in Hyde Park, a much
larger pond, the shape of which, however, is not
favourable to the development of waves, I measured
those produced in a strong SW. breeze, going out

1 The calculated length of a i -second wave in deep water is
5 feet. The velocity of the wind in London was 50 statute
miles per hour.

28 WAVES OF THE SEA

in a boat not very far from the lee end, where I
was sure of a sufficient depth of water for the
purpose. Measurements with a wooden rule re-
peated during the course of half an hour gave
3 feet wave -length and a height from trough to
crest of about 2 inches.

In ponds, therefore, we see that when the wind
raises waves at all they must be numerous, and
that even the longest must be a small fraction of
length of the series, and that the fraction decreases
as the length of the pond increases. The steepness
of the waves formed by wind upon ponds is also
found to be small as compared, for instance, with
the waves which may sometimes be seen caused
by obstructions in a river. Thus the height of the
waves in the Serpentine was only i-i8th of their
length.

WAVES ON LAKES

Coniston Water

We now proceed to observations on a larger
sheet of water, the Lake of Coniston, or Coniston
Water, in Lancashire. They were taken near the
upper end of the lake, at a distance of 7 statute
miles from the lower end. The sheet of water is
narrow and nearly straight, the lower end about

AND OTHER WATER WAVES 29

S. by W. from the upper. When the wind blew up
the lake with the force of half a gale I found that
the waves near the upper end succeeded each other
at intervals of 2 seconds, corresponding to a wave-
length in deep water of 20 feet. At a later date
Mr. Hamil, a seaman of experience, and captain
of the steam gondola which plies on the lake, sent
me the following observations which he made upon
the larger waves produced in a whole gale of wind.
On September 3, 1902, at 8 a.m., there was a
light wind blowing up the lake, i.e., from the soutji.
At 10 a.m. it rose to a gale, the wind shifting to a
little W. of S. Mr. Hamil timed the waves at
Yew dale Beck, near the upper end of the lake,
with the following results :

Waves passing point of observation. Waves breaking

on beach.
10.30 a.m. ... 27 per minute

10.32 a.m. ... ... 24 per minute

u.oa.m. ... 23 „ „

n.2a.m. ... ... 22 „

11.30 a.m. ... 21 „ „

11.32 a.m. ... ... 20 „ „

12.0 a.m. ... 21 „ „

12.2 a.m. ... 20 „

Thus the period appeared to be constant after
1 1.30 a.m. — i.e., an hour and a half after the gale
commenced. The length of wave in deep water
corresponding to the observed period of 3 seconds

30 WAVES OF THE SEA

is 46 feet. The distance from the lower end of the
lake being 7 statute miles, or 36,960 feet, the
length attained by the waves is i-8o3rd of this dis-
tance. If we take the average length of the series
of waves as 23 feet (since when they commence
their length is very small), the number of waves in
series from end to end of the lake was 1,608.

The wind conditions were similar to those
described for the Round Pond at Kensington and
for the Rock Pool at Sidmouth. Thus we see that
the length of the storm-waves is increased when
the length of the sheet of water is increased, but
more slowly.

The above, however, are not the greatest waves
which can be formed on Coniston Water, although
they are probably about as large as are formed in
ordinary gales. The following observations sup-
plied to me by Mr. Hamil illustrate the way in
which waves larger than ordinary are produced.
They indicate a fact (which we shall find illus-
trated later when dealing with the great waves
of high southern latitudes — e.g., between the Cape
of Good Hope and Australia) that the wave -raising
power of wind is much greater when operating
upon water already in waves than upon nearly
smooth water.

Mr. Hamil finds that the largest waves on

AND OTHER WATER WAVES 31

Coniston Water are only formed when, after about
three days of steady wind blowing along the length
of the lake has produced a steady " run " of waves,
it comes on to blow very hard in the same direction.
Under such circumstances he recorded, near the
upper end, a wave-length of 65 feet and a height of
5 feet. These measurements were made against the
side of the steam gondola. He relies upon the length
to less than 5 feet either way — i.e., is sure that the
waves were more than 60 and less than 70 feet
long. The determination of height he found more
difficult. The wave-length attained under these
somewhat rare conditions was 1-5 69th of the length
of the whole series. The length of wave was 13
times the height. Assuming the same steepness of
water for ordinary gales as for the above unusual
storms, the height of wave corresponding to the
wave-length of 46 feet would be 3^ feet, and this,
I suppose, is seldom much exceeded on Coniston
Water.

The Lake of Geneva

On Lake Leman, or the Lake of Geneva, Dr.
F. A. Forel records during storms wave-periods
of 4.7 seconds at Morges and 5.0 at the town of
Geneva. The longest run which a wave could
have before reaching Morges is 27 statute miles,

32 WAVES OF THE SEA

and the calculated wave-length in deep water for
a period of 4.7 seconds is 113 feet. The length
of run possible at the town of Geneva, which is
situated at the lower extremity of the lake, is
43 statute miles, and the wave-length corresponding
to a period of 5 seconds is 128 feet. At Morges,
therefore, the length of the storm -waves was
1-1261 of the length of the series and at Geneva
1-1774. If we suppose the wind blowing down
the lake, and at the Geneva end making waves
1 28 feet long, then if we take as before the average
length of waves on the lake to be one -half as
long, the number of the waves in the series, from
end to end of the lake, is 3,548.

The following heights of waves on the lake are
recorded by Thos. Stevenson * as having been
observed by Buckie at the distances stated from
windward shore, viz. :

Height of Wave Length of Fetch

in feet. in miles.

7-0 31

7-0 38

8.0 38

8.0 40

1 Vide article, " Harbours," " Encyclopaedia Britannica," Qth
edition. Of all the bodies of water cited by Stevenson in his
table of the increase of height with length of fetch, the Lake of
Geneva is the only one which is wholly enclosed. Many of
the others are, moreover, shallow or affected by strong currents.

AND OTHER WATER WAVES 33

The greatest length (calculated from the
observed period) is 15.4 times the greatest height.

Lake Superior

On Lake Superior waves have been carefully
measured from the shore by Colonel D . D . Gaillard,
Corps of Engineers, U.S.A. For the size of the
waves out in the deep water of the lake, he has,
however, had to obtain evidence from the captains
of vessels. He writes : l

" As the result of inquiries of vessel captains
who have navigated Lake Superior for many years,
and who have, in some cases, made a special note
of the fact that in unusually severe storms the
hiorizon could not be seen from the wheelhouse
when the ship was in the trough of the sea, on
account of adjacent wave -crests, it seems probable
that during unusually severe storms upon Lake
Superior, which occur only at intervals of several
years, waves may be encountered in deep water
of a height of from 20 to 25 feet and a length of
275 to 325 feet."

He adds that the waves on Lake Superior are
larger than occur on any other of this chain of great
lakes.

1 " Wave Action in Relation to Engineering Structures "
(Washington Government Printing Office, 1904), p. 82.

34 WAVES OF THE SEA

In the Duluth Canal at the western end of Lake
Superior Colonel Gaillard during 1901 and 1902
frequently measured waves 200 feet in length,
occasionally 250, and once 275 feet, in a depth
of not more than 27 feet of water. The velocity
of such waves is reduced in water of this depth
and they close in upon one another, their wave-
length diminishing. The measurements taken by
Colonel Gaillard in somewhat shallow water there-
fore show that the estimates of wave-length made
by the captains of vessels were not excessive, and
that we may safely say that a length of 300 feet
is attained during exceptionally severe storms by
the waves of Lake Superior. The possible length
of fetch of wind and length of run of the waves
at Duluth is 298 statute miles or 259 nautical miles,
so that the greatest wave-length is 1-5 248th of the
length of the lake, and if the average wave-length
of the series be 150 feet, there would be 10,496
successive waves simultaneously between windward
and leeward shore. Thus again we find the steady
growth of wave-length with the length of the sheet
of water, the increase of wave-length taking place,
however, more slowly.

Taking the height of the waves during severe
storms on this lake as 22j feet and their length as
300, we find that the length is 13.3 times the

AND OTHER WATER WAVES 35

height, which is nearly the same as that (13) found
for an exceptional storm on Coniston Water.

WAVES IN SEMI-ENCLOSED SEAS OF CONSIDERABLE

DEPTH

Waves in the Western Mediterranean

The Western Mediterranean is about 1,000
statute miles from east to west, but its area is
somewhat broken up by islands. The depths are
great and the tidal currents small, so that observa-
tions of waves are useful for the determination of
dimensions due to the mere action of wind on deep
water.

On April 7, 1899, I sailed from Marseilles at
4 p.m. on the Orient liner Orizaba, bound for
Naples, the weather being fair. Next morning,
the 8th, when nearing the Straits of Bonifacio,
there was a heavy sea directly following the ship,
the wind having risen during the night and having
now the force of a moderate gale. The waves
were not running in a single series of parallel
ridges, but with a good deal of crossing, and the
characteristic feature of the scene was the number
of bursting billows of more or less pyramidal form
produced by the meeting at an acute angle of
waves running not quite in the same direction,

36 WAVES OF THE SEA

These waves, curling over in a cusp and breaking,
flecked the surface of deep blue water with white
foam which reflected the bright beams of the sun
shining through the spray. I set myself to measure
the height of these waves at the times of their
greatest elevation. Standing on the bulwark rails
of the spar deck, while holding to the steel uprights
which supported the promenade deck, I found that
my eye was on a level with the crests of the highest
waves when 22 feet above the flotation line. The
position of the latter I obtained from the com-
mander, who informed me that its then position
was 3 feet below the Plimsoll mark. The height
of the deck above the Plimsoll mark was known
from the scale plan of the ship. The ship did not
pitch, and her rolling was so slow that it was fairly
easy to make the observation when on an even
keel. Thus the height from trough to crest of the
pyramidal waves, which were the characteristic
waves of the day, was ascertained with some
approach to accuracy to be 22 feet.

I desired to ascertain the length of the waves,
which were travelling in the same direction as the
ship, but as usual was unable to watch a wave-
crest running the whole length of the vessel. The
length between two convexities near the ship's
side, viewed simultaneously, I judged to be

37

AND OTHER WATER WAVES 39

130 feet, using the length of the promenade deck
as standard of measurement. This estimate is quite
out of harmony with the successive observation of
following waves. The speed of the vessel was
14 knots and the waves travelled past the ship at
a very considerable speed. They succeeded one
another at an average interval of 17 seconds.
This determination by itself does not permit
the wave-length to be calculated from a
simple formula,1 but it is satisfied by a true
period of 8 to 9 seconds with length of 328 to
415 feet. Seven seconds (with a wave-length
250 feet) is definitely too small, and 10 seconds
( with wave length 512 feet ) is definitely too
much. It is quite inconsistent with a length pf
130 feet, which corresponds to a speed of only
i 5 knots, which is scarcely greater than that of the
ship, and it seems likely that this estimate of the
wave-length was in fact due to the transverse
waves caused by the ship's own motion, which for
her then speed of 1 4 knots have a length of 1 1 o feet .

It appears, therefore, that the average wave-
length was not less than 328 feet (an 8 -seconds
wave).

The wind was westerly, and the sea -room about

1 It can be calculated, however ; see Monthly Chart, North
Atlantic, September, 1909, published by the Meteorological
Committee.

40 WAVES OF THE SEA

300 statute or 260 geographical miles. This dis-
tance from the windward shores is the same as
the maximum possible on Lake Superior, but the
area of the Western Mediterranean is many times
greater. The height which I observed in the
Western Mediterranean in a moderate gale (speed
of wind estimated by the captain of the vessel at
30 miles per hour) is the same as that recorded for
gales of exceptional severity upon Lake Superior,
in which the velocity of the wind would not be
less than 53 miles an hour. The height, therefore,
attained by the largest waves in very severe storms
in the Western Mediterranean must be greater.
The storms of the Gulf of Lions situated to the
westward of my place of observation are notorious
for their severity and for the dangerous sea which
rises. Admiral W. H. Smyth, in his book upon
the Mediterranean,1 writes that in the worst weather
in the Gulf of Lions the waves attain a height
which cannot be much less than 30 feet. Perhaps
we may interpret this as meaning that they cannot
be less than 27 to 28 feet.

Waves in the China Sea

The China Sea is a body of water lying between
the mainland of Asia and the open Pacific, from
1 Quoted by Cialdi, " Moto Ondoso del Mare."

AND OTHER WATER WAVES 41

which it is screened by the Philippine Archipelago
and other islands. The uninterrupted expanses of
water are greater than in the Western Mediterranean.
The following observations were made by the late
Lieutenant Paris, of the French Navy, whose careful
methods of work will be described later. Off Cape
Varella, in a violent storm from the north-east
which lasted several days, the highest wave was
21.3 feet and the average wave-length 328 feet.
The sea -room to windward was about 750 statute
or 650 geographical miles. Thus the difference
in the sizes of waves in great lakes and in the
much larger semi -enclosed seas respectively is less
than we should have expected from the observed
difference between their size in the smaller and
in the larger lakes. We find, however, a great
increase when we go from the semi -enclosed seas
to the open oceans.1

1 In the Caribbean Sea also, where I have made five voyages,
the waves are not quite like those of the open ocean. Between
Colon and Kingston they have a clear run of more than 500
nautical miles in the direction of the prevailing NE. wind, which
blows strongly. The waves, which I have seen attain a height
of above 20 feet during ordinary strong Trade winds, remind
one more of those of the Mediterranean than of the Atlantic,
and there is an absence of the long swell accompanying the
rough sea which is characteristic of the open ocean.

CHAPTER II

Observations of waves on the North Atlantic — Conclusion as
to height of North Atlantic waves— Waves on the North
Pacific— The effective length of fetch of strong winds on
the North Atlantic Ocean— The numerical relation between
the length of fetch of wind and height of storm-waves—
Waves on the South Atlantic and Southern Indian Oceans
—Waves on the South Pacific Ocean— The discrepancy
between wave-lengths determined respectively by simul-
taneous and by successive observation of wave-crests.

Waves on the North Atlantic Ocean

I NOW pass on to the records of storm-waves on the
North Atlantic Ocean. One of the best is that of
the Rev. William Scoresby,1 which I give almost in
his own words.

The height of the waves was recorded on the
east-bound voyage from America to England on
board the S.S. Hlbernla. The construction of the
ship afforded several platforms of known elevation
above the water-line. On March 5, 1848, the ship

1 British Association Meeting of 1850, Report, published
1851, Part II., pp. 26-31.

4*

WAVES OF THE SEA 43

was in latitude 5i°N. and longitude 38° 5o'W<.,
the wind about WSW., and the ship's course true
N. 52° E. By sunset of the previous day the wind
was blowing a hard gale, which continued with
heavy squalls during the night, so that all sail was
taken in except a storm stay-sail forward. The
barometer, which had stood at 29.50 inches at
8 p.m. on the previous day, had fallen to
28.30 inches by 10 a.m. on the 5th. On the after-
noon of this day Dr. Scoresby took up his post
of observation on the saloon deck, which gave an
elevation of the eye 23 feet 3 inches above the
water-line. He found, however, that every ap-
proaching wave intercepted the horizon, so that
from this position he could decide little except
that the average height, reckoned from trough to
crest, was more than 24 feet. He therefore
ventured upon the paddle-box, which was about
7 feet higher, giving an eye elevation of 30 feet
3 inches. This level was well maintained during the
moments of actual observation, because the whole
of the ship's length (220 feet) was clear within
the trough of the wave when the next following
crest was at its greatest apparent height, and the
ship at these moments was on an even keel. From
this position quite one half of the waves which
overtook and passed the ship were above the level

44 WAVES OF THE SEA

of the observer's eye . Sometimes a crest extending
in a ridge 100 yards long would be from 2° to 3°
above the invisible horizon. This Dr. Scoresby
says would give a height from trough to crest of
more than 40 feet, but I confess I regard this
rather as a guess than a measurement. Sometimes,
he says, the crossing of two wave -crests would
send up a sharp peak of water to a height which
he believed to be 50 or 55 feet, or the crest of a
breaking wave would shoot up to a similar height.
The average height of the waves during the
observations on March 5th was more than 30
feet.

On the following day, when, the wind being
less violent, the waves had subsided to an average
height of 26 feet and were more regular, Dr.
Scoresby determined the wave-length in the follow-
ing indirect manner. The waves overtook the ship
every 16.5 seconds and each wave took 6 seconds
to run the whole 220 feet of the ship's length.
Then the distance between two succeeding wave-
crests as thus observed was :

220 x ^g-5 = 605 feet ;

but the ship was not running in exactly the same
direction as the waves, and a line from crest to

AND OTHER WATER WAVES 45

crest measured at right angles would of course be
shorter. Making due allowance for the observed
angle, the true wave-length was determined to be
560 feet.

So far Dr. Scoresby.

I proceed to consider the position of his vessel
at sea so as to be able to compare the sea-room
with that possible on Lake Superior, which we have
stated to be (at Duluth) 259 nautical miles.

At noon on March 5th, the day when the waves
were highest, the vessel was about 600 geographical
miles from the coast of Newfoundland, the direc-
tion from which the wind blew, and by 4 o'clock
in the afternoon 36 miles farther from this, the
nearest shore. At noon on the 6th the distance
from shore was about 800 geographical miles. If
the highest waves were measured at 4 p.m. on the
5th, the ship had been running twenty hours in a
hard gale, and was 180 geographical miles from
the point where the full force of the gale first
struck her. The cyclone was, presumably, travelling
in the same general direction as the ship, but how
close to the shore the westerly wind first attained
the force of a gale we do not know. This much
is certain, that where the waves attained an average
height of more than 30 feet, and an occasional
maximum estimated at more than 40, the sea -room

46 WAVES OF THE SEA

or stretch of water to windward l was 600 geo-
graphical miles or more, as compared with the
259 geographical miles which is the maximum
amount of sea-room possible upon Lake Superior,
where we have accepted 22j feet as the height
of waves in exceptionally severe storms.

The wave-length of 560 feet 2 was measured on
the Atlantic with a sea -room of 800 geographical
miles as compared with the 300 feet of Lake
Superior with a possible sea -room of 259 geo-
graphical miles.

The length of the waves on March 6th was
21.6 times as great as the height, but on the
previous day they must have been steeper.

We will next consider the case of another strong
gale in the North Atlantic with sea-room of at
least 1,000 instead of 600 geographical miles, in
which we shall find that the waves are of about
the same height as in the last case.

The waves in question were observed by myself
on December 7, 1900, when outward bound from
Liverpool to Boston by the Cunard S.S. Ivernia.

1 The " room" which concerns a navigator is more often that
to leeward, but the expression for space to windward is useful
for our purpose.

2 From the building line in Bond Street to the front of the
Royal Geographical Society's House, i, Savile Row, is the
length of a lo-second wave, 512 Jfeet.

47

AND OTHER WATER WAVES 49

Leaving Queenstown on the morning of the 5th,
we met a rather heavy swell on our westerly course,
which continued and somewhat increased during
the 6th. We drove into a strong gale that night,
and the highest waves which I saw during the
voyage were on the morning of the 7th. The force
of the wind on that day was logged as 9 on
Beaufort's scale of 0-12, the number 9 being called
" a strong gale." We continued to drive through
a gale during the whole of the 7th, 8th, and 9th,
the winds varying from S. by W. on the morning
of the 7th to WNW., always therefore producing a
head sea, at first on the port, afterwards on the
starboard. The morning of the 7th (bar.
29.15 inches) was the only time during the three
days when the waves were " running true " — i.e.,
in long parallel ridges exactly at right angles to
the wind, of which ridges six or seven were simul-
taneously visible when looking upwind from the
weather side of the ship. There was no long, flat
swell noticeable, neither were there minor waves
of such prominence as to distract attention from the
principal waves. In the course of eleven voyages
across the Atlantic this is the only occasion on
which I have seen this " regular sea " during a
storm, and the waves were the highest which I
have ever observed in a storm. Our noon position

50 WAVES OF THE SEA

was N. 50° 56', W. 250 33', so that the distance
from the Newfoundland Banks was about 1,000
geographical miles. This was the direction in
which we were steaming and apparently the direc-
tion from which the bad weather was coming. The
wind, however, came from a direction in which there
was no land for 2,000 geographical miles. I was
able to judge the height of the waves more readily
than usual on account of several favourable circum-
stances. The ship, though pitching, did not roll,
being heeled over to starboard at a moderate angle,
which did not vary. Stationing myself amidships,
I was subject to neither pitching nor rolling, but
merely to a lift and fall as each of the large waves
passed beneath us. The two promenade decks
afforded platforms which happened to be at just
the right altitudes for judging the height of the
usual, and of the maximum, waves respectively.
The altitude of these decks above the water line of
the ship I obtained from the scale section of the
ship in charge of the chief engineer. The heeling
over of the ship was measured, and its amount
allowed for, on the assumption that the height of
the deck above the water was reduced, on the lee
side, to the full extent possible. The height of the
waves is recorded as equal to the height of the eye
above the ship's water-line, where they just topped

AND OTHER WATER WAVES 53

the horizon, nothing being added for the small
amount by which they actually exceeded the height
of the eye. Thus, when observing on the lower
deck, I found that the waves commonly attained
29 feet, and from the upper deck that they occa-
sionally attained 43 feet. My lower platform was
about the same altitude as Dr. Scoresby's highest
position, and my estimate of the height of the
ordinary waves is about the same as his. I had
the advantage, however, of a second and higher
platform, which brought me on a level with the
highest waves. Their height as measured by me
from this point of vantage is practically the same
as that guessed by Dr. Scoresby from his lower
platform. The force of the wind was about the
same in both cases, his determination with 600
geographical miles sea-room, mine with 1,000
miles.

Next day, December 8, 1900, the wind had
shifted to WNW. with force 8 (a " fresh gale ") ;
the waves were irregular and not so high, and again
on the 9th, with wind SW. of the same strength,
there was an irregular sea with no very high waves,
though they were magnificent from the tumult of
their headlong rush and the white fury of the broken
water. The sea was, indeed, covered with spume
and veiled in spindrift. A small schooner sighted

54 WAVES OF THE SEA

in the afternoon was running before the storm under
a minimum of sail, and rolling very heavily. From
on board this vessel such waves would tower above
the horizon, but none were as high as 30 feet.
The position of our ship on the 9th was not far
S. and E. of that of Dr. Scoresby's ship when he
measured the 56o-feet wave-length.

Although the higher platform of my larger vessel
gave me an advantage for the measurement of the
highest waves, her great length, and the structure
of the upper works usual on modern liners, made
it very difficult for me, unassisted, to measure wave-
length. I have found the same difficulty every
time I have been at sea, as I have always voyaged
in ships measuring from nearly 500 to 600 feet in
length. It has usually happened that when there
were large regular waves their course made a con-
siderable angle with that of the ship, and even
when the waves ran more nearly in our own direc-
tion, it was generally . impossible for me to watch
the wave -crest during the whole of its passage along
the length of the ship. I have, therefore, been
generally reduced to judging the wave-length in
terms of the known length of the ship from the
simultaneous position of two crests. The length
of the Ivernia is 600 feet, and the regular waves
which we encountered in the strong gale of Decem-

AND OTHER WATER WAVES 55

her 7th I judged by the above method to be about
350 feet in length.

I have never yet seen storm-waves on the North
Atlantic in which the distance between the wave-
crests, viewed simultaneously, appeared to me
nearly as long as the 6oo-feet ships on which I
have voyaged, nor, indeed, any which appeared
more than 400 feet in length. This was the ap-
parent distance between crests during a heavy
swell without wind which I observed from the Red
Star S.S. Vaterland in March, 1901, east-bound in
N. Lat. 48° 30', W. Long. 21° 40'.

The second, and latest, opportunity which I have
had of measuring very large waves on the North
Atlantic was on board the Atlantic Transport
Company's S.S. Minnehaha, east-bound from New
York to Southampton, on February 9, 1907, in
N. Lat. 48° 54', W. Long. 18° 20'. There was
only a moderate breeze from NW., but a huge
north-westerly swell came upon us at about 45°
abaft the beam. The vessel did not pitch, her slow
and stately rolling motion was perfectly rhythmical
and regular, and in the absence of strong wind
observation was unusually easy. It was evident
from the great height of the swell that we were
only just outside the storm area, and this conclusion
was confirmed by a wireless message received

4

56 WAVES OF THE SEA

during the day from the White Star s.S. Cedric
to the northward of us reporting that she was in
a strong NW. gale. Standing on the lower prome-
nade deck, one long ridge after another obscured a
considerable arc of the horizon after passing
beneath the ship, and continued so to obscure it
when at a distance estimated at 400 to 600 feet
from us. I allowed 2 feet as a minimum estimate
for the excess of height above my eye, based on
an observation made a short time before. The
observation was simply this, that when sitting in
my deck chair I had seen a wave similarly obscure
the horizon, and on my rising at once, the horizon
remained obscured. The increase in the elevation
of eye upon rising was found afterwards to be
2 feet.

The roll of the ship at the time of the obscuration
of the leeward horizon was in each case to the
weather side, so that the deck on the lee side was
tilted upwards. The amount of the tilt was
measured for several rolls, which were quite
regular, and assuming that the full amount ought
to be added to the deck height, I obtained 2 feet
so to add. I was standing during the observations,
and my eye-height is 5 feet 9 inches, or say 5^ feet,
so that there is altogether 9^ feet to add to the
height of the deck. This, measured with a heavy

57

AND OTHER WATER WAVES 59

rope hung over the lee side, I found to vary with
the oscillations of the ship and of the water from
2 9 2- to 332 feetJ giving an average of 31^ feet
for smooth water. Two days later, with lighter
bunkers, the height above the smooth water pf
the Solent was found by the rope to be 32^ feet.
Taking, therefore, the height of the deck at the
time of observation as 31^ feet, the height of the
waves which repeatedly passed us was :

Height of deck 31^ feet

Added for roll 2 „

Height of eye above deck 5i ?,

Height of wave above the eye (at least) ... 2 „

Wave height (at least) 41 feet.

Whilst this is 2 feet less than that determined
for the highest waves during the strong gale of
December 7, 1900, there was much less variation
in size from one wave to another, and the average
height in this north-westerly swell was no doubt
quite as great as that during the strong southerly
gale.

The sea-room on February 9, 1907, reckoned
from the coast of Greenland — the direction of the
wind — was about 1,100 geographical miles, and
from the Newfoundland Banks to the westward
about 1,200.

60 WAVES OF THE SEA

Conclusion as to Height of North Atlantic Waves

Thus concordant observations indicate that any-
where in the North Atlantic with sea-room of from
600 up to certainly 1,000 and perhaps 2,000 miles
the height of the large waves during ordinary
strong gales is practically constant, being not less
than 43 feet.1

With regard to the height which is momentarily
attained by peaks of water shooting upwards where
waves cross, the late Lord Kelvin informed me that
he had measured one 60 feet high, and this
measurement confirms the concordant guesses of
several officers on North Atlantic liners whom I
have consulted on the subject. I have not myself
seen anything nearly so high.

Accounts not infrequently appear in the news-
papers of some great wave encountered by the
fast Atlantic liners. These are sometimes reported
as 80, 90, and even 100 feet high. This height
invariably relates to the altitude above the flotation
line of the superstructures which have been deluged
with water. This is not, properly speaking, the
height of a wave, but merely the height to which
a body of water is thrown when a wave breaks
on board. This increases with the speed of the
1 See Note on p. 138.

AND OTHER WATER WAVES 61

ship, which dips her bows into the rising billow
in a head sea. The recorded heights also tend
to increase as the ships are built of larger dimen-
sions, on account of the fact that the greater height
of the navigation bridge and wheel-house allows
the attainment of a greater altitude to be recorded
with certainty. The wheel-house of the Lusitania,
e.g., is 80 feet, or rather more, above the flotation
line.

Waves on the North Pacific Ocean
The North Pacific Ocean has a breadth of open
and deep sea about twice as great as that of the
North Atlantic. The passage from Victoria, B.C.,
to Yokohama is about 4,000 geographical miles,
as compared with the 3,000 from Liverpool to New
York. This route is traversed by a number of liners
similar to the medium -sized Atlantic liners. I made
this passage once, east-bound from Yokohama to
Seattle, in fair weather, when we only encountered
a moderate swell similar to that met with in similar
weather in the same latitudes on the Atlantic. The
great circle course which is followed took us as
far north as Lat. 49° 40'. I had opportunities
during this long voyage of collecting opinions upon
the size of the waves on this route as compared with
those of the North Atlantic and of the Southern
Ocean from seamen who knew all three. The late

62 WAVES OF THE SEA

Dr. Elgar, F.R.S., designer of the Campania, who
was also a passenger, gave his views. There was
a complete consensus of opinion —

First, that the type of storm was the same as on
the North Atlantic routes.

Second, that the storm-waves on the Pacific route
were certainly not higher than those on the Atlantic,
and I did not gather that they were any longer.
They were said to be as irregular as those of the
North Atlantic and not to " run true " as the waves
do in the steadier winds of the Southern Ocean, a
circumstance which was attributed to the storm
being generally of the rotatory character, with a
fairly rapid change in the direction of the wind.
I conclude from this evidence that the greater size
of the ocean does not in this case lead to the
development of greater storm -waves than those
of the North Atlantic.

Thus I have not found in northern latitudes any
increase of height of storm -waves beyond a distance
of 600 geographical miles from the windward
shore. Nevertheless the size of waves observed
by Scoresby is not nearly equalled in enclosed seas
of 500-700 miles in breadth.

I attribute the difference to a smaller size pf
cyclonic systems on the semi -enclosed seas.1

1 Cf. A. Buchan, " Meteorology," " Encyclopaedia Britannica,"
9th edition.

AND OTHER WATER WAVES 63

On the Effective Length of Fetch of Strong Winds
on the North Atlantic Ocean

The volume of charts illustrating the weather
in the North Atlantic from December 18, 1898,
to February 15, 1899,* provides detailed and reli-
able information as to the effective length of fetch
of winds in that ocean. The storms were of unusual
strength and persistence, so that the charts give us
maximum values. The positions and distances
stated below are measured from the charts. At
noon, January i, 1899, a west wind of force 7-8
of Beaufort's scale and upwards (i.e., in no place
less than a moderate gale) is shown to obtain from
N. 49°, W. 40° to N. 49°, W. 60°, a distance of
Ij3°° geographical miles or rather more. But,
in order that the waves at the lee end should be
reinforced by those at the weather end of the strip,
time must be allowed for the travel of the waves.
Waves of about 8 seconds period would be preva-
lent in such winds, and we will consider their move-
ment. Their speed is 8X3=24 knots, and even
when going as forced waves before the wind they
will only travel 576 geographical miles in 24 hours.
Now, an examination of the charts for Decem-

1 Charts illustrating weather of the North Atlantic Ocean in
the winter of 1898-9, Met. Council, 1901.

64 WAVES OF THE SEA

her 3 ist and for January 2nd shows that on
neither day was there so long a strip of water
simultaneously subject to west wind of force 7-8
as on January ist. Therefore the apparent length
of fetch on that day never became effective. But
we see on comparing the chart of December 3 ist
with that of January ist that a strip of 550 geo-
graphical miles was continuously subject to west
wind of force 7-8 for 24 hours, and towards the
end of this period this was the effective length of
fetch of the wind for 8 -second waves, and for
any swifter waves which the force of the wind may
have been capable of producing.

At noon on January 10, 1899, winds of Beaufort
force 7-8 with direction a little W. of N. prevailed
from N. 47°, W. 46° to N. 48°, W. 32°, a distance
of 600 geographical miles. On the previous day
(January 9th) at noon the wind was blowing in the
same direction between the same two positions,
with a force of 9-12, so that for 24 hours there
were winds of constant direction, with a force vary-
ing from a moderate gale to a hurricane, simul-
taneously and continuously affecting the water over
a stretch of 600 geographical miles. Towards the
end of the period, therefore, there was an effective
length of fetch of wind of 600 geographical miles
for all waves of rather more than 8 seconds period.

.

AND OTHER WATER WAVES 67

Throughout the whole of the nine weeks of ex-
ceptionally stormy weather which is covered by
these charts I cannot be sure of any greater effec-
tive length of fetch of wind than 600 geographical,
or 700 statute, miles. This is the wave -making1
length of wind-fetch for the North Atlantic which
we have to compare with the 259 geographical or
289 statute miles of Lake Superior. The wave-
making effect of a strip of wind of 600 geographical
(700 statute) miles long on the mid-Atlantic is,
however, increased by the swell which is always
entering at the weather end. This result agrees
with the conclusion already arrived at that Scoresby
observed, at 600 geographical miles from the wind-
ward shore, waves of the greatest height producible
in the Atlantic by the then force of wind.

The Numerical Relation between Length of Fetch
of Wind and Height of Storm-waves

Thomas Stevenson's empirical formula ( height of
wave in feet = 1.5 X square root of length of fetch
in geographical miles) was shown by him to apply
to distances of rather more than 100 geographical
miles. Colonel Gaillard observed waves 23 feet
high in the Duluth Canal with a length of fetch
of 259 nautical miles, the height calculated from
Stevenson's formula being 24. i feet. The same

68 WAVES OF THE SEA

formula gives 36.75 feet for 600 geographical
miles from the windward shore, which is in
fair agreement with Scoresby's observations on
March 5, 1848 (see ante, p. 42).

Wares on the South Atlantic and Southern Indian

Oceans

Sailors agree that storm -waves are seen in their
fullest and most typical development in those
Southern latitudes where the ocean uninterruptedly
encircles the globe. They are observed from ships
which go round the Cape of Good Hope, and by
those which go round Cape Horn. I proceed to
the observations made by the late Lieutenant Paris,1
of the French Navy, in 1867, when proceeding by
the corvette Dupleix to the China station via the
Cape of Good Hope. The Dupleix was a sailing
vessel with auxiliary steam. She ran before a
prolonged westerly gale during the last days of
October, 1867, having passed the Agulhas Bank,
but being still west of the Island of St. Paul. The
vessel seems, therefore, to have been somewhere
between 40° and 8o°E. Long, and about 40° S. Lat.
After this storm the vessel proceeded northwards
under steam through the calms of Capricorn,

1 See Revue Maritime et Coloniale, vol. xxxi. (1870), pp. m-
127, " Observations sur 1'Etat de la Mer."

AND OTHER WATER WAVES 69

accompanied by a swell from the south-west.
Lieutenant Paris made regular observations of
waves during the whole of this voyage, and when
cruising in the seas of China and Japan, but his
opportunities of measuring large ocean waves
occurred only in the southern ocean, and principally
during the storm above referred to. For obtain-
ing data as to the size of full-grown storm -waves
from his valuable paper, we are, in fact, almost
restricted to a single day's observations, but the
value of this day's work is greatly enhanced by
his daily practice in observing. His method, as
he explicitly states, is that of Dr. Scoresby, the
wave-lengths being usually obtained by noting the
time occupied by the wave in running the length of
the ship combined with the interval elapsing be-
tween the arrival of the waves. The height he
calculates as equal to that of the eye when the
wave just obscures the horizon ; but his observa-
tions in this respect are superior to Dr. Scoresby's,
for, by nimbly running up or down the shrouds,
he got on a level with each succeeding wave, and
was not reduced to Scoresby's expedient of guessing
the height above him of the largest waves. His
results are as follows. On October 25th, 1867,
between the Cape of Good Hope and the Islands
of St. Paul and Amsterdam, during a strong gale

70 WAVES OF THE SEA

from the north-west with violent snow squalls, he
measured at different times of the day 30 waves
which averaged 29.5 feet in height, and of these
6 succeeded one another in a procession, all the
members of which were of equal height, viz.,
37.7 feet (11.5 metres). Later in the day he
saw waves which he says were " certainly higher "
than these, but he was not at the time so placed
as to be able to measure them. Their height, we
may safely conclude, was not less than 40 feet
and probably a little more. Several sailors on
board who had been much at sea had never seen
waves so high. They occurred on what appears
to have been the fourth day of the gale, but the
narrative is not quite clear upon this point.

It will be noticed that both in average and
extreme height the results are practically the same
as were obtained during strong gales in the North
Atlantic by Scoresby on March 5, 1848, and by
myself on December 7, 1900.

The waves were, however, much longer in the
Southern Ocean, the greatest average on any day
being 771 feet, with not a few of 900, and several
waves surpassing 1,312 feet (400 metres) in
length. Scoresby, measuring in the same indirect
way, found the Atlantic waves 560 feet long.

Although at the outset of our discussion of the

AND OTHER WATER WAVES 71

relation between the size of waves and the size
of the basin in which they were formed, I used
either observed lengths, or lengths calculated from
the period, according to which were available, I
find that in observations from shipboard in the
open ocean there is in this matter a troublesome
discrepancy. Most of the " wave-lengths " given
in published records such as those of Scoresby
and Paris were not really observed as an apparent
distance separating two ridges of water viewed
simultaneously, but are deduced by calculation from
observed speeds. The speed is obtained in the
way described by Dr. Scoresby, viz., the observa-
tion of the time taken by a wave -crest to run the
length of the ship, combined with the interval be-
tween the arrival of two wave -crests, the speed
of the ship being known. When the ship is broad-
side on to the waves their apparent period should
enable one to calculate at once the wave-length.
I found, however, when observing at sea, that the
length so calculated was much greater than the
apparent distance between successive convexities
of the water's surface. I have also found that many
officers on the Atlantic liners disclaim ever having
witnessed in the North Atlantic waves of the great
lengths which are measured indirectly by system-
atic observers from the observed speeds of, and

72 WAVES OF THE SEA

the interval of time between, successive waves. The
discrepancy I suppose to be in some way con-
nected with the fact that in a storm there are
always waves of different length and speed run-
ning in the same direction. The waves made by
the ship, which are stationary with respect to the
ship herself, also I think produce a confusing
effect on the direct method of estimation by in-
creasing the height of the progressive waves at
certain definite positions. I do not think it desir-
able to set aside either mode of observation, and
in what follows I shall record both. The reader
will in consequence find that, while the records
of heights provide consistent numbers which are
comparatively easy to interpret, the records of
length are more confused.

Lieutenant Paris remarks of the great series of
six waves above described that, as they passed,
they left the ship, which was 230 feet long, in
a valley "a cable's length" (600 feet) across.

The following is a case of a great wave-length
recorded by direct observation in the same part
of the ocean, viz., on the route from the Cape of
Good Hope to Australia. Major Leonard Darwin,
who communicated the facts to me, was on this
voyage in a vessel 400 feet long, when they fell
in with a gale of such unusual severity that the

AND OTHER WATER WAVES 73

Captain went twelve hours out of his course in
order to partly avoid its fury. Major Darwin made
a special effort to judge the distance separating
crest from crest of the great rollers, and came
to the conclusion that it was three times as great
as the ship's length— /.£., 1,200 feet. Thus we
see that if we compare the wave-lengths, calcu-
lated from the velocity of the waves, as observed
between the Cape of Good Hope and Australia
with those obtained by the same process in the
North Atlantic, the Southern Ocean has much the
longer waves, and, again, if we compare the eye-
estimated length in the Southern Ocean with that
in the North Atlantic, the Southern Ocean has
also much the longer waves.

The following observations by Captain Hugh F.
David, of the White Star S.S. Corinthic,1 were made
during August, 1907, somewhere between S.
Lat. 45° 30', E. Long. 61° and S. Lat. 46° 45',
E. Long. 98° 25'. This is between the Island
of St. Paul and Kerguelen Island, and about 600
geographical miles farther south than the position
where Lieutenant Paris made the observations
above described. The direction of the wind was
westerly, and its greatest force was logged as 9,

1 Letter to Captain Campbell Hepworth, R.N.R., of the
Meteorological Office, and log of the Corinthic,

74 WAVES OF THE SEA

which on the Beaufort scale of o- 1 2, is equivalent
to a wind-velocity of 44 statute or 38.2 geo-
graphical miles per hour, and is termed " a strong
gale." An interesting photograph was taken at
the after -end of the promenade deck, with camera
26 feet above the sea level, showing a neighbouring
wave following the ship and eclipsing the distant
horizon. Captain David writes :

" With regard to the lengths and heights of the
waves at the time of the photograph, I did take
quite a few observations, more particularly of the
heights, which ranged from 38 to 45 feet,
though I have a vivid recollection of one which I
think was quite 50 feet in height. Standing on
bridge at 50 feet above sea level, the crest of this
wave appeared level with the eyes of jigger rigging
just before ship's stern commenced to rise. The
height of rigging from the horizontal line drawn
from bridge rail to jiggermast taken from scale
slightly exceeds 50 feet. This was, of course,
an exceptional wave, and I felt quite glad when
it passed without doing any damage. Referring
to their length from crest to crest, I would not
be quite so definite, though an average would be
about 600 to 750 feet during the worst part of
the storm and indeed afterwards." (The length
of the Corinthic is 500 feet.)

AND OTHER WATER WAVES 75

In the absence of any statement to the contrary
it may be safely concluded that the wave-length
was judged by eye, not determined by indirect
measurements as in the cases of Paris and Scoresby,
eye estimation of the distance between two crests
simultaneously observed being the almost universal
practice of officers on the bridge. Thus this
length for Southern (Indian) Ocean of 600-
750 feet should be compared with my eye estimate
of 350-400 feet for similar weather in the North
Atlantic, and not with Scoresby's indirect measure-
ment there of a length of 560 feet.

Captain Percy Howe, who has voyaged on the
same route, informs me that between the Cape of
Good Hope and Adelaide he was in 1907 subject
to a gale of 21 days' duration, from July i 5th to
August 5th, much the most prolonged which
he has ever experienced. During the most violent
parts of the storm the waves which passed the
ship obscured his horizon when the ship was on
an even keel. His eye-height on the bridge of
the Owe sir y Grange was 45 feet, so that the
waves exceeded this height. The ship's length was
480 feet, and she was wholly within the trough
of the waves, the length of which he estimates at
750 feet. These estimates, which are almost the
same as Captain David's, are for a part of the same
series of exceptional storms.

76 WAVES OF THE SEA

Waves on the South Pacific Ocean

Leaving now that part of the Southern Ocean
which is on the routes from the Cape of Good
'Hope to Australia and New Zealand, we will
examine records from the Cape Horn route from
New Zealand to Europe, which touches higher
latitudes .

The following observations for height were given
me by Mr. G. T. Ogilvie. He came home (east-
bound) by this route in 1880 on a i,3oo-ton ship,
with a length of 230 feet. Whenever it blew hard
he used to get into the mizzen rigging and sight
on to the horizon from various heights. Near Cape
Horn, and therefore more than 53° S. of the
Equator, in a full gale blowing from about SW.,
he estimated the highest wave as 2 feet above
his plane of observation, which, on the Captain's
estimate, was then 40 feet above the water-line,
making a total wave -height of 42 feet. Waves
30 feet high were comparatively common. He
thought he saw one or two rollers not less than
45 feet in height from trough to crest, and possibly
48 feet, but attaches little weight to the figures
for the altitude of a wave apparently so far above
the line of sight.

The following observations by the Hon. Ralph

AND OTHER WATER WAVES 77

Abercromby 1 relate to waves observed in the
South Pacific Ocean on a voyage between New
Zealand and Cape Horn on S.S. Tongariro in 1885.
On July 1 6th the ship was in S. Lat. 55°, W. Long.
105°, in a hard gale from SW. The waves were
the largest seen on the voyage. For the measure-
ment of their height he used a 4^-inch aneroid
barometer with a very open scale divided to
.01 inch. He found (on the assumption that a
difference in .001 inch in the aneroid reading was
equivalent to a change of i foot in level) that
in passing from trough to crest the greatest lift
experienced by the aneroid in the cabin was
40 feet. This was a solitary instance. The next
greatest was 30 feet. Now, on a previous day, he
had found by measurement with a piece of string
that, when the wave -crest passed the cabin, the
porthole was 6 feet nearer the water than it was
at the trough of the wave. Assuming the same
difference to hold during the day of heavier sea, he
adds 6 feet to the lift of 40 feet in order to obtain
the total height of the greatest wave, which he
therefore considers to have been 46 feet. He
reckons the liability to error of the aneroid read-
ing at 2 to 2.5 feet, and that of the measurement

1 Phil. Mag., April, 1888 (vol. xxv., 5th series), " Observa-
tions on the Height, Length, and Velocity of Ocean Waves."

78 WAVES OF THE SEA

of water-level by the string at not less than 2 feet
either way. Thus, his determination of a single
wave -height of 46 feet may really be due to a
wave of anything from 41 J feet to 50^ feet in
height, and therefore, as is the case with so many
other measurements in storms at sea, can only be
taken actually to establish a wave -height of a little
more than 40 feet. Dr. G. Schott, using a sensi-
tive aneroid with microscopic reading, recorded a
maximum wave -height of 39.4 feet in the South
(Atlantic) Ocean.

On the Discrepancy between Wave-lengths deter-
mined respectively by Simultaneous and by
Successive Observation of Wave-crests

On March 15, 1903, I was on the S.S. Hitachi,
of the Nippon Yusen Kaisha, in N. Lat. 28° 26',
E. Long. 125° 53', bound for Kobe, from Hong-
kong. The position is in the East China Sea,
which is here only partially screened from the open
Pacific by the Loo-choo Islands. We encountered
in the afternoon a heavy northerly swell, which
met the ship at an angle estimated by eye at 45°.
One crest was at the stern when the next following
was at the bow, and, knowing the length of the
ship, the true distance from crest to crest, reckoned
at right angles to the course of the waves, was

AND OTHER WATER WAVES 79

known to be 280 feet. But the interval between
the arrival of the waves was 8f seconds, and, as
the vessel was travelling in a direction somewhat
opposed to the direction of the waves, the true
wave-period must have been somewhat greater.
An 8 J -seconds wave has a length in deep water of
370 feet and a 9-seconds wave of 41 5 feet.

Assuming the determination of the period to be
fairly accurate, as the observation is an easy one,
and the application of the mathematical formula
to be valid, as there is every reason to suppose,
we must seek some reason why the apparent wave-
length should be quite 90 feet less than the true.

Two possibilities suggest themselves. The first
is that minor sea-waves are noticed in the simul-
taneous observations of wave -crests, but are passed
over by the eye when watching the progress of
the more rapidly moving crests of the principal
sea -waves.

The second possibility is that the shortening of
apparent wave-length was due to the increased
height of the sea -waves in the vicinity of the bow
and the stern of the vessel. A large vessel pro-
ceeding at a fair speed — in the above case a vessel
of about 6,400 tons going at 12 knots — produces
a short, steep wave, several feet high, at the bow,
and a similar one at the stern. In smooth water

80 WAVES OF THE SEA

these are stationary relatively to the ship, and
have a constant height. In a slight head sea,
however, the stationary bow-wave is replaced
by an intermittent wave, rising up, when the
sea-wave meets the bow, and subsiding at the
trough of the sea-waves. In a heavy head sea
the ship's own bow-wave becomes inconspicuous,
but, nevertheless, contributes as much as before
to the total height of the sea-waves as they reach
the bow and the stern. Now, looking aft, the
steeper ship-wave will maintain the apparent crest
of the flatter sea -wave for some distance after the
crest of the true sea-wave has passed. Conversely,
looking forward, the steep bow-wave will cause
an anticipation of the true crest of the advancing,
flatter sea -wave. Consequently the above measure-
ment of wave-length by simultaneous position of
crests along the ship's side was too small by twice
the distance through which the steeper ship-wave
shifted the position of the combined wave-crest.1

Where the sea waves are large and regular and
long, and the ship small and slow, this error is
least. With a moderate sea and a large and swift
ship the error is greatest.

Officers of the Atlantic liners generally estimate

1 The presence of ship's waves need not affect the deter-
mination of wave-length from observed velocity, for the interval
between the arrival of a sea-wave at st^rn and bow is the same
as if there were no ship-wave.

AND OTHER WATER WAVES 81

wave-length by the position of crests with relation
to the bow and stern of the vessel. Thus, when
sailing by the Allan liner Tunisian, in 1901, the
chief officer informed me that in a storm in the
Atlantic the ship generally " took three waves/'
which means that when one crest is at the bow
and another at the stern there would be a third
crest between. In other words, there would be
two sea -waves to the ship's length. The Tunisian
is 520 feet long, which would make the apparent
wave-length 260 feet.

In my endeavours to get at the truth about the
dimensions of sea -waves, I have done three
things : first, made measurements myself ; second,
examined the records of measurements made by
others ; third, consulted officers on all ships by
which I have travelled as to what their experi-
ence leads them to suppose the height and length
of waves to be. Now, the officers of the Merchant
Service have far more experience of weather in
the open oceans than most naval officers, for ships
of war keep mostly to the vicinity of land. A
fortiori their experience is far greater than that
of landsmen such as myself. On the other hand,
those to whom I have spoken on the subject have
not actually made measurements. The result of my
three lines of inquiry is as follows :

As regards the height of waves, the general

82 WAVES OF THE SEA

opinion of the officers of the Merchant Service
accords with remarkable closeness with the
measurements which have been made by Dr.
Scoresby, Lieutenant Paris, Captain David, and Mr.
Ogilvie. My own measurements confirm both, as
far as the heights of waves in the North Atlantic
are concerned. " About 40 feet " for the fairly
frequent larger waves in an ordinary North Atlantic
storm is the general verdict of the officers on the
liners, and they are generally prepared to concede
a few feet more for waves in exceptional storms,
especially in the region of westerly winds in the
Southern Ocean. From the records discussed in
detail above I find that the larger waves in ordinary
North Atlantic storms attain 43 feet and in ex-
ceptional storms both here and in the South Indian
Ocean attain, and perhaps surpass, 45 feet. The
possibility of an occasional peak of water shooting
up to a height of 60 feet before breaking is some-
times admitted, but those whom I have consulted
generally feel that there is little to be gained by
guessing at the figures applicable to such circum-
stances when they have had no reliable standard
of measurement.

In the matter of wave-length in the North
Atlantic, however, I find the general opinion pf
officers on the liners to be that 600 feet would be
an enormous wave-length, and, if intended as an

AND OTHER WATER WAVES 83

average, and not merely the distance between a
single pair of crests in a confused sea, would not
be met with there in ordinary storms.

Such a sea, in which a large ship of 500 feet
long running directly before the wind is left, time
after time, within the trough of the wave, they
have only witnessed in the Southern Ocean, par-
ticularly in the part east of the Cape of Good
Hope, where the sea is more regular and is prob-
ably longer than that near Cape Horn, though
perhaps not higher.

Thus, it is only in the Southern Ocean, par-
ticularly in the eastern parts, where the waves are
not only large but regular, that the officers' estimate
of wave-length agrees with the measurements from
speed and periodic time.

I have not yet traversed the Southern Ocean,
but in my efforts to judge wave-length from on
board ship in the Irish Channel, the Mediterranean,
East China Sea, Caribbean, North Pacific, and
North Atlantic I almost despaired of getting any
results worth recording on account of the dis-
crepancies above described. It seems as if the
measurements from velocity and period were a
nearer representation of the natural state of the
sea than those gained by officers from their ex-
perience on the bridge. Yet the latter must not
be lightly dismissed, and more attention should

I
84 WAVES OF THE SEA

be given to unravelling this part of the subject.
My explanation of the systematic effect of the
ship's waves to shorten the apparent wave-length
I believe to be an important part of the whole
explanation, but it may not be the sole cause.

It is possible that the observed elevation of the
wave-crest above the ship's flotation line is some-
times increased on account of the presence of a
ship -wave tending to make the recorded heights
of waves too great, especially when observed from
large, fast ships.

On the other hand, a large vessel, among waves
shorter than herself, neither rises to the crests nor
sinks to the troughs, so that in observations such
as my own on the Minnehaha and the Ivernia the
recorded height of the wave-crest above the still-
water-line of the ship is probably less than the
height above the trough.

Thus, these two possible sources of error tend
to neutralise each other, and as the heights
recorded by eye on large ships agree with those
recorded on smaller ones, and both are in accord-
ance with aneroid determinations, as far as these
have been carried, we may regard them as probably
free from any large systematic error such as that
which the ship-wave, and perhaps other superposi-
tion, introduces in one of the methods of measuring
wave-lengths.

CHAPTER III

The wave-length of the swell which reaches the shore after
storms — The height of the swell at sea during storms —
The co-existence of waves of different lengths — The
give and take between air and water in the develop-
ment of waves.

The Wave-length of the Swell which reaches the
Shore after Storms

WHEN the waves produced upon the deep sea run
into water of which the depth is less than i-4th
the wave-length, theory shows that their speed is
reduced 6.7 per cent., and when the depth is no
more than i-8th of the wave-length their speed
is only 4-ioths of what it was in deep water.1
This reduction of speed goes on as the wave
approaches the shelving shore. Finally, in water
of which the depth is only a small fraction of the
original wave-length, the wave -speed is the same
in all cases, no matter what was the original speed
and wave-length in deep water. This progressive

1 Vide Sir G. G. Stokes' " Admiralty Manual," 1886.

85

I
86 WAVES OF THE SEA

change of speed causes the wave -crests to close
up, so that the space separating them gets less and
less as they approach the shore, but the interval
of time between the arrival there of successive
crests is unchanged. Consequently, by timing the
arrival of a number of breakers, or the passage
of a fixed point by a number of waves just before
breaking, we know at once the period of these
waves, not only as we see them in shallow water,
but as they were in water so deep that the wave dis-
turbance did not reach nearly to the bottom. From
the period we can calculate the speed in deep water
by the mathematical theory of waves, using the
formula :

Period (in seconds) = speed of wave in feet per second ~ 5^
(nearly), or, more roughly :
Period (in seconds) = speed of wave in knots per hour -r- 3 ;

and we can calculate the wave-length for deep
water thus :

Square of period = length of wave -f- $J.

The breakers which arrive somewhat irregularly
during storms do so at intervals which, as far as
I have noticed them, do not differ much from the
intervals observed on board ship in the deep sea
during storms ; but after storms the period of the

AND OTHER WATER WAVES 87

breakers is sometimes much greater. Now, this
means that their wave-length in deep water was
much greater than that observed during storms at
sea, and that the speed in deep water of these
subsequent waves was also much greater than that
of the waves then observed. But when the wind no
longer acts upon the water, there is no agent to
accelerate the waves. Theoretically, they should
travel by gravity at the same speed as that which
the action of the wind has induced, or, if there be
any change of speed while in deep water, it could
only be some very gradual diminution. A real
increase in the speed of transmission may be pro-
nounced with confidence to be an impossibility in
the absence of any new source of energy.

The only possible explanation, therefore, is that
the waves of longer period which come in upon
the shore after storms are present, but escape
observation, during storms at sea. Not only so,
but they have attracted comparatively little atten-
tion from on board ship even after storms.

The following observations of the swell, follow-
ing a westerly storm, were made by myself at
Branksome Chine, on the Dorsetshire coast,
between Bournemouth and Poole. The storm had
been violent and long at Bournemouth, and the
weather in the Atlantic exceptionally stormy.

I
88 WAVES OF THE SEA

On the morning of December 29, 1898, the
wind, now light, having drawn more to the north,
the sky was brighter and the weather pleasant,
as it generally is here when the wind blows from
the north-west after the passing of a storm from
the Atlantic . At 1 1 a .m . an unusually heavy surf
came rolling in upon the sandy beach, the waves
maintained unbroken almost to the shore by the
action of the off-shore breeze, which, at Branksome
Chine, always favours the production of a well-
formed breaker.

At ii a.m. came four large breakers at the
following intervals, viz. :

22, 1 8, 20, average 20 seconds.

They were followed by an almost smooth sea ; and

then, after a short time, came a second series of

four large breakers at the following intervals, viz. :

16, 22, 19, average 19 seconds.

At 11.25 a .m . a fine series of seven breakers*
arrived at the following intervals, viz. :

21, 17, 22, 23, 23, 20, average 21 seconds.

I did not notice any minor waves between the
members of the series.

At 1 1.35 a.m. a set of six breakers came at the
following intervals, viz. :

16, 19, 25, 16, 24, average 20 seconds.

AND OTHER WATER WAVES 89

And at 11.50 a.m. a set of seven breakers at
the following intervals, viz. :

17, 21, 16, 22, 23, 18, average 19.5 seconds.

The general average of the periods of the five
sets of waves is 19.9 seconds.

Later in the day large breakers followed one
another in continuous succession without the occur-
rence of any smooth water, and for three-quarters
of an hour I noted, watch in hand, a succession
of 139 consecutive breakers, occurring at the
following intervals, viz. (reading from left to
right):

20, 20, IQ, 21, 19, 19, 17, 12, 20, 20, 19, 22,

21, 21, 20, 22, 15, 18, 19, 17, 17, 20, 22, 2O,

18, 12, 15, 19, 16, 18, 18, 22, 21, 19, 20, 18,
J5(?), i5(?)i 16, 19, 20, 18, 20, 25, 16, 21, 25, 10,

12, 22, 21, 18, 21, 19, 21, 21, 23, l8, 14, 15,

15, 19, 19, 14, 21, 18, 19, 14, 15, 21, 18, 15,

22, I9, 17, I9, I3, 20, 23, 24, 15, I4, 17, 21,

19, 20, 28(?), 12, 24, 19, 20, 19, 19, 21, 18, 16,
17, 22, 26, 20, 16, 21, 22, 23, 25, 17, 15, 16,

23, 21, 20, 15, 15, 18, 19, 26, 19, 21, 21, 18,
21, 19, 19, 18, 23, 18, 19, 22, 20, 20, 15, 23,

20, l8, 2lJ, 2l£, 21, 20.

The average interval was 19 seconds, and this
determination is accurate to a degree not attained
by observations from moving ships. The recorded
intervals between the successive breakers probably
vary more than the real intervals, because if the

I
90 WAVES OF THE SEA

observer is too late in his determination of the time
of breaking for any wave, he not only makes that
interval too long, but the next too short. Thus
we see that we had here a fairly uniform series
of waves whose average period, 19 seconds, shows
that their velocity, when in deep water, was 57
knots, or 66.5 statute miles, per hour, and their
average wave-length 1,850 feet.1

It was not easy to make exact comparison
between the height of these breakers and those
which I have seen at Branksome Chine during
storms, for the latter break farther out and in
deeper water. However, the impression conveyed
to the eye is that there is no very great difference
between the heights of the breakers above the water
in front of them in the two cases. Branksome
Chine is sheltered from the west by the promontory
called Purbeck Island, so that the waves of
westerly gales and the swell which follows are both
reduced by change of direction in rounding the
promontory. If, however, we recall to mind the
numerous references in nautical writings to the
great breakers which come in during calm weather
upon oceanic islands and other shores directly ex-
posed to the ocean, we shall recognise that their

1 This is about equal to the distance from Park Lane to
Devonshire House, measured along Piccadilly.

AND OTHER WATER WAVES 91

height must be of the same order of magnitude
as that of the breaking waves of storms.

On December 29, 1898, in N. 47°, W. 19°, waves
45-52 feet high were reported from S.S. St. Simon.
In absence of details I have not used these in the
above records of height of waves, but I take them
here to calculate a maximum length of storm -wave
in the Atlantic during the exceptionally wild
weather prevailing at the time of my observation
at Branksome. We have already seen that when
the length of waves is determined in the manner
which gives the highest values (viz., by recording
speed and period of arrival from on board ship),
tnaximum waves of 40 feet are associated in the
North Atlantic with lengths not more than 600
feet, or fifteen times the height . The corresponding
length for a height of 45 feet is 675 feet, and
for 52 feet, 780 feet. The latter is a figure prob-
ably considerably in excess of the real average
wave-length during the storm, for which 600 to
700 feet would be a more likely estimate. Never-
theless, if we took the excessive value of 780 feet
for the average length of the storm -waves, this
would be less than one-half the average length of
the swell observed at a distance.

On February i, 1899, I recorded at the same
place a swell of even longer period. The day

6

92 WAVES OF THE SEA

was calm, after some days of light winds from
north and east. A heavy swell began to come in
upon the shore at about n a.m., and between
3 and 4 p.m. I timed the arrival of twelve succes-
sive breakers, between which the eleven intervals
were as follows :

23, 23, 22, 22, 22, 23, 21, 24, 24, 22, 22, average 22-5 seconds.

This is the longest period which I have ever
observed for a group of waves. It was noted at
the time as a good observation — i.e., the determina-
tion of the times was rendered easy by the regu-
larity in the form and progress of the waves.
Multiplying the period by three, we obtain with
sufficient accuracy the speed in deep water, ex-
pressed in knots, which is therefore 67.5. This
multiplied by 7-6 gives the speed in statute
miles per hour, viz., 78.75. The corresponding
wave-length in deep water is 2,594 feet. Although
observed in the English Channel, it is an accepted
view that such a swell is due to an Atlantic storm.
The period is almost twice as great as that (11.7
seconds) recorded by Dr. Scoresby in the storm of
March 5-6, 1848, and the speed therefore is like-
wise nearly twice as great. In a later chapter
an account will be given of the probable origin of
this set of breakers and of the distances they had

travelled ( see p . 1 1 8 ) .

AND OTHER WATER WAVES 93

On September 16, 1900, in fine weather at
Branksome Chine, I heard the boom of surf, and,
looking from my window, timed a set of well-
formed though not large breakers at the following
intervals, viz. :

18, 17, 19, 23, 19, 21, average 19-5 seconds.

The following observation of a swell from the
Atlantic was made on the north coast of Ireland,
near the Giant's Causeway, in the autumn of 1870,
by the late Sir G. G. Stokes.1 One morning a
grand surf came rolling in. There had been, some
days before, a long succession of heavy gales in
the North Atlantic. The period determined from
different sets of six or eight waves was 1 7 seconds .
The average difference between the mean periods
of the different sets of waves was only about i-5th
of a second. The differences between the periods
of individual waves is not recorded, but would, of
course, be much greater. Somewhat later the
period sank to 16 seconds, in the latish afternoon
to 14, and next day to 13. The surf was highest
for the 1 7 -second period. During several other
summers, when Sir G. G. Stokes spent a month
or two on that coast, he never saw anything so
striking.

1 Discussion in Section A, British Association, Dover, 1899,
on a paper by the present author.

I
94 WAVES OF THE SEA

Some interesting deductions can be made from
the above record.

The mean between the period at commencement
(17 seconds) and that next day (13 seconds) is
15 seconds; and in 24 hours 5,760 waves of this
period would have discharged themselves upon the
shore. The length of a i 5 -second wave is 1,153
feet, so that 5,760 such waves in series would
occupy a space of 1,090 geographical miles. The
length of the waves at the front of the group was
1,481 feet, and of those at the rear 866 feet. If
we suppose the waves travelling freely after the
storm, the rate of progress of the group, if reckoned
by that of a 15 -second wave, would be, not 45,
but 22| knots,1 so that the advance per 24 hours
would be 540 geographical miles, and the interval
between the storms and the arrival of the swell
was " some days."

The character of the group of waves at the
moment when the storm ceased must have been

1 Vide Nature, vol. xvi., 1877, p. 343, for Osborne Reynolds on
the relation between group-velocity and wave-velocity in deep
water. In deep water a group of trochoidal waves travelling
freely under the action of gravity advances at half the speed
of the individual waves. If we follow the motion of the first
wave of the group, we shall find that it dies out, and the wave
behind it has now taken the lead. If, on the other hand, we
watch the last wave of the group, we shall soon find that
another one has appeared behind it, and the sum total of these

AND OTHER WATER WAVES

95

very different from that at the end of their long
journey. In the first place, the waves which would
have been noticed and measured from ship-board
would have comprised none of the length of even
the shortest seen at the Giant's Causeway. They
would have been the waves from 400 to 600 feet
long, with periods of less than 1 1 seconds, and they
could not have arrived at the Giant's Causeway
until later. But when they did arrive — as arrive
they must— it is evident that they gave rise to no
remarkable breakers, for the surf was decreasing

two effects may be represented by the following scheme, in
which we take the front wave and place it at the back : —

1234567
7123456
6712345
5671234
4567123
3456712

2345671
1234567.

In each succeeding horizontal row the individual waves have
moved forward two places, but the group has advanced only
one. The late J. Scott Russell's early recognition of two wave
velocities appears to have been forgotten. He says, in his
Report on Waves, B. A. meeting at York, 1844 : " I have found
that the motion of propagation of the whole group is different
from the apparent motion of wave transmission along the
surface ; that in the group whose velocity of oscillation is as
observed, 3-57 feet per second, each wave having a seeming
velocity of 3*57, the whole group moves forward in the direction
of transmission with a much slower velocity."

96 WAVES OF THE SEA

as the period decreased, and observations were dis-
continued when the period was 13 seconds. Theory
shows that when deep-sea waves are left to them-
selves, the time which they take to flatten out so
as to become invisible is proportional to the square
of the wave-length.1 Hence the longer waves are
more permanent. Again, waves of all lengths are
reduced to the same small speed by the time they
break upon the shore ; so that waves originally long
and swift are shut up, or telescoped, to a much
greater extent than the slower ones, and they
undergo in the process a correspondingly greater
increase in height. On both accounts, therefore,
the height of the breakers given by the swifter
waves is increased out of all proportion to their
original height during the storm.

T<he Height of the Swell at Sea during Storms

I shall now attempt to arrive at some conclu-
sion as to the height during storms of the waves
longer than those then measured, or th^at part of
the wave -disturbance which is termed then, and
afterwards, " the swell." On board ship during
storms the swell is felt in the movement of the
vessel more distinctly than it is seen, but it often
can be perceived as a sort of broad band, lighter
1 Vide ]. Boussinesq, Comptes Rendus, cxxi.

AND OTHER WATER WAVES 97

or darker, where the whole group of shorter waves
seems slightly raised, and this broad, heaved-up
piece seems to travel with great speed, like the
shadow of a scudding cloud.

To take the example afforded us by Sir G. G.
Stokes' observation, let us think of the group of
waves which he observed as they were when the
wind first dropped, and think of them first apart
from the shorter waves with which they were then
really associated. They were not then a band
1,100 miles broad of almost perfectly harmonic
undulations with length from 866 feet to 1,481
feet, but a much narrower band in which the
water undulated with less regular motion, the
surface having a less regular form. I shall take
the average period of undulation of the water in
this band as 15 seconds, and the wave-length,
therefore, as 1,150 feet. This part of the total
wave -disturbance I call the swell, and I inquire,
What was the height of the swell? Now, the
height of the principal waves shorter than the swell,
i.e., the dominant, or storm waves, we know fairly
well from the preceding records. Most of them
were 30 feet high, with fairly frequent larger in-
dividuals of 40 feet, and some of them were not
much more than 20 feet high.

The diagram shows how such a condition can

J M
w >J-

Is

as w

CD w

£ ta

o

W ^*
S II

AND OTHER WATER WAVES

99

be represented by replacing the theoretically
infinite number of wave-lengths by two, which
I call the storm -wave, or the dominant wave, and
the swell, the former 30 feet high and the latter 20.
The lengths arbitrarily chosen are 600 feet for
the former and 1,150 for the latter. It will be
noticed that the combined wave in the third line
represents fairly well the appearance of a toler-
ably regular sea, and it would do so still better
if the curves had been drawn in the form of a
trochoid instead of a curve of sines, which makes
the trough similar to the crest.

Measuring from left to right, the vertical distance
from each crest to the trough next on the right is :

22*50 feet
37-50 „
1875 „
40-00 „

27-50 n

Average 28-30 feet.

The average, if carried on through the whole
gamut of the combined wave, would be 30 — i.e.,
the same as the height of the dominant or storm-
wave. Thus, in the above example we have
a range of observed wave -height from rather less
than 20 feet up to 40 feet. This result, correspond-
ing to the heights observed by me in the storm of

100 WAVES OF THE SEA

December 7, 1900, is due to a swell of two-thirds
the height of the storm -wave and nearly double
its length, the hypothetical height of the swell
being 20 feet. This, however, is not an observation
but a case chosen for examination.

On June 10, 1885, Abercromby, using an
aneroid as already described, observed individual
wave-heights of 26, 21, 23.5, and 26 feet (average
24), but obtained an absolute difference of level
between lowest trough and highest crest (not,
however, one of those recorded above) of 35 feet.

Let x = height of storm-waves,

„ y = height of swell,
Then x + y = 35 feet ;

and, as we saw from the diagram referred to

above —

x = 24 (the average apparent height),

therefore—

y = 35 -24= ii feet.

This recorded case, therefore, is consistent with
an amplitude of swell nearly one half as great
as that of the storm -wave which dominates the eye.
Had I not drawn for myself combined curves to
test the effect produced by combining together un-
dulations of a certain length with others nearly
twice as long, I should not have supposed it possible
to obscure a longer undulation of such considerable
amplitude.

AND OTHER WATER WAVES 101

The diagrams, which I published in Knowledge
in 1 90 1, and afterwards in the Geographical Journal,
May, 1904, show what is geometrically and
numerically possible in the way of such obscuration.
The observations made on the north coast of
Ireland by Sir G. G. Stokes (as well as my own
observations) show how necessary it is to allow
for the presence with the storm -waves of longer
waves of considerable amplitude. Abercromby's
single observation supplies a confirmation of the
apparently somewhat extreme case shown in the
figure given on p. 98. It is, however, much
to be desired that further observations similar to
those of Abercromby should be obtained, for it
must be confessed that it is a narrow foundation
upon which to build.

On the Co-existence of Waves of Different Lengths

In studying deep-sea waves one is often called
upon to decide whether to fix the attention upon
the actual surface of irregular or complex form
and deal with it as the concrete wave, or to think
of this irregular wave as composed of, or resolved
into, a number of simple harmonic waves each of
regular form and of a different speed. As a matter
of mathematics all irregular waves can be so re-

102 WAVES OF THE SEA

solved, and the behaviour of the roughened sea,
when the wind drops, exactly performs this act of
analysis — i.e., of resolution into components. On
account of this physical circumstance it is impos-
sible to obtain a thoroughly satisfactory under-
standing of deep-sea waves as long as we restrict
our mental view by the limitation of our eyesight,
which generally shows us only one set of waves of
somewhat irregular form running in any particular
direction. Other sets of waves crossing these may
be perceived by the eye, but for the present I am
only concerned with those which run in one
direction.1

The following is a generalised description of
what I actually see when the wind blows upon
water.

1 A curious condition occurs when two deep-sea swells meet
one another from exactly opposite directions. I observed such
a case from R.M.S.P. Atrato on June 27, 1910. We were
bound for Barbados from Southampton, and had passed a
few hours before St. Michael's, in the Azores. All the way
out from the English Channel we had been accompanied by
a north-westerly swell. From the Azores to Barbados the sea
and swell were from a south-easterly and easterly direction.
On the day in question the south-easterly swell met the north-
westerly, both being of only moderate height. The appearance
was that, again and again, a great round-topped billow formed,
which did not travel, but (a furrow appearing along its
summit) quickly became double-crested, the two crests then
travelling away in opposite directions.

AND OTHER WATER WAVES 103

First comes the simultaneous creation of a
uniform pattern of minute waves all over the sur-
face, then the growth of the waves to leeward,
so that after a time there is a certain size of wave
corresponding to the distance from the windward
shore, which size is not afterwards exceeded. The
growth of these larger waves at any place is accom-
panied by the failure and partial obliteration of
the shorter waves which were there before, and
this is due to the circumstance that the growth in
height of the shorter waves is hampered by the
vortex or eddy of the air caused by the larger
series of waves. At each position there is finally
a definite length of wave which is the dominant
wave for that locality for the actual force of wind
—i.e., the class of wave which so dominates the
eye that any shorter wave there appears as a mere
ripple upon its surface and any longer wave is only
to be detected by the presence of a sort of heaving
motion which runs through the whole system of
the dominant waves. On small sheets of water, or
near the windward shore at sea, this swell is insig-
nificant, but as the length of fetch of the wind
increases it becomes an important part of the whole
disturbance. This fact is most easily understood
if we consider what happens when the wind ceases
and the waves are left to themselves. Travel over

104 WAVES OF THE SEA

a considerable distance analyses the originally com-
plex, irregular waves into series of simple, regular
waves of graduated length. The longer and
swifter are in front, the shorter and slower are
in the rear. But this is not all, for the shorter com-
ponents flatten out very quickly as they travel,
whereas the longer components preserve their
height with but little diminution for long distances.
Consider now the effect of this upon the surface-
water at a place far distant from the windward
shore. The short -length (and therefore short-
period) waves will reach this place so flattened
that they will produce no appreciable effect, and
may, therefore, be regarded as not reaching it at
all, and the water will heave with a long-period
undulation, the surface exhibiting therefore only
long, swift waves. Now, this gravitational travel,
with its accompanying analysis of the wave -com-
ponents, must go on in just the same way when
the wind is blowing as it does after storms. There-
fore at a considerable distance from the windward
shore the state attained by the sea during a storm
does not depend only upon what the wind does
there, but also upon the transmission by gravity,
independently of the wind, of the longer -period
components of the irregular waves which the storm
has created to windward. The greater the length

AND OTHER WATER WAVES 105

of fetch the greater is the distance from which
the surface-water draws the reinforcement of its
long-period heaving, and the greater, therefore,
is that part of the wave disturbance which is of
greater wave-length than the dominant wave.

What, now, precisely is this dominant or storm-
wave, and how is it evolved? The answer is not
difficult if we think of the mode of motion of the
wind as it blows over the wave -water. There
must be a continual give and take between the
wind and the water, such that the air above tends
to go into a regular series of travelling vortices or
eddies, with long -extended horizontal axes, rolling
along in the hollows between the crests of a regular
series of travelling water-ridges. Above this series
of travelling eddies the air must flow in undulating
lines, the amplitude of the undulations diminishing
with the height above the water -surf ace, so that
at a considerable altitude the air flows in straight
lines. When the sea has attained to an approxi-
mately steady wave condition under the action of
the wind, there is superposed upon it a train of
wind-eddies (and above them, aerial undulations),
which are of regularly increasing size for a long
distance from the windward shore. At each suc-
cessive position as we recede from the windward
shore there is a characteristic, and successively

106 WAVES OF THE SEA

larger, size of dominant or storm-wave, and this
is the wave of length identical with that of the
air-eddy. These air-eddies, as has been already
said, hamper the development of shorter waves
whose full growth would require the existence of
shorter air -eddies ; but they have little effect upon
the longer and flatter swell, which possesses great
energy, stirs the water to considerable depths, and
is continually reinforced by gravitational transmis-
sion from great distances.1 Thus it seems that in
the attempt to extract precise and even numerical
results for the visual observation of waves at sea,
we may neglect that part of the wave disturbance
which is of shorter wave-length than the domi-
nant or storm-waves ("the waves" of common
parlance), but that we must not ignore the swell,
which is of greater wave -length.2

1 I suspect the existence of another mechanism contributing
to the same result. Referring once more to the swell running
by gravity — suppose this to have attained a regular gradation
of wave-length. Then each section will presumably be opaque
to and absorb vibrations of its own period and transmit or
be transparent to vibrations of greater period.

2 The theory of the action of wind to increase the height of
waves already running before it is that the horizontal velocity
of the air being greatest at the crest, the downward pressure of
the atmosphere is least there. Conversely at the trough, where
horizontal velocity is least, downward pressure is greatest.
Hence the trough is pushed farther down and the crest is
sucked up.

CHAPTER IV

The velocity of the wind at sea — The numerical relation
between velocity of wind and average height of waves —
The relation between the velocity of the wind and the
velocity of the waves — The connection between the rate of
progress of cyclones and the character of the waves — The
effect of squalls and gusts upon waves — On wave-fronts
in a veering wind, and on the irregularity of the waves in
the region of the Trade winds — The observed profile of
waves at sea — The mountainous appearance of waves.

The Velocity of the Wind at Sea

IN order to arrive at an opinion upon the rela-
tion between the velocity of the wind and the size
and speed of the waves of the sea, we have to rely
mainly upon the conventional numbers entered by
the navigating officer in the ship's log, by which
he expresses the force of the wind as he judges it
to be. The watch on the bridge being of four
hours' duration, the number generally represents
the average force of the wind throughout this time.
The connection between these conventional num-
bers and the velocity of the wind has been deter-
mined by experiments with anemometers. In the

r 107

108 WAVES OF THE SEA

case of the ordinary cup -anemometer the number
of revolutions recorded during " strong breeze,"
" moderate gale," &c., had been compared with
those obtained by whirling the instrument on a
turn-table, by which means a counter air-current
of known velocity is produced. The earlier experi-
ments indicated that the number of revolutions of
the standard cup -anemometer must be multiplied
by three to give the velocity of the wind in statute
miles per hour. More complete experiments,
however, have shown that this " reduction factor "
was much too high, and the factor, or multiplier,
now adopted by meteorologists is 2.2. Hence the
velocities of wind found in records of some years
back are greatly in excess of the values now
adopted. Wherever the actual logged number ex-
pressing the sailor's estimate of the force of the
wind can be obtained, it is, however, easy to calcu-
late anew the velocity of the wind in statute miles
per hour, and this has been done in the present
book. Thus the velocities of wind quoted by me
as observed by Lieutenant Paris are not those
stated by him in metres per second, but those
recalculated from his logged numbers. The follow-
ing table is taken from a paper l by Mr. R. H.

1 Q.y.R.M.S., Jan., 1897, vol. xxii., No. 101, pp. 24-55,
discussion on pp. 56-61.

AND OTHER WATER WAVES 109

Curtis on " An Attempt to Determine the Velocity
Equivalents of Wind Forces Estimated by Beau-
fort's Scale"

The third column gives what is usually called
the velocity of the wind, by which is meant its
average velocity. But the velocity of the wind
varies very rapidly. This is particularly noticeable
when the wind is strong. Every gale is gusty and
affected by squalls, and columns 4 and 5 sho.w
the average range of wind velocity, corresponding
to each of the numbers or degrees of the Beaufort
scale.

Description.

Beaufort's
Number.

Average Velocity
of Wind in Statute
Miles per Hour
or "the Velocity"
of the Wind.

Average
Maximum
Velocity of
the Wind.

Average
Minimum
Velocity of
the Wind.

Calm

O

2

O

Light air

I

4

5

3

Light breeze

2

7

9

5

Gentle breeze ...

3

10

J3

7

Moderate breeze

4

14

18

10

Fresh breeze ...

5

*9

25

J4

Strong breeze ...

6

25

33

18

Moderate gale ...

7

31

41

22

Fresh gale

8

37

47

27

Strong gale

9

44

58

31

Whole gale

10

53

73

36

Storm

ii

64

83

45

Hurricane

12

77

?

?

110 WAVES OF THE SEA

The Numerical Relation between Velocity of Wind
and Average Height of Waves

The heights of waves discussed in detail in pre-
ceding chapters are those produced when the wind
has had opportunity to develop them fully, and most
attention was given to the size of the maximum
waves then produced. Circumstances frequently
prevent the waves from attaining the full size which
the velocity of the wind is capable of producing1,
of which fact examples were noted in my voyage
on the Ivernia (p. 53). The numerical relation
between the velocities of wind and average height
of wave, obtained from the records of daily obser-
vations on long cruises, depends in part on
cases where the velocity of wind has no physical
relation to the height of the waves. Such averages,
therefore, blur the truths, which the writer, as a
student of physical geography, desires to eluci-
date. There is, however, a practical point of view
from which these averages may be useful — that,
viz., of the naval architect. As the ships which
he designs may have to sail on any seas and to
encounter all weathers, it is sometimes desirable
to eliminate local conditions.

The tables given in my paper in the Geogra-
phical Journal, May, 1904, show how closely con-

AND OTHER WATER WAVES 111

cordant are the results from the data of Desbois,
of Paris, and of Antoine, when recalculated by
the modern reduction -factor of wind velocity. On
an average the velocity of the wind in statute miles
per hour was found to be 2.05 times the height of
the wave in feet. Thus the average height of
the waves in a whole gale, Beaufort's force 9,
wind velocity 44 s.m.p.h., is :

44 -r- 2-05 = 21-5 feet.

As already explained, this average would be
exceeded when the wind had full opportunity to
do its work.

The Relation between the Velocity of the Wind
and the Velocity of the Waves

The greatest average length of storm -waves on
any one day recorded in the preceding pages is
that observed by Lieutenant Paris, viz., 771 feet,
which corresponds to a wave velocity of 43 statute
miles per hour. The average velocity of the wind,
as re-calculated from the conventional number in
Paris 's table, was 46 statute miles per hour. The
gale had lasted (or the ship, running before the
wind, had been in it ) for four days, or, say,
100 hours. During the first day of the gale the
wave-length was only 371 feet, corresponding to

112 WAVES OF THE SEA

a speed of 30 statute miles per hour. Thus, during
the first day the air blew over the travelling wave-
crests at 16 statute miles per hour, and during
the last day at 3 miles per hour.

During the storm in the Southern Indian Ocean
(described on p. 73) Captain David, of the
S.S. Corinthic, estimated the average length of
the waves at about 675 feet, which corresponds
to a wave velocity of 40 statute miles per hour.
The wind was logged as 9 on Beaufort's scale, so
that its average velocity must be taken as
44 statute miles per hour. The air, therefore,
blew over the ridges of the travelling waves at
an average speed of 4 statute miles per hour.

During the storm in the North Atlantic (de-
scribed on p. 42) the wind was recorded by
Scoresby on March 5th as a " hard gale," which
I take to be the same as a " strong gale," number 9
on Beaufort's scale, corresponding to an average
velocity of 44 statute miles per hour. Now, the
average length of the waves measured by Scoresby
on March 6th was 560 feet, corresponding to an
average velocity of 38 statute miles per hour. The
ship, which was running before the wind, had
then been exposed to the gale for about 40 hours,
but the force of the gale had by this time some-
what abated. When the gale was at its height

AND OTHER WATER WAVES 113

the wind was therefore 6 s.m.p.h. swifter than
the waves at their swiftest.

In the Mediterranean and other semi -enclosed
seas, even where the water is deep, the length
and speed of the waves are much less. Conse-
quently the effective velocity of the wind, which
maintains the eddy on the lee of the travelling
ridges, is much greater.

In all the above cases, which are typical, the
velocity of the storm -wave is a few miles per hour
less than the velocity of the wind as averaged
over a period of from 4 to 100 hours.

The period of the swells which break upon our
shores after storms shows that they travel when
in deep water at much greater speeds than do the
highest waves of storms. Thus the calculated
speed of the unbroken series of 139 waves which
I observed at Branksome Chine on December 29,

1898, was 66.5 statute miles per hour, and that
of twelve successive waves observed on February i ,

1899, was ?8 -5 statute miles per hour. Other
observations recorded at the same locality, of which
particulars have already been given, show that
velocities of between 68 and 78 statute miles per
hour are normal, though not frequent, for break-
ing swells coming to our shores from the west after
storms in the Atlantic.

114 WAVES OF THE SEA

Many considerations crowd in upon the mind
when we endeavour to reason upon the physical
connection between the swells of this speed #,nd
the pressure of the wind during the storm. How
far, for instance, can we regard the longest of these
subsequent swells as having had an independent
existence during the storm? Eor the present, at
all events, I shall set aside such refinements, and
simply consider the numerical speed-relation of
the swiftest observed swells to the swiftest observed
winds in the same part of the world, and see where
this will lead us.

The storms in the North Atlantic during De-
cember, 1898, and January and February, 1899,
were of such exceptional violence that the Meteoro-
logical Council made them the subject of a special
inquiry, which has beene mbodied in a valuable
report,1 commenced by Lieut. C. W. Baillie, R.N.,
and completed by Commander Campbell Hep-
worth, R.N.R. The charts show that between
December 25th and 29th very strong westerly
winds prevailed between the Newfoundland Banks
and the entrance to the English Channel. In the
notes to these charts it is recorded that the velocity
of the wind at Alnwick Castle, Northumberland,

1 Charts illustrating the weather of the North Atlantic Ocean
in the winter of 1898-9 (Meteorological Council, 1901).

Hwi^ * v

\ v'S-'-rr-rrX^'^

ski

LOCAL NOON
301" JANUARY, 1899.

WEATHER IN THE NORTH ATLANTIC.
(From a report of the Meteorological Council, 1901.)

AND OTHER WATER WAVES 117

attained 77 statute miles per hour at 10 p.m. on
the 27th, and 7 i statute miles per hour at 2 a.m. on
the 28th. Beaufort's 11-12 (i.e., 64-77 statute
miles per hour) was recorded at sea in N. 49°, W.
35°, on 28th, and N. 52°, W. 19°, on 29th. Thus it
is proved that the winds that blew had at times
an average velocity 10 statute miles per hour
greater than that of the swell observed at Brank-
some Chine on December 29th. I am not able,
however, to derive the observed swell from the
hurricane arrows shown on the charts for noon
December 28th and 29th, for they are too far
off for the swell, if travelling with the group
velocity of 34 statute miles per hour, to reach
Branksome Chine at the observed time. A feature
of the chart for the 29th which is worth noticing is
the existence of W. and SW. winds of Beaufort's
9-10 (44-53 statute miles per hour) near the
entrance to the English Channel. In the moderate
depths of the Channel the speed of the swell must
have been so reduced I that the observed velocity
of wind on the morning of the 29th was sufficient to
exert pressure upon the swells. This may account
for their reaching Branksome Chine with a height
unusually great for this locality, and much greater

1 The maximum speed of a wave in 20 fathoms is about 43
statute miles per hour.

118 WAVES OF THE SEA

than the height of the swells observed on
February ist.

The charts throw a clearer light upon the swell
observed at Branksome Chine on February ist.
This had a period of 22.5 seconds, and therefore
a speed in deep water of 78.5 statute miles per
hour. A group of these swells travelling freely
for a long distance under the action of gravity
advances at 39.25 statute miles per hour. Now,
the charts for the days January 29th to Febru-
ary ist show Beaufort's 11-12 (64-77 statute miles
per hour) only on January 3Oth, and the positions
of the arrows showing force 9-10 on 3 ist and ist
are too distant to affect the water at Branksome
Chine on ist. The cyclonic system of Janu-
ary 3oth half-way between North America and
England is a very deep isolated depression, with
wind of force 11-12 in N. 45°, W. 41°, the direc-
tion of this wind being a little S. of W. This
wind, and that a little in advance of the black
arrow, would send a swell almost directly to the
entrance of the English Channel. The distance
of the straight run from N. 45°, W. 41°, to Cape
La Hogue (which I shall take as the distance to
Branksome Chine) is 28°, 1,680 geographical
miles, 1,960 statute miles. The difference of time
between local noon January 3oth in W. 41° and

AND OTHER WATER WAVES 119

3 p.m. February ist at Branksome Chine (about
W. 2°) is about 48 hours. The westerly swell at
N. 45°, W. 41°, if starting at noon on January 3Oth,
would reach Branksome Chine at the required time
if it travelled at the speed of 1,960 -~ 48 = 40.8
statute miles per hour. Now the observed group-
velocity of the swells recorded at Branksome Chine
on February ist was 39.25 statute miles per hour.
There is, therefore, strong ground for regarding
that swell as being the result of the storm which
occurred two days before at a distance of nearly
2,000 statute miles.

From Mr. F. J. Brodie's paper » on " The
Prevalence of Gales on the Coasts of the British
Isles during the Years 1871-1900 " we learn that
in the great storm of December 22, 1894, the
wind had a velocity of not less than 53 statute
miles per hour for 14 hours (as observed, of course,
at a fixed station), 64 statute miles per hour for
9 hours, and 76 statute miles per hour for 2 hours.
On January 12, 1899, 53 statute miles per hour
was maintained for 6 hours and 70-76 for i hour.
The velocities attained in gusts are recorded in
another paper.2 In January, 1899, a rate of 90
statute miles per hour was recorded at Southport

* Q.y.R.M.S., 1902.

2 Symonds, Met. Mag., May, 1900.

120 WAVES OF THE SEA

in one gust and between 80 and 90 in several
others. The highest recorded velocity in any gust
was that registered by a Dines' pressure tube
anemometer at the Rousdon Observatory, South
Devon, viz., 101 statute miles per hour. The
results may also be expressed in this way, viz.,
that, at a fixed station, a wind velocity of above
70 miles per hour has been maintained for as
long as 2 hours, but velocities of from 80
to 100 s.m.p.h. have only been maintained for
minutes or seconds.

The greatest period of any short group of swells
which I have observed is 22.5 seconds, with a
speed, therefore, of 78.5 statute miles per hour.
M. Bertin ' says that 24 seconds (speed 84 statute
miles per hour) is certainly beyond all observed
periods in European waters. The greatest speed
which I have observed in a group of many swells
was 66.5 s.m.p.h. on December 29, 1898. The
greatest recorded average velocities of wind in that
weather were 77 and 71 s.m.p.h. on 27th and
28th of the same month.

The greatest speed which I have recorded for
a group of a few swells is 78.5 s.m.p.h. on
February i, 1899. The greatest speed of wind

1 " Experimental Study of Waves," Inst. of Naval Architects,
1873.

AND OTHER WATER WAVES 121

in gusts during that weather was frequently
80 s.m.p.h., ranging up to 90 s.m.p.h. in one
case. This was in January.

As far as the evidence goes in this difficult part
of our subject, the indication is that the maximum
average velocity of wind maintained for i hour
is a few s.m.p.h. greater than the average maxi-
mum velocity of any long group of swells
originating therefrom and forming breakers upon
the shores of England. It is conceivable that
shorter groups of greater speed may owe their
origin to gusts, but during lulls these would be
running against a current of air. The maximum
recorded wind velocity in gusts in 1898-99 was
n| m.p.h. greater than that of the swiftest of
the short groups of swells.

On the Connection between the Rate of Progress
of Cyclones and the Character of the Waves

Strong winds in the North Atlantic are developed
in that part of an area of low atmospheric pressure
where the barometric gradient is steep. These
atmospheric depressions are very frequently of the
form and nature known as cyclones, of which the
general character is that shown in the accompany-
ing diagram.

122

WAVES OF THE SEA

The oval indicates the area covered by the
depression, the long arrow the direction of
advance, the short arrows the direction of wind
in certain parts of the cyclone. In the position
marked A the direction of the wind is contrary
to the direction of advance of the cyclone. Hence
in this quadrant the cyclone is continually re-
ceding from the waves which its wind creates, and

A CYCLONIC SYSTEM.

along the line of advance of this part we should
not expect that there would be any great develop-
ment of waves, even if the winds there were strong,
which they are usually not. Obviously, for a given
velocity of wind, the position most favourable to the
development of waves is that where the direction
of the wind coincides with the direction of advance
of the cyclone. This is where the direction of

AND OTHER WATER WAVES 123

the wind is shown by the arrow B. Here,
moreover, at about 4-ioths the distance from
centre to edge, the strongest winds are usually
developed. The line of advance of B will, there-
fore, be the line along which the greatest wave-
development will occur. There is not any constant
relation between the rate of advance of a cyclone
and the velocity of the winds locally developed
within its area. Considering only the critical posi-
tion B in the cyclone, the rate of advance of the
cyclone is, from our present point of view, simply
the rate of advance of the locus of the force which
is there creating the waves ; we have to do, in
fact, with waves created by a travelling disturbance .
Let us consider groups of simple harmonic waves
of different lengths, and therefore different speeds,
to be already formed and to be travelling together
(and therefore superimposed upon one another)
as forced waves pressed upon by the wind. This
wind, however, in a progressive cyclone is a
" travelling disturbance," and while it will, to some
extent, increase all the waves beneath it which it
can press upon at all, the waves which move slower
than the travelling disturbance are being left behind
all the time. On the other hand, all waves whose
velocity is greater than that of the travelling dis-
turbance run ahead of it, and are no longer subject

.
124 WAVES OF THE SEA

to the reinforcing action of the wind. The waves
whose speed is identical with that of the travelling
disturbance will be continually subject to the re-
inforcing action of the wind during the whole life-
time of the cyclone. I think, therefore, that the
wave-length of the principal, or dominant, or
storm -wave generated in Atlantic storms should
depend, not only upon the velocity of the wind,
but also upon the rate of advance of the cyclone.
It is, I believe, a matter of common remark that
in some storms a short, steep sea is soon formed
and in others a longer sea.

The general rate of advance of Atlantic storms
towards our shores has been investigated,1 and the
figures are worth examining in connection with our
subject. Storms advancing from points between
WSW. and WNW. to ENE. and ESE. travel at
an average speed of 28.9 statute miles per hour.
Of the 264 storms examined, only 60 travelled at
more than 35 statute miles per hour, and of these
only 10 travelled at more than 52^ statute miles
per hour.

It appears, therefore, taking the average of a
large number of storms coming from the Atlantic,
that waves travelling about 30 statute miles per

1 Q.J.RM.S., 1902, loc. oil

AND OTHER WATER WAVES 125

hour1 (length 371 feet) should enjoy special
opportunities for development in depressions where
the wind exceeds that velocity.

We see, therefore, that waves of 68-78 statute
miles per hour, which are the greatest speeds I
have recorded for swells after Atlantic storms,
would in almost all cases outrun them, even when
the depression advances along a straight path.
The reason that such waves are not developed to
greater heights is, therefore, not only that the wind
is, during most of the time, not strong enough,
but also that the cyclones advance too slowly.

The above method of theoretical treatment is
of only occasional application on account of the
fact that there are generally several neighbouring
cyclonic systems on the North Atlantic and that
the actual winds are a compromise between them.
Fortunately, the charts for December 27, 28, and
29, 1898, enable us to examine an instance of
this commoner condition. A series of cyclonic
systems were following one another across the
North Atlantic from S. of W. to N. of E., and
strong westerly winds prevailed during the whole
of these three days between N. 50°, W. 40°, and

1 This is a wave of a little more than 8 seconds period. The
8-seconds wave has a speed of about 28 statute miles per hour
and a length of 328 feet.

8

126 WAVES OF THE SEA

the entrance to the English Channel. The unusual
force of Beaufort's 11-12 was at local noon on
December 28th recorded in the neighbourhood of
N. 50°, W. 37°, and not elsewhere, and on local
noon December 2 9th in the neighbourhood of
N. 49°, W. 19°, and not elsewhere. As the storm
does not appear to have abated meanwhile, we may
infer that the locus of the hurricane wind progressed
continuously along this path of 840 statute miles
in the course of these 23 hours. This is at the
rate of 36.5 statute miles per hour. The average
wind velocity for 11-12 is 70.5 statute miles per
hour. Waves travelling at nearly this speed would
be running on ahead all the time. The waves
which would be all the time from noon Decem-
ber 28th to December 29th subject to the maxi-
mum force of wind would be those with a speed
of 36.5 statute miles per hour, and, therefore, with
a length of about 558 feet. As they would
be subject to an effective wind velocity of
70.5 — 36.5 = 34 statute miles per hour, there
would be a great deal of spraying from their
crests.

Two hours at a fixed station is the greatest time
recorded above for wind with an average velocity
of more than 70 statute miles per hour. If the
locus of that wind force were advancing at 36.5

AND OTHER WATER WAVES 127

statute miles per hour, as in the above case, the
length of fetch, or stretch of water, at any one
time subject to this wind would be 73 statute miles,
in which there would be a train of only 200 of
the 1,918 foot -waves.

It may in this connection be noted that in a
gust lasting i minute, and in which the locus pf
application is advancing at the same rate (36.5
statute miles per hour), the length of fetch would
be only about half a mile — i.e., less than two pf
the above wave-lengths. The absence of breakers
with speeds nearly as great as the maximum wind
speed of gusts may, therefore, be properly attri-
buted as much to their insufficient length of fetch
as to insufficient time of action.

The charts for February 2 and 3, 1899, in the
publication of the Meteorological Council to which
I have so often referred, afford an excellent
example of a long -continued hurricane -force of
wind which was stationary in position for 24 hours.
After examining these two maps, I made the
following note, viz :

" Maps for Eebruary 2nd and 3rd show
hurricane -force (centre about N. 45°, W. 45°),
with no appreciable length of fetch indicated,
occupying almost the same considerable frontage
for 24 hours. In this area must have been a

128 WAVES OF THE SEA

very wild sea with the waves spraying very much,
from which must have emerged a very long swell."

After making this memorandum I referred to
the notes on page 6 of the publication, and found :

" On February 2nd . . . the Quernmore, in
N. 41°, W. 46°, reported that during the storm
the atmosphere was so heavily charged with
spoondrift as to appear as a heavy snowstorm."

My reason for diagnosing an exceptional amount
of spraying was that the locus of the hurricane -
force did not advance, so that the wind would
not have been able to develop the longer waves.

The Effect of Squalls and Gusts upon Waves

On December 22, 1906, I was on board the
Leyland S.S. Jamaican, bound for Puerto Colombia
from Liverpool, in N. Lat. 38° 21', W.
Long. 35° 43. There was a heavy sea and a
moderate gale. At 4 p.m. a violent squall of
wind, with rain, occurred, lasting about 4 minutes,
which was accompanied by very big waves, and
succeeded by comparatively calm water. I guessed
the largest waves during the squall to be 7 feet
higher than those which preceded or followed.

On the following day, December 23rd, we were
in N. Lat. 35° 47^', W. Long. 39° 4$', with a

AND OTHER WATER WAVES 129

strong breeze verging on a moderate gale — i.e.,
a wind velocity of about 28 statute miles per hour.
At 3 p.m. there occurred a squall lasting 3 minutes,
which converted a moderate to a large sea. I esti-
mated that the height of the waves increased ,at
least 2 feet per minute, finally attaining rather
more than 20 feet. Not only did the waves
increase in height, but the crests lengthened out
transversely, so that the waves ran in longer and
more regular ridges. The squall came from the
starboard and abaft. Two minutes after it had
passed us we were among waves no larger than
before, but I could see a group of about four
great ridges travelling away with the squall. The
length of the waves, as judged by their appearance
in relation to the ship's length, was never more
than 200 feet. As has been already explained,
this estimate is generally less than the measure-
ments obtained by following the waves in their
course .

In another squall, occurring at 5.2 p.m. and
lasting 5 minutes, the height of the waves was
perceptibly increased.

Next day, December 24th, we were in
N. Lat. 33° 3$', W. Long. 43° 58'. The princi-
pal " waves " were mounds of water, produced by
the crossing of two sets of waves. At 3.30 p.m.

130 WAVES OF THE SEA

the wind began to fall, and at 4 p.m. the sea was
slight, except for the occasional formation of a
larger mound of water. At 4.55 p.m. a black
being very dense and apparently rainy. The part,
head. It reached from the horizon on one side
of us to the horizon on the other side, the two ends
being very dense and apparently rainy. The part
of the cloud directly overhead was thin, and dis-
charged only a few small drops of rain. The
passage overhead of this central part was accom-
panied by only a slight additional breath of wind,
but iwith it came a big swell, comprising 1 2 or
more large waves, and the ship, previously steady,
began to roll heavily. In 5 minutes the cloud had
passed, and in another i o minutes the sea had quite
returned to its former state.

These observations relate to squalls occurring
towards the end of stormy weather, coming upon a
fairly large swell running in the same general
direction as the wind. They show that (according
to my guesses of height) a sudden increase of wind
can restore the height of waves at the rate of i or
2 feet per minute. They illustrate the fact that,
when the system of travelling ridges is already
formed, the wind, falling into eddies between them,
has greater power to raise the crests and depress
the troughs, a power of swift and immediate action

AND OTHER WATER WAVES 131

which contrasts strongly with the slight power of
the wind when blowing upon smooth water. My
observations from the S.S. Jamaican relate, as I
have said, to the action of squalls at the tail end
of a storm.

Their action during the height of a storm is
often to lower the waves. Thus, during my
voyage from Liverpool to Boston on the Cunard
S.S. Ivernia, December, 1900, of which some par-
ticulars have already been given, I often saw the
effect (which others have frequently described) of
showers of spray from every wave -crest during each
gust. The steepness and the slowness of the waves
were such that the cohesion of the water at the
crests could not resist any increase of the upward
suction and the horizontal pressure there. Hence
in the gusts the water was torn in showers of
spray from the crests, falling finally, one must
presume, mainly in the sheltered troughs, thus
tending to flatten out the sea.

On March 1 1, 1901, on the Red Star S.S. Vater-
land, east-bound from New York to Southampton, I
saw the much greater lowering effect of a wind meet-
ing the waves. We were in N. Lat. 44° $6'*
W. Long. 36° 54', with a rough sea from the star-
board, the waves occasionally rising above the
horizon of our promenade deck. At about 4 p.m.

132 WAVES OF THE SEA

the wind quite suddenly chopped round and blew
from the opposite direction, meeting the waves in
their advance. The ridges of the waves, as usual,
were not uniform, but had, on the contrary, an
undulating outline. The wind caught the higher
portions, and bit huge pieces out of them which
momentarily formed a milk-white cloud, which in
its turn was quickly dissipated in spray.

On Wave -fronts in a Veering Wind, and on the
Irregularity of the Waves in the Region of
the Trade Winds

Wind is never really steady. Not only is it
always more or less gusty, but it is always veer-*
ing — i.e., changing its direction. Apart altogether
from the progressive variation in the general direc-
tion of the wind which is characteristic of a
cyclonic system, there is a rapid veering about a
mean position, even in the Trades. The amount
of this veering is sufficient to exercise an important
effect upon the character of the waves and the
appearance they present.

It results in the formation of waves running
simultaneously in slightly different directions, and
thus, even in the regions of the Trade winds, the
open sea does not present a series of parallel ridges,

AND OTHER WATER WAVES 133

each one of uniform height, with a lateral extension
many times greater than the distance from crest to
crest.

In 1907 I made the following observations on
the want of regularity of waves created by the Trade
winds. On January 8th, en route from Colon to
Kingston, Jamaica, in a strong NE. Trade wind,
I estimated the height of the principal waves at
15 feet. Their apparent length was about 200
feet. I noted at the time that this strong breeze
had continued, to my knowledge, for eight days,
and that for some days past there had been no
increase either in the size of the waves or in their
regularity, indicating, therefore, not only that the
maximum size is soon attained (as M. Bertin l has
pointed out), but also that there is no continuous
approximation towards regularity. The captain of
the vessel (S.S. Jamaican) stated that on such a
day as this the wind would not vary more than
one point of the compass in the course of a four-
hour watch, and this is reckoned a very steady
wind. But one point of the compass is 1 1 J degrees
of arc, which is a very appreciable angle. If one
watches the arrow of a sensitive weathercock in a
strong breeze, in our own country, it will be seen

1 Memoir on the " Experimental Study of Waves," Inst. of
Naval Architects, 1873.

134 WAVES OF THE SEA

that it never remains stationary for more than one
or two seconds, but is continually shifting through
a large angle.

Another cause can also be divined for the unlevel
tops of the wave -ridges and their small lateral ex-
tension. This cause is a greater force of wind to
right or left of the ship's course. Suppose, in the
first place, that the ship is in a calm, and that to the
starboard and in front there is a head wind blowing.
Then a swell will spread out laterally from that
area, meeting the ship obliquely on the starboard
quarter. Secondly, if a lighter head wind be blow-
ing where the ship is, the wind-waves will be crossed
obliquely by this swell from the starboard, even
though the wind there be blowing in the same
direction as that where the ship is. The velocity
of the wind being less where the ship is, it will
not be able to regularise the obliquely-running,
swifter swell.

The wind -formed waves which run in the most
regular ridges (i.e., of the greatest lateral exten-
sion as compared to their wave length) are of two
orders of magnitude. First, the small waves of a
few feet in length and not more than one foot
high; second, the large ocean waves. The regu-
larity of the first is not affected by long-period
veering of the wind, for they die out completely in

AND OTHER WATER WAVES 135

the interval and fresh sets are formed. The regu-
larity of the second is not visibly affected by short-
period veering, being too massive. Waves of
intermediate size are affected by both kinds of
veering and several crossing sets are formed.

The Observed Profile of Waves at Sea

Both during a wind and in the case of a swell
travelling calmly in deep water, the trochoid repre-
sents the apparent form of the wave much more
nearly than the curve of sines, for it is easy to
observe that the convex part of the wave has a
steeper curve than the concave part, the crest being
narrower than the trough. But, except in the case
of a somewhat flat swell, the greater steepness of
the front face of the wave is obvious to the
eye, and most markedly so when the wind is
blowing. Now, Sir G. G. Stokes found * that
waves of permanent type in deep water, what-
ever be the order of approximation to which the
calculation is pushed, must be symmetrical with
respect to vertical planes passing through their
ridges. I conclude, therefore, that steep waves at
sea are never waves of permanent type. Again,

1 " Math, and Phys. Papers," vol. i., p. 193, from Trans.
Camb. Phil. Soc., vol. viii., p. 441.

136 WAVES OF THE SEA

both Stokes and von Helmholtz showed that for
a single series of waves of permanent type the
condition under which greatest steepness could be
attained was that the speed of wind and wave should
be equal.

Now, according to observation, the steepest
wind-waves in deep water are formed where the
speed remains small relatively to that of the wind—
e.g., in lakes and small seas. Also in the Trades,
where the wind is perpetual, there is no sign or
symptom of an approach to the " highest wave "
of Helmholtz and Stokes. I conclude, therefore,
that observation indicates that under natural con-
ditions of wind there is no tendency to progressive
approximation towards the state of one set of waves
of permanent type.

In this connection, I note that Professor Horace
Lamb, who has investigated water-waves as a
mathematician, writes l that " the possible form of
waves of permanent type ... is very interesting
mathematically . . . but no reason has been
given, so far as I know, why free water-waves
should tend to assume a form consistent with per-
manence."

1 Presidential Address, Section A, British Association, Cam-
bridge Meeting, 1904.

AND OTHER WATER WAVES 137

On the Mountainous Appearance of Waves

The phrase " waves mountains high " has long
given offence to literary landsmen, who quote
measurements to show that waves are not even as
high as hills. I have never met a seaman who
either supposed or pretended that waves were as
high as mountains, but there are conditions when
waves look like mountains, or, at any rate, like
large hills.

This happens when the majority of the crests rise
well above the line of sight, especially if the atmo-
sphere be rather thick, so that minute detail is
obliterated. Four or five ridges, with the inter-
vening three or four troughs, then fill all the space
between the eye and the horizon. Being mounted
on a deck, there is a feeling or impression that the
horizon is at the distance which it would have on
land with such an eye -elevation. This would mean
a mile or more from ridge to ridge, which is ten
times the actual distance ; and the apparent height
is consequently increased in the same ratio, making
a wave of 40 feet look as high as a hill of 400.

I have seen, and recorded,1 a case where absence

1 Geographical Journal, Jan., 1900, "On Desert Sand-dunes
Bordering the Nile Delta."

138 WAVES OF THE SEA

of surface detail produced a somewhat similar illu-
sion of great size among desert sand-dunes. Par-
ticularly when under a low sun they produced as
great an impression of size as mountains thousands
of feet high — i.e., of ten times their real height.

NOTE TO PAGE 60.

In storms of exceptional duration as well as of more than
ordinary severity, such as are not encountered every year,
the waves are somewhat higher. Thus in February, 1910, the
R.M.S.P. Oruba, between Southampton and Barbados, en-
countered waves which, from the account given me by
Captain C. P. Langmaid, appear to have attained 45 feet.
In March, 1904, Captain J. G. K. Cheret, on another of the
R.M.S.P. steamers, encountered between Southampton and the
Azores exceptional weather, of which he has given me an
account. When he was on the bridge the waves frequently
obscured the horizon at times when the ship was on an even
keel, from which it appears that they surpassed 45 and may
have attained 50 feet.

PART II

ON THE ACTION OF SEA WAVES TO
TRANSPORT SHINGLE, SAND, AND MUD

CHAPTER V

On the depth to which wave-agitation extends, and on the
transport of fine mud — The action of waves to drive
shingle shorewards — The effect of percolation to promote
the building-up of beaches — The movement of sand by
waves — The undertow.

On the Depth to which W<ave Agitation Extends,
and on the Transport of Fine Mud

WHEN the surface of the deep sea is in waves, the
agitation extends to some depth. Eor our notion
of what goes on below the surface we have to
depend mainly upon theory, observations being
almost wholly wanting. According to theory, if
there be one set of regular trochoidal waves
running, the repeated motion of any particle of
surface-water is a vertical circle.

In the upper half of the circle the motion of
the particle is forwards — i.e., in the direction of
advance of the wave. In the lower half it is back-
,wards. Thus the return flow of the wave-water
in a travelling wave is not a precise reversal pf

9 141

142 WAVES OF THE SEA

the onward flow, for it takes place at a lower
level.

Below the surface trochoid are jsub-surface
trochoids, in which the diameter of the circle which
the particles of water describe diminishes with
increasing depth.

The diameter of the circle and the velocity of
the oscillating currents diminish in geometrical
progression as the depth increases in arithmetical
progression, the diameters being halved for an
additional depth of i-9th wave-length below the
mid-level of the surface wave. Thus, at a depth
equal to one wave-length, the diameter of the circle,
and the velocity of the moving particle of water,
is i -5 1 2th of that at the surface. Thus, in the
case of a wave with a length of 600 feet and a
height from trough to crest at the sea's surface of
40 feet, the particles of water at a depth of 600 feet
will revolve in a circle of 40 feet -H 512 =0.94
inch diameter. The period of a 6oo-foot wave is
about 1 1 seconds, and this is the time in which the
particle at a depth of 600 feet would describe
a circle of about I inch diameter.

We have seen that waves of the greatest height
are seldom more than 600 feet long in the North
Atlantic, and it is seldom that very long swells,
being much lower, would give a greater agitation

143

AND OTHER WATER WAVES 145

than this at a depth of 600 feet. The line of 600

feet,

depth

• 100 fathoms, is a very important
in the seas, for it is approximately that to which
the edges of the continents are submerged. From
this line the sea bottom descends abruptly to the
vast depths of the great plains where the soundings
are reckoned in thousands of fathoms.

At such depths the agitation caused by wind-
waves must be absolutely insensible, but within
depths of 100 fathoms, i.e., on the continental plat-
form, continual slight oscillations of 10-20 seconds
period, and even as little as i-inch amplitude, must
exert an effect in hindering the deposition of the
finest kinds of mud. Mud, or dust, when so finely
divided that it settles through air or through water
with indefinite slowness, only comes to rest where
the fluid is free from agitation, unless some agency
—e.g., chemical or electrical— precipitates the par-
ticles. Every student has noticed that it is not
the exposed papers which he is handling frequently
on his desk which become dusty, but those put
away — e.g., on the top of a high bookshelf.

We may say with confidence, as a theoretical
inference, that the agitation of wind-formed waves
affects the bottom of the sea as far as the edge
of the continental platform to such an extent as
(in co-operation with tidal and other currents) to

146 WAVES OF THE SEA

keep very fine mud moving about until it has an
opportunity of subsiding over the edge of the conti-
nental shelf— in the absence, that is to say, of
chemical or other coagulation of the fine particles
into clots or lumps.

The Action of Waves to Drive Shingle Shorewards

It is matter of common experience that the stones
brought on to the sea -shore (e.g., by the wasting
of gravel cliffs or by the wash of stone -carry ing
torrents), though swept along the coast and thus
distributed, are to a great extent rejected by the
sea and piled up in a bank, so that some of the
stones are only reached again by the largest waves
at the times of high water of the greatest tides.
Classifying the detritus brought to the sea -shore
into three sorts, viz., shingle, sand, and mud, we
may say that those parts of the sea bottom which
are subject to wave disturbance afford no abiding
place for either the first or the last.

We have seen how the mud travels on the whole
in a direction contrary to that of the swell, which,
having " felt the bottom," is advancing shore wards.

I now put forward a theory which I think shows
that the oscillations of the bottom water where
agitated by progressive waves has a proper action
of its own to heave forward— /.£., in the direction

i

I

i

150 WAVES OF THE SEA

of the waves' motion — all detritus which they can
wholly or partly lift from the bottom, but cannot
maintain more than momentarily in suspension. I
will first suppose the waves to be symmetrical,
which is the condition least favourable to proving
my case, and I will begin by supposing the bottom
to be horizontal. The vertical currents are as
shown in the first figure ; i.e., an upward current
begins when the trough passes and continues until
the arrival of the crest, after which subsidence
commences and continues until the next trough
arrives.

The horizontal currents are as shown in the
second figure. The shoreward current begins in
the midst of the upward current. The material
which has been raised by the upward current is
caught thereby and heaved shoreward, and the
shoreward current, acting after the commencement
of the down current, continues to drive the material
forward during the first part of its period of sub-
sidence. The backward horizontal current Jhen
sets in when the water has been clarified from
all coarser and rapidly subsiding materials, so that
at its commencement it only finds fine material in
suspension, which it carries backwards. During
the last part of its period of action the backward
horizontal current is accompanied by an upward

AND OTHER WATER WAVES 153

current, and coarser material begins to be carried
backwards ; but this backward movement is more
than neutralised by the succeeding forward current,
which has the advantage of acting upon material
already suspended, or, in the case of large stones,
already loosened from their anchorage.

Next, let us consider the case of waves approach-
ing the breaking condition ; and here I can rely
upon personal observation, particularly upon the
moderately flat, sandy shore between Bournemouth
Pier and Branksome Chine, Dorset. When the
wave is in this stage the front is much steeper
than the back, the upward current (trough to crest)
is short -lasting, but very violent. The reversal of
horizontal current sets in very suddenly, the shore-
ward current attaining its maximum speed very
quickly, while the water is heavily charged with
the coarser sediment. The change from shore-
ward to seaward current and from upward to down-
ward current is, on the other hand, very gradual.
At its commencement the seaward current is also
very gentle, and it only attains great intensity just
in time to have its effects upon the coarser sedi-
ments reversed by the sudden onset of the shore
current which accompanies the advancing: wave-
crest.

When the wave actually breaks upon a bare

154 WAVES OF THE SEA

shore there are two additions to its mode of shore-
ward action upon pebbles. In the first place,
and obviously, the cataract which is discharged
obliquely upon the ground drives pebbles forwards.
In the second place, if we look at what happens
just behind the fallen front, we see that, instead
of subsidence and backward flow, there occur up-
welling and shoreward flow. The reason is evi-
dently that the head of water .in front has been
destroyed, the pressure is now from behind, and
the breaking wave has, in fact, rolled over.

It is evident that this predominantly forward,
or shoreward, action of nearly, and quite, breaking
waves upon pebbles could be neutralised by set-
ting the waves to roll the pebbles up a slope.
There would be a slope of some particular steep-
ness on which gravity would just neutralise the
forward action of the waves.1

Moreover, since the advantage of the forward
action over the backward action so much depends
upon quick subsidence of the particles, it appears
a proper inference that upon a moderate seaward
slope there will be a travel of large material shore-
ward, while material of a somewhat smaller size
will merely oscillate.

1 This is a reason against the construction of steep groynes.

A WAVE BEFORE AND AFTER BREAKING,
155

AND OTHER WATER WAVES 157

The Effect of Percolation to Promote the Building
of Beaches

When I have watched the action of the breakers
upon a natural sloping platform of hard rock, cut
at the foot of a cliff, it has seemed to me that the
stones thrown forward by the breaker roll down
so freely in the backwash that a moderate slope
is sufficient to return to the breaker as many stones
as it rejects.

It is otherwise, however, when the shore is
already covered with a sloping bank of shingle.
The wash from the breaker, rushing up this bank
in virtue of the speed with which it starts, travels
over its surface, filling only the interstices between
the upper layers of stones, and leaving the inter-
stices of the greater part of the bank above the
mean sea level unsaturated and void. When the
wash of the breaker has reached its limit and the
water begins to run downhill, a great part of it
subsides through the interstices of the shingle in-
stead of flowing as a surf ace -current, so that the
latter is weakened in two ways. There is the
diminution of momentum which lessens its power to
roll stones down, and secondly there is the diminu-
tion of depth which results in the larger of these
stones being only partly submerged. They are

158 WAVES OF THE SEA

thus often stranded through loss of buoyancy. This
stranding effect is seen best, however, in the wood,
seaweed, corks, &c., which are left in a marginal
fringe at the furthest reach of the wash from the
waves .

The proper effect of waves, when acting with-
out complicating circumstances, upon a sufficient
supply of shingle is to construct a bank or ridge
upon the top of the beach, the face of which is of
very steep and uniform slope. These banks are
called Fulls, and are a characteristic feature where -
ever shingle beaches extend seawards upon our
shores — e.g., at Dungeness.

The Movement of Sand by Waves

Sand neither remains suspended indefinitely, as
mud, nor drops instantaneously, as shingle, but
settles through water at a moderate rate, which for
the beach sand at Branksome Chine, Dorset, is
about 2 inches per second. Unlike fine mud, which
the wave -water of the sea passes on to the great
depths ; unlike the shingle, which the waves reject
upon the shore ; the tnovement of the sand is very
variable, changing more than that of the mud or
shingle with the varying agitation of the sea. 'My
own observations on seashore sand have been made
on the coasts of England, Scotland, and Wales, but

WAVE BURSTING AGAINST A VERTICAL WALL.

159

AND OTHER WATER WAVES 161

chiefly in the English Channel, and almost daily
during some years on the beach near Branksome
Chine, between Bournemouth and Poole Haven.
They do not apply to lakes or tideless seas.

Usually the floor of our seas is covered with
clean sand, from the lower parts of the beach which
are uncovered daily by the recession of the tide,
to depths as great as enable the bottom to be seen
from a boat. In greater depths the sand dredged
up is less clean and homogeneous. In addition
to this covering of sand upon the floor of the
shallow sea there are here and there great banks of
sand rising nearly to the surface from water of some
depth. Such are the Skerries Bank, east of Start
Point (Devon) and the Shambles Shoal, east of
Portland Bill (Dorset). Also, where shingle is not
too abundant, the whole of the surface of the beach
is often composed of sand (which buries the occa-
sional stones). In such localities one may often
see the breakers piling up a ridge of sand on the
top of the beach in the manner already described
for the shingle Fulls. The water does not, however,
drain out of the sand-ridge so completely between
waves, and the influence of percolation upon accu-
mulation is, therefore, not so great as in the case of
shingle, although it is still a main factor in the accu-
mulation of the ridge at the summit of the beach.

162 WAVES OF THE SEA

From time to time, and generally after
storms of exceptional severity or long duration, or
accompanied by high tides, the clean sand is wholly
removed between the levels of high and low tide,
and much is also removed at even lower levels.
We then see during low tide the eroded rock which
is the real floor of the foreshore. At high tide the
sea, even if calm, then reaches its bounding cliffs,
and we realise that the sandy covering of the fore-
shore, though generally there, is not a permanent
deposit, but only a covering which is stripped off
when the forces of the sea are really set to work.

After the beach has been stripped by storms near
Branksome Chine the slope of the shore has been
much reduced, and in the calm weather succeeding,
especially with an off-shore wind, I have often
watched the sand being brought back and piled up
by the breakers in a sand Full, or ridge, often with
a lagoon behind it at high tide. The waves have
then the shoreward action on the sand which has
already been described in the case of shingle, the
settlement of the sand being, I presume, sufficiently
rapid in the case of these small waves in the pres-
ence of little other agitation — as, e.g., of tidal or
other currents. When the wind is off-shore there is
probably a slight shoreward undertow assisting, as
to which I shall have more to say. Apart from this,

163

AND OTHER WATER WAVES 165

however,, the mere action of a small swell from
the offing appears to bring the sand in here when
the slope of the shore has been reduced almost
to nothing. The shoreward action does not then
cease with the breaker ; for the waves, breaking
far out, produce another kind of wave, the bore,
a wave of permanent form with a precipitous foam-
ing front. There is always a procession of these in
advance of the breaker -line, and they thin them-
selves from less and less to nothing as they advance
to the shore. Sand -ripples over which they pass
(when not wholly obliterated) are no longer sym-
metrical, but face shorewards, and, presumably,
travel shorewards. The action of these waves upon
quickly subsiding material is predominantly shore -
wards, being an exaggeration of that already
described for waves about to break.

After a time of fair weather, a moderately sloping
foreshore and a beach of clean sand is once more
formed here, and equilibrium is re-established for
such weather, the slope being a measure of the
excess of shoreward over seaward action proper
to the waves.

All this process which I have described differs,
however, but little from that already specified for
shingle, and the reader will naturally be more in-
quisitive as to the explanation of the reversal of
this in prolonged rough weather.

166 WAVES OF THE SEA

An important part of the explanation is in the
seaward currents generated during such weather,
with which I shall have to deal presently, and
for the moment I will only specify that part of
the mechanism of removal which is due to the
waves considered as merely oscillating — /.<?., with-
out any resultant current. When the sea is very
rough the agitation of the bottom-water is so
violent that the sand cannot settle. It must be
remembered that wherever there is a swirl of water
with an upward velocity of even as little as
2 inches per second the sand cannot sink. Thus,
as may be readily perceived by the eye, the rough
water becomes turbid with the sand, as if the sand
were so much mud, and the mechanism of shore-
ward transport of quickly subsiding particles no
longer applies. The sand behaves, in fact, more
like mud or dust, and (even if there were no sea-
ward undertow or other seaward currents) it would
tend to shift to deeper water where the bottom
agitation is not too great to allow it to settle.

On the Undertow

At Branksome Chine there is a typical sandy
shore of moderate slope, which is not exposed to
strong tidal currents. The exposure is southerly,
and there is a headland a few miles to the westward.

AND OTHER WATER WAVES 169

Thus in an ordinary cyclonic storm, advancing from
the Atlantic, the principal waves, rounding Old
Harry Rocks to the westward, come in directly
upon the shore with a south-westerly wind more
or less behind them. In the clearingi weather which
generally follows, with north-westerly wind, the
waves generated at a distance continue to advance
upon the shore, but the wind is now against them,
and spray is often torn from the crest of the breaker
and driven seawards. Under these different condi-
tions the position of the breakers is quite different.
In the first case — i.e., with strong on-shore wind —
there is more than one line of breakers, but even
the final line is situated far from the shore, and
between it and the beach there is a somewhat
numerous series of bores, or roll waves.

When, on the other hand, the wind is off-shore,
with a rough sea in the offing, waves do not break
until they come quite close to the beach. The
breakers, moreover, curl over in a well -formed cusp
and occasion a loud report. This noise is ap-
parently due to the escape of the air which has
been momentarily imprisoned when the cusp has
curled over upon the front of the wave. Although
they come so close to the shore before breaking,
their height, reckoned above the antecedent trough,
is sometimes as great as that of the breaking waves

170 WAVES OF THE SEA

during the previous on-shore wind. I found that
when the water was but little above my knees
the crest of the wave about to break close by
was considerably above my head, showing that the
wave remained unbroken when the depth of water
immediately in front was considerably less than
the height of the wave from trough to crest. In
a rough sea with on-shore wind the cusped break-
ing waves were formed much beyond the limit
of a man's depth. These waves not only broke
farther out, but also when the cusp was not per-
fectly formed. The upper part of the crest folded
itself down upon the front face, becoming a mass
of seething water, and the wave then travelled on
as a bore with its head of froth. The motion in
the frothing head was violently shorewards, and
it was impossible to swim in it.

Many measurements have been made by en-
gineers to determine the depth of water in which
waves break. Very roughly the general result may
be expressed by saying that the depth of water
(reckoned from the undisturbed sea-level) is equal
to the height of the crest above the trough. I
shall not pause to discuss the somewhat unsatis-
factory mode of expression, the point I wish to
bring out being that the more those measurements
have multiplied the clearer it has become that the

AND OTHER WATER WAVES 171

ratio is not even approximately constant. It is
quite different, not only for shores of different
slopes, but also for a given shore it is quite dif-
ferent during on-shore and off-shore wind respec-
tively. Thus Colonel D. D. Gaillard, U.S.A.,
found ' that with a given locality and a given slope
a wave broke in a depth of water equal to ij times
its height when there was a strong wind blowing
shorewards, while with an equally strong wind
blowing off-shore the wave remained unbroken
until the depth of the water was only f of its height.

When there was no wind and the breakers were
due solely to the ocean swell the wave broke in
a depth of water equal to the height of the crest
above the trough when the slope was i in 100,
but when the slope was i in 1 2 the wave broke
when the depth was more than twice the wave
height.

The breaking of a wave is, of course, due to the
water near the surface in the crest of the wave
moving much more quickly forward than the water
immediately below it. This condition must be
reached sooner or later when ordinary waves from
the deep sea advance in the continually shallow-
ing water caused by a sloping bottom. On the

1 "Wave Action in Relation to Engineering Structures,"
Washington, 1904, Chapter VII.

10

172 WAVES OF THE SEA

steeply sloping shore of a shingle beach at the
highest level of the tide we can at any time see
that strong rushes of water are poured back in
a shallow sheet to the foot of the breakers. It is
not difficult to understand that the effect on the
bottom water just beyond the breaker of this strong
intermittent current will be to diminish the velocity
of the bottom current under the crests and increase
the seaward velocity of the current under the
troughs.

The more the shoreward bottom current is
checked under the crests, the deeper will be the
water in which the wave will break.

It is well established that wind at sea causes
a current which is strong at the surface, but of
which the intensity decreases rapidly with depth.
Thus, quite apart from any slight translation of
water which may be theoretically deduced for
trochoidal waves, there is a surface drift in a storm
at sea which has the following effect upon the
oscillations of a particle of water at the surface,
viz., at the end of each complete oscillation it has
advanced in the direction of the wave when the
wave is running before the wind. Thus, in an
on-shore gale there is a surface drift, which takes
place in jerks, towards the shore, and this goes on
as long as the gale endures. But the level of the

173

AND OTHER WATER WAVES 175

water does not rise proportionately to the amount
driven shoreward, for a head of water accumulates
which in time prevents a further rise. The surface
drift, indeed, continues, but the undertow is in-
creased, so that the amount of water receding from
the shore is equal to that approaching it. In the
case of a prolonged storm when the wind blows
into a bay and there is a steep beach, it seems
quite possible that the undertow may be so strong
that the bottom current is continuously seaward,
although it would, no doubt, be jerky, the seaward
motion being checked as each wave -crest passes.
These are the conditions under which even shingle
may travel seawards from the foot of the breaker.

If, however, there be no terminating cliff or sea-
wall, so much of the shingle as is only reached
by the extreme wash of the water discharged from
the breaker will, I think, still be driven shoreward,
owing to the effect of percolation.

That off-shore wind produces up-welling of water
against a coast -line has been proved on the large
scale by observations of temperature and salinity,
and it follows that there must then be a sort of
shoreward undertow. Its intensity must be much
less than that of seaward undertow during on-shore
winds, but it doubtless increases the normal shore-
ward action of the waves.

CHAPTER VI

On the actions which determine the 'longshore transport of
beach shingle — On the causes which give rise to an arrange-
ment of pebbles according to their sizes along the Chesil
Beach and certain other beaches — On the production and
maintenance of the Shambles sand-bank near Portland —
The formation of patches of shingle upon a sandy beach by
the action of breakers.

On the Actions which Determine the 'Longshore
Transport of Beach Shingle

WHEN the sea is smooth, the shingle of our beaches
lies undisturbed by the tidal currents. The 'long-
shore drift of beach shingle is therefore ultimately
due to the wash of the breakers, and in order to
judge of the effect of the tidal currents upon 'long-
shore drift, we have to consider how the motion
of this wash -water is affected by them. Where
the shingle beach is on a straight line of coast
where the tidal current runs strongly past the shore
while a fairly heavy surf is breaking, the appear-
ances presented to the spectator on the shore are
deceptive. The breakers discharging at right
angles to the shore are noisy and conspicuous ; the

176

WAVES SHOWN BY DISTORTED REFLECTION OF MASTS (KINGSTON, JAMAICA).

177

AND OTHER WATER WAVES 179

steady current parallel to the shore is silent arid
invisible. Yet all the water of the sea has this
lateral drift, including the wash -water of the
breaker. The motion of the stones which it then
carries is not simply up and down, but a zigzag,
the general direction of which is that of the
current's motion.

Where small beaches are formed on the shores
of torrential rivers, small progressive waves charge
in upon them ; but here the current is more con-
spicuous than the wave, and I have then observed
ripples in coarse sand facing the shore and impelled
by the waves, whilst the coarse sand grains could
be seen to travel much fasterMn the direction of the
current than in that of the wave.

When, at sea, the wind is obliquely on-shore there
is not only a 'longshore current, producing the effect
explained above, but waves also break obliquely.
Their effect to drive shingle along the shore is then
obvious to the eye. On a gently sloping sandy
beach the waves running directly before the wind
cross the swell coming in from the offing. Just at
the breaker -line they combine with the swell and
cause it to break sooner than it otherwise would.
Thus a number of short, oblique breakers are pro-
duced where the crests coincide, and these drive
sand along the shore.

180 WAVES OF THE SEA

On a steeply sloping beach obliquely breaking
waves are even more common and conspicuous.
It is scarcely necessary to insist upon the fact that
longshore drift due to wind will depend upon the
length of fetch of the wind as well as upon its
velocity, since large waves are only produced by
the action of wind upon a long stretch of water.

The effect of the tides to determine the 'long-
shore drift of beach shingle by waves is, on the
other hand, a complex matter, and it is of the
highest importance that the general principles
governing this effect should be definitely laid
down. I will endeavour to do this for our
own coasts.

Twice a day a current flows from the Atlantic
Ocean into our narrow seas, and produces a rise of
water-level there. Wherever the tide runs freely
the currents follow the same rule as the forward
and backward currents of the ordinary wind -waves
of the sea, viz., when above the mean sea-level
they are forward ; when below mean sea -level,
they are backward.

Thus, wherever the tide runs freely along a coast
—e.g., on a straight shore or past a headland —
the current is what we may call up -channel during
the whole time that the water is above mean sea-
level. This means eastwards for the English

AND OTHER WATER WAVES 183

Channel. Now, wherever there is much shingle
it accumulates mostly near the highest level reached
by the wash from the breakers . In such situations,
therefore, most of the shingle is out of reach of
breakers during the outflowing current of the tide.
Moreover, 'for the same roughness in the offing,
the breakers are very much smaller when the water
is below mean sea -level, on account of the gentler
slope of this part of the beach. Thus it is evident
that for straight coast and for headlands the effect
of the tides (apart altogether from the wind-currents
and from oblique waves) is to cause the waves to
transport shingle predominantly in the direction of
the inflowing current, or up-channel. The pre-
dominance should be most marked in the case of
the larger shingle. This predominance is inde-
pendent of any excess of speed of the inflow
current. Where the tide is impeded, the course
of affairs is somewhat different. Thus, at the head
of a bay or inlet, or where, at a nodal point, tidal
currents from opposite directions have met, a
" head " of water accumulates which stems the in-
flowing tidal current and causes the outflow to com-
mence sooner than it otherwise would. The
extreme case is that in which the outflow com-
mences immediately the highest level is reached.
In this case it is possible for the average water-

184 WAVES OF THE SEA

level during the outflowing current to be the same
as that during the inflowing current, so that the
resulting 'longshore transport by waves running
dead on shore may be nil, their effect during out-
flowing tide being equal and contrary to that during
inflowing tide. Leaving out of account for the
present the exceptional and rare positions where
tidal nodes occur, we see from the above that the
combined action of tides and onshore waves is to
sweep shingle rapidly up-channel from all salient
positions. In bays, the transport will be, on the
whole, up-channel, but much more slowly, on
account of the inflow and outflow currents of the
tide occurring at more nearly equal levels. Thus,
removal of shingle from headlands and accumula-
tion in bays would still be general even if there
were no co-operating causes, such as oblique waves
and stronger currents.

Dr. Owens and Mr. Case, in their valuable book
on " Coast Erosion and Foreshore Protection," have
already called attention to the importance of the
relation between the times of commencement of
flood and ebb currents and the times of high and
low water in connection with the littoral drift, and
have cited the case of Southwold, Suffolk, where
the upper part of the foreshore is only exposed
to the flood current. I have worked out as above

183

AND OTHER WATER WAVES 187

the general law governing the application of their
valuable suggestion.

In the case of our south coasts the general
direction of the inflowing tidal current coincides
with that of the greatest length of fetch and the
strongest winds. Hence the effect of the above
principle has been to a great extent overlooked
there. Similarly,, on our east coast the direction
of the inflowing current is the same as the direction
of the greatest length of fetch.

There is, however, one part of our coast which
appears particularly suited to demonstrate the im-
portance of the principle of high-level inflow as
contrasted with low -level outflow of tide as a con-
trolling factor in the longshore transport of shingle.
This is the coast of Cumberland, as to which the
following evidence was given to the Coast Erosion
Commission,1 viz., that the current of the inflowing
tide is from north to south, the prevailing wind
from the south-west, and the travel of beach
material from north to south as far as Morecambe
Bay. Even if the bare statement that the pre-
vailing wind is south-west should need some quali-
fication, there is no question that the prevailing
westerly winds, combined with the greater length
of fetch to south-west, would produce the largest
waves from that quarter.

' By Mr. G.iA. Abernethy, M.I.C.E.

188 WAVES OF THE SEA

Here, therefore, we have a case in which the
circumstances appear to show the operation of the
high level of the inflowing tidal current to be pre-
dominant against the other factors of 'longshore
transport .

With regard to the velocities attained by the
tidal currents on our coasts, I am not aware that
it is possible to declare that those during the in-
flowing tidal current are, on the whole, either
greater or less than those of the outflowing tide,
although it would probably not be difficult to cite
local cases on both sides.

There remains a peculiarity of the inflowing tidal
current, or part of it, which presumably assists in
the transport of shingle. This has been pointed
out by Mr. iW. H. Wheeler, who says that the
flood tide comes along in wavelets of its own
making, whereas the waters of the ebb tide are
essentially calm.

I have on one or two occasions noticed the
effect in a narrow channel and on tidal rivers
during the inflowing current. I do not know if it
lasts during the whole period of the inflowing
current, or if it only continues while the level of
the water is rising. I do not think we have proofs
as yet that the amount of transport due to this
cause is considerable.

AND OTHER WATER WAVES 189

On the Causes which give rise to an Arrangement
of Pebbles according to their Size along the
Chesil Beach and certain other Beaches

When considering on and off-shore action of
waves, we have seen that a sorting of materials
takes place. It is assisted by the seaward slope
of the shore. In the arrangement of pebbles along
a shore there is no such gravitational assistance
in sorting, except such as is given after the arrange-
ment is effected — e.g., by the greater steepness of
a coarser beach. The origin of a longitudinal
arrangement of pebbles on a tidal shore is there-
fore to be sought in the longshore action of the
wash from the breakers during all the phases of
the tide.

The effect of the action of the waves to determine
the size of the shingle is, of course, best studied
upon those parts of the shore where the beach is
not supplied with new stones by wastage of cliffs
at the back of the beach, or by a torrent entering
the sea. In beaches replenished by 'longshore drift
the replenishing material consists mainly of stones
not easily broken into smaller fragments. The
approximate permanence of such a beach, as a
whole, is apt to mislead the observer into sup-
posing the rate of 'longshore travel of individual

190 WAVES OF THE SEA

stones to be much less than it really is. Mr.
Nelson B. Richardson and I arranged an experi-
ment upon the rate of travel of materials of which
he has given a full account.1

On the beach opposite Fleet Coastguard Station,,
in a slight breeze from NNW., with breakers 2 feet
high, and a current running eastwards at I foot
per second, a brickbat, or half -brick, travelled 56
yards in 2,\ hours. Supposing this wind to remain
constant, the shingle would not travel westwards
even when the current is running to the west.
Therefore, allowing six hours out of every twelve
for the east -running current, which is less than
what it is, the brickbat would then travel from
Bridport Harbour to Chesilton (18 miles) in 108
days. Given strong wind from the westwards,
the time of transit would be very much less.
Another brickbat travelled 574 yards to the east-
ward in 28 hours, which would make the time of
travelling the 18 miles 142 days during fine
weather. A stone, 4 inches long, which was caught
by a wave, appeared to move more quickly than
either of the brickbats ; but even if the stones
were moved somewhat more slowly than the brick -

1 " An Experiment on the Movements of a Load of Brickbats
deposited on the Chesil Beach," by Nelson B. Richardson, B.A.
(Proceedings of the Dorset Field Club, vol. xxiii., 1902).

192 WAVES OF THE SEA

bats, yet the observation of the latter shows that
with the ordinarily prevailing westerly winds a stone
may travel from Bridport Harbour to Chesilton
in a time to be reckoned in days, weeks, or months,
and not in decades or centuries. When dealing
with the arrangement by sizes of worn beach
pebbles, we should therefore seek an explanation
in the rapid shifting of the material and not
in its relatively slow attrition. Thus I found the
average weight of a pebble at Chesilton to be
12.8 oz., and at Burton Bradstock, 16 miles away,
.028 oz. — i.e., 457 times smaller. Prestwich ex-
plained this difference of size on the supposition
that the pebbles travelled from Chesilton towards
Burton (and Bridport), and in transit were
reduced from the size seen at the former to that
seen at the latter place. Apart from the circum-
stance that all the known agencies are to make
the principal travel in the opposite direction, let
us see what his supposition would involve. It is
useful to consider it because of its possible mis-
application to other causes where it may be less
easy to disprove. In the first place, it would mean
an extraordinarily short life for a pebble. In the
second place, it would involve the presence all
along the beach of an enormous proportion of sharp
shingle -chips. My own observations lead me to

AND OTHER WATER WAVES 193

think that the reduction in the size of pebbles is
accomplished mainly by fracture. Although the
principal pebble has its fractured surface rapidly
smoothed and rounded, the sharpness of the chips
tells the true tale. It is the same with wind-borne
sands — the larger grains are the best rounded. If
comminution really proceeded mainly by rubbing
down, it would be the smaller particles which would
be the best rounded.

I was fortunately able to observe on the Chesil
Beach, in July, 1897, a part of the wave action by
which the sorting of shingle is accomplished. I
was on the beach opposite Chickerell when there
was a light easterly wind, and the small breakers
made by it were depleting the steep face of the
beach. A glance at the map shows that wind from
the east has a small length of fetch, and that the
waves it makes cannot be very large anywhere
on the beach, and, near Chesilton, must always be
very small. The tide was falling at the time of
my observation, and the shingle in the band of
wet stones exposed above the waves was coarser
than that out of their reach. It was evident that
the backwash was removing the smaller pebbles
and drifting them westwards, leaving the larger in
their place.

The secret of the gradation of shingle upon
beaches sheltered at one end from large waves

194

WAVES OF THE SEA

is that whilst both large and small pebbles travel
in the one direction before the big waves which
come with great length of fetch, only the small
pebbles are driven back by the small waves which
come from the small length of fetch.

I took samples of the shingle all the way along
the Chesil Beach in July, 1897 (see plate), and the
following table shows their weights :

Locality.

Miles
from
Bridport
Harbour.

Av. Weight
of a Pebble
inoz.

Reference to
Photograph of Portions
of the Samples

Cliff End, Burton Bradstock

2

•028

Group of stones
on left.

Opposite Coastguard Station,
Puncknowll

Opposite west end of the
Fleet

5
8

•067
'III

Second from
left.

Third from left.

Opposite Coastguard Station,
Langton Herring

ii

•294

Fourth from left.

Opposite Coastguard Station,
Chickerell

13

•342

Fifth from left.

Opposite " Passage "

16

783

Sixth from left.

200 yards west of the Chisel-
ton end of the beach

18

12 '8OO

4

Last on right.

As we go eastward for the first 16 miles, the
weight of the pebbles is doubled every 2 miles,

•••P&t & I

SHORE BETWEEN EAST END OF CHESIL BEACH AND BLACKNOR POINT.

STONES ON THE BEACH NEAR CHESILTON AND THE GRADA-
TION OF STONES FROM BURTON BRADSTOCK TO
CHESILTON.

195

AND OTHER WATER WAVES 197

but in the last 2 miles it is doubled every
J-mile.

Most of the beach is, in fact, composed of small
shingle, but close under the eastern shelter of Port-
land Bill the shingle is large. At the Chesilton
end the beach receives new material from the steep
shore of Portland. It mostly consists of large stones
of the Portland stone, which is derived partly from
the waste of the steep shore but not a little largely
from the foot of the tips of the stone from the great
quarries on the summit. It is the larger frag-
ments chiefly which reach the foot of the tips.
A glance at the map shows that large waves can
travel towards Chesilton, not only from the direc-
tion of Bridport Harbour, but from the direction
of Portland Bill. I found many very large pebbles
of Portland stone on the beach at and near Chesil-
ton, which must have been driven there from the
coast of the promontory by these large waves.
But an examination of length of fetch on the map
shows at once that there can be no large waves to
drive these great pebbles far along the beach to
the westward. At Chesilton, or Chesil Cove, the
direction of the shore changes through nearly a
right angle. The corner is open directly to the
south-west. The Cove is a focus towards which
large breakers can and do come in winds from

11

198 WAVES OF THE SEA

north-west to, say, south-by-west, and it is a pocket
into which, if a large pebble be driven, it cannot
escape in either direction.

Finally, we must not omit to notice the co-
operation of the tides with the eastward drift along
this beach. High water on days of full and new
moon occurs at about 5^ hours at the Bill of Port-
land. But there is a strong outsetting current from
the West Bay for 9 hours out of every 12, viz.,
from 2 hours to 1 1 hours on the days of full and
new moon. This comprises all the time when the
water is above mean sea-level. Thus, even such
waves as do run westward along the beach
( especially near Chesilton ) either have the tidal
current against them or else are only beating
against the lower part of the beach, where much
of the shingle is out of their reach.

Before leaving the interesting subject of the
arrangement of beach shingle, I will give some
particulars of my observations between Lyme and
Bridport Harbour. Looking at the map, and at
a map of the South Coast of England, we see that
Lyme Bay is the largest bay on that coast, and
that the sudden change in direction of the coast
so as to face the south-west occurs, not at Brid-
port Harbour, but at Charmouth. It occurred to
me, therefore, that Bridport Harbour was not the

AND OTHER WATER WAVES 199

proper place from which to commence the study
of the great accumulation of shingle, and I decided
to supplement my observations by a visit to the
shore between Lyme and Bridport Harbour. I went
in a boat, rowing close under the shore, and landing
from time to time. I found that the accumulation
of beach material began at Charmouth. From
thence to Golden Cap the size of the shingle
and the height of the beach increase. Golden Cap
is only slightly a promontory at high water, but
there is a considerable ledge projecting above low-
water mark, so that on the whole its effect as a
groyne is considerable. Eastward of Golden Cap
there is a curved beach as far as the promontory
of Thorncombe Beacon, which again is prolonged
by a ledge of rocks above low -water mark. On
this piece of coast we see again the increase of
height of beach and size of shingle in the angle
under the west side of the promontory. Close
under the east side of the promontory the sea
reached the cliffs at high water,1 but at low water
there was exposed a firm bed of particles of the
size of very coarse sand. This bed of material

1 The same effect is seen on the lee side of groynes which
have been built up to the highest reach of the waves, and
erosion results. The groyne should be low enough to allow
shingle to be washed freely over its shoreward end so that the
foreshore on the lee side may be kept covered and protected.

200 WAVES OF THE SEA

consisted of sharp angular fragments with cutting
edges, as different in shape from the sand -grains
of a sandy shore as from the large rounded pebbles
on the west side of the promontory. The con-
clusion is obvious that they were the chips from
the attrition of the large pebbles on the west side,
which are banged against each other by the
breakers at high tide. If the current be then
running eastwards, as the general information on
the chart indicates, there would be a strong under-
tow from this position with a horizontal circula-
tion of water on the east of the promontory. Here,
except in easterly winds (which are not prevalent
during most of the year), the water is smooth and
the chips deposit. A true beach, where the sea
does not usually reach the land at high tide, begins
again at Eype mouth with very small shingle.
There is no natural promontory between here and
Portland, but the solid western pier of Bridport
Harbour has 14 feet of water against it at high
water of spring tides, and projects nearly to low-
water mark. Close to the western side of this
artificial promontory the shingle becomes much
larger, whilst on the east side of the harbour it
is again quite small. This is the situation usually
reckoned as the beginning of Chesil Beach, and
from here to Chesilton the shingle gets coarser

f

SAND BROUGHT BACK AFTER A STORM AND SAND DRIFTED ALONGSHORE.

201

AND OTHER WATER WAVES 203

and the height of the beach greater. The increase
in the size of the shingle, however, is for most of the
way a very gradual process, becoming rapid only
when near the shelter of the Portland promontory.

Thus I found that wherever there was shelter
from the east there was a pocket filled by. a high
beach composed of large shingle. The arrange-
ment is therefore due to the normal sorting action
by the waves, in which the local tides happen to
assist .

I have shown why the large stones collect at
Chesilton, but I must add a word on the probable
mode of removal from the steep shore in that
agitated corner, of the large quantity of small
angular fragments which are mixed up with the
boulders between the end of the true Chesil Beach
and Blacknor Point. There is little trace of them on
the beach at Chesilton, and the bottom off there is a
good holding anchorage of clay. A strong under-
tow setting towards Portland is a matter of local
knowledge, and Captain King's " Pilot's Handbook
for the English Channel " furnishes detailed in-
formation on the subject of the outsetting current.
It runs for 9 hours out of every 12 (so long does
it take to relieve by a narrow stream the water from
the broad bay which has piled up in the Chesilton
corner), and closely skirts the rocky shore, gradu-

204 WAVES OF THE SEA

ally increasing in strength as it approaches the
Bill, where it has acquired such velocity as to
extend far beyond that point before it turns to
the east. This tide out of the west bay acquires
its greatest velocity when the tidal stream in this
part of the English Channel is running to the east-
ward. While, therefore, the large shingle is driven
to the focus of the waves at Chesilton, the smallest
shingle, the sand, and chips are presumably re-
moved by the undertow. What becomes of some
of the material so removed is suggested in the
section relating to the Shambles Shoal.

Marked gradation in size of shingle is a charac-
teristic of beaches sheltered at one end by a
natural or artificial groyne. I have not heard of
conspicuous cases of such gradation on long
beaches with a nearly uniform exposure — such,
e.g., as that at Aldeburgh in Suffolk. This being so,
my explanation of the grading as due to one-sided
shelter would probably have found readier accept-
ance but for the attractions of a previous sugges-
tion by Sir John Coode. He noticed that a large
pebble isolated on a surface of small shingle was
rolled about by the wash of the waves even when
this travelled over the interlocked smaller pebbles
without disturbing them. He said that large stones
would travel quickly along the Chesil Beach from

AND OTHER WATER WAVES 205

the westwards until they reached a bed of pebbles
of the large size, when they interlock and cease
to travel readily ; and this, in his opinion, ex-
plained the accumulation of large stones at
Chesilton. The observation, as far as a horizontal
current of shallow water is concerned, is correct.
It is a mode of motion readily seen in fine weather,
and with water of a depth of i or 2 inches. It
is a mistake to suppose that what is then seen
is a measure of the relative mobility of large and
small shingle in really rough weather, and nearer
the position where the wave breaks. Here, with
a depth of many inches, or a foot or two, and
with strong upward swirls, it is less easy to see
the motion of individual stones, but there is no
doubt that the smaller, loosened from their inter-
locking and lightened by the upward current, are
driven about much more freely than the large
stones. It is under such circumstances that most
pf the movement of shingle takes place.

What, however, I particularly wish to point out
about Sir John Coode's theory of the Chesil Beach
is riot so much the partial truth of the observa-
tion as the logical error of supposing it to be an
explanation of the origin of the observed grading.

The logical error is this, that in order that the
stones shall travel in the required manner we have

206 WAVES OF THE SEA

to suppose the stones already arranged according
to size along the beach. In other words, the results
of the process must be already appreciable before
it can commence to operate.

The most that can be claimed, therefore, would
be that the process tends to preserve an arrange-
ment already achieved by other means, and the
considerations already advanced as to the action
of upward currents in stormy weather show that
even for this purpose the process is probably much
less effective than observation in fine weather would
lead one to suppose.

On the Production and Maintenance of the
Shambles Sand-bank near Portland

The great heap of sand called " the Shambles "
is similar in shape and situation to the banner
cloud which is formed in the eddy, of air on the
lee side of an Alpine peak. The Bill of Portland,
projecting outwards into the currents of the
English Channel, corresponds to the mountain peak
projecting .upwards into the currents of the air.
If the promontory of Portland were removed, the
Shambles sand-bank would be washed away. If,
on the other hand, the sand -bank were removed
by dredging, the promontory of Portland remain-

AND OTHER WATER WAVES 207

ing, I think it is very probable that a sand-bank
would re-form in the same position.

When a small vessel is taken through the
race on Portland Ledge during somewhat rough
weather the decks are covered with sand deposited

'iofrj I// ij 14 16 TS

uWEST BA'lf

Geographical Miles

CHART SHOWING THE SHAMBLES SHOAL.

from the water which splashes over her. I have
already shown that it is probable that the 9 -hour
outset from the West Bay removes shingle chips
and sand from the Chesil Beach and the Portland
cliffs, and I suppose the Shambles shoal to be

208 WAVES OF THE SEA

maintained by this and other detritus settling from
suspension in the repeated horizontal circulation
of water eddying round a vertical axis on the east
side of Portland.

The course of the currents is as follows : ' The
outset from the West Bay from 2 hours to 1 1 hours
on the days of full and new moon, having assumed
its eastern course, rushes with great violence over
Portland Ledge. High water at the Bill occurs at
about 5^ hours F:. and C. (i.e., on the days of
full and new moon). At 6 hours 20 minutes this
stream is met at right angles a short distance east
of the ledge by a strong stream from East Portland
Bay. This stream lasts for 9^ hours. " These
united streams press on towards the Shambles,
which they cross about east by north, running
3f knots."

The bank, which is composed of coarse ,sand
and gravel, rises suddenly on the south from the
depth of 10 fathoms. The approach on the north
is more gradual. The streams run across the shoal
at 3 to 4 knots during spring tides, and waves
break heavily upon it. The surface is strongly
rippled, and the ridges are in motion even in
fine weather. The shoal does not persist, there-

1 See " The Pilot's Handbook for the English Channel," by
Commander J. W. King, R.N., twelfth edition, 1893.

L fr.

RELATION OF THE VERTICAL AND HORIZONTAL COMPONENTS OF THE TIDE
NEAR PORTLAND.

210 WAVES OF THE SEA

fore, on account of its enjoying shelter from dis-
turbance. I suppose its maintenance to be due
to horizontal circulation caused by meeting of two
currents at right angles, this repetition of
path giving time for the somewhat slow rate of
subsidence of sand to take effect. High water at
the Bill occurs in the middle of the 9 hours' outset
from the West Bay, and less than an hour after-
wards occurs the meeting at right angles with the
outset on the east side of the Bill. Thus the pre-
sumed rotation is set up at the time of greatest
wave action on the Chesil Beach, when the outset
from the West Bay must be most heavily charged
with sediment.

The outset from the East Bay of Portland pre-
sumably contributes sediment to the Shambles
when the main tidal current is setting to the east-
ward. The tidal current sets westward at the
Shambles at about 1 1 hours F. and C. — i.e., about
the time of low water and at the time of cessa-
tion of the outset from West Bay. The outset
from the East Bay is then running, and continues
to do so for another 5 hours — i.e., until 4 hours
F. and C. That no shoal corresponding to the
Shambles is formed by the west-flowing current
on the west side of Portland Bill is to be ascribed
largely to the lower water-level and consequent
lesser wave action on the shores.

AND OTHER WATER WAVES 211

In this connection the position of the Skerries
Bank, north-east of Start Point, should be com-
pared with that of the Shambles. Portland Bill
terminates, on the eastern side, the largest bay
on our south coast. Start Point similarly termi-
nates the second largest bay. On the up-channel
side of each is a sand-bank, which, from its situa-
tion, and from the absence of a corresponding bank
on the west of the promontory, suggests rather
the continuous current of a river than the alter-
nating currents of the tides. Of all the causes
which produce this curious arrangement the rela-
tion of the time of turn of the tidal stream to
the turn of the tidal level is, perhaps, the most
important and the most likely to escape notice.

The accompanying diagrams show the relation
between the times of the vertical and horizontal
oscillations of the tide at Portland Bill.

The Formation of Patches of Shingle upon a Sandy
Beach by the Action of Breakers

The surface of the bearfi at Branksome Chine
is usually pure sand, but many stones derived from
the wasting of the gravelly cliffs are buried beneath
it. Under certain conditions the wash of the
breakers begins to convert the sandy to a shingly

212 WAVES OF THE SEA

beach, and the action often proceeds as far as
the formation of isolated patches of shingle.

The occasion upon which I saw the process pro-
ceeding best was during a heavy swell succeeding
a storm, when the wash of the breakers carried
the sand away in suspension. The shingle remain-
ing behind became concentrated in the manner illus-
trated by the photographs. The plate facing p. 214,
from a photograph, taken on a later occasion, and
about 4 miles farther east, shows more distinctly the
characteristic wedge -shape of the isolated patches
of shingle. If the process were to continue, these
patches would coalesce into a single ridge of
shingle. This sorting action of the waves is at
once taken advantage of by builders or others re-
quiring shingle, carts being sent to remove it before
the smaller waves and offshore winds have again
smothered it with sand.

SHINGLE SORTED FROM SAND BY THE WASH OF A HEAVY SWELL
(BRANKSOME CHINE, NEAR BOURNEMOUTH).

213

215

Yi

w •

ss?

=
si

PS

o

217

PART III

ON STATIONARY AND PROGRESSIVE
WAVES IN RIVERS

CHAPTER VII

The flood-wave of rivers — The roll-wave in the Tees — In the
Ure — In the Nikko torrent — On the advance of a flood over
dry ground.

On the Flood-waves of Rivers

A PROGRESSIVE wave is not an obvious phenome-
non in ordinary river floods ; nevertheless, a
careful consideration of the matter shows that
wave -transmission is an important factor in the
disposal of the flood-water of a river. Let us take
the case of a river receiving an accession of
water from a suddenly swollen tributary. The
threatened congestion of water is avoided by
wave-transmission down the main stream. The
length of the wedge of newly added water is suffi-
cient to originate a " long " wave, and the wave-
velocity down -stream is therefore the greatest that
is compatible with the depth, viz., the velocity
which a body would acquire if falling in vacuo,
under the action of gravity, through a height equal
to one-half the depth of the stream. If the calcu-

12 «

222 WAVES OF THE SEA

lated velocity of a " long " wave in different depths
of water be compared with the observed velocities
of current in large rivers, it will be seen at once
that the wave -velocities are many times greater
than the velocities of the currents. Thus the flood-
water obtains room for itself, not so much by rush-
ing forward as by causing the waters for a long
way in front to lift or swell slightly. The trans-
mission of pressure through the current is so rapid
that there is (except under special circumstances,
to be described later) no visible wave, but the river
lower down is found to be rising long before the
arrival of the floating and suspended matter which
accompanies the arrival of the actual waters of
the flooded tributary. The speed at which this
wave -transmission of the flood progresses down the
channel is equal to :

Velocity of current plus velocity of " long " wave.

In the case, however, of a shrunken river flowing
through alluvial soil the rate of advance of the
" first rise " of water after a drought may be much
diminished by the absorption of water by the
porous ground over which the river has to spread.

When a river increases in depth in its
lower reaches, the wave -velocity increases, and
the amplitude of the wave is thereby dimin-

AND OTHER WATER WAVES 223

ished, and the increasing width of the river
further diminishes the amplitude of the wave.
Thus the very perfection of the mechanism of
wave-transmission down-stream in rivers usually
prevents the accumulation of a wave -face suffi-
ciently steep to be visible. The rise of a river
before the arrival of the actual flood-water which
originates the rise is, moreover, less obviously
wavelike in character than the rise of level in a
river due to the tide, for in the former the rise is
accompanied by increased velocity, just as it would
be if the river were running at a steady, but higher,
level. In the case of the first rise of a river due
to tide, however, there is a slackening of the
current .

We see, therefore, that causes commonly co-
operate to mask the progressive waves due to floods
in non -tidal rivers.

In the upper reaches of certain rivers, however,
the sudden arrival of a wall of water, travelling
down -channel at a great speed, is a normal occur-
rence after heavy rain in the hills where the river
and its tributaries take their rise. Thus, on the
River Tees, during one summer and autumn the
roll-wave, as it is called, was seen on no less than
six occasions by Mr. F. R. Glyn, E.R.G.S. The
following description of the phenomenon is taken

224 WAVES OF THE SEA

from a letter written by Mr. Glyn to the author,
January 14, 1902 :

' This river [ the Tees ] has its source at the
foot of Crossfell, in Westmorland, and with a con-
siderable watershed is fed by mountain streams
and a number of tributaries between Middleton
and Crossfell, running through the extensive moors
in that district.

" One of the peculiar characteristics of this river
is the roll -wave, 2 feet or 3 feet high, which sud-
denly, and sometimes quite unexpectedly, comes
down the river, filling from bank to bank the
stream, which but a minute previously had,
perhaps, been at low summer level. Many lives
have in consequence been lost, while I personally
experienced a most unpleasant sensation some
years ago. I happened to be fishing for salmon
from a dry rock in the centre of the river, some
few miles below Barnard Castle, when I suddenly
heard a rushing noise, as if the wind had suddenly
risen and caused the branches of the trees to rustle .
I looked up the river and saw the roll-wave almost
upon me . Before I could get to land it had washed
me several yards down, and but for a side stream
that, fortunately, brought me to land, I should not
have been able to record the facts. As it was,
I lost my salmon -rod, cap, &c., but was most
thankful for such a providential escape.

AND OTHER WATER WAVES 225

"It is at all times a naturally rapid river,
winding its way over large masses of rock and
boulder, and the most accomplished swimmer
would have but little chance of saving himself.

" In the neighbourhood of Barnard Castle, a
few miles below that town, we generally allow seven
hours for the river to come down after rain in
one's locality ; and such calculations are very near
the mark, but, of course, occasionally after heavy
thunderstorms above Middleton and otherwise the
wave descends without any warning whatever to
anglers and others in the lower districts. As there
is sometimes an entire absence of rain locally, these
sudden and sometimes unexpected spates make the
Tees in summertime dangerous even to the most
experienced."

The Ure is somewhat similar in general character
to the Tees. At Aysgarth it is well known to
lovers of the picturesque on account of the beau-
tiful Fall, or " Force." The pavement -like rock
bed of the river outcrops horizontally, and the depth
of the river is fairly uniform in cross -section,
although longitudinally it consists of pools and
shallows. The Tees also, where I have seen it
near Barnard Castle, was of uniform depth (cross-
wise), owing to the nature of its bed of hard
and homogeneous rock. I may note in passing

226 WAVES OF THE SEA

that uniformity of depth across the stream is im-
portant for the preservation of a roll-wave. In
a channel with deep longitudinal grooves and
shallow shores such waves would change their
direction and discharge laterally upon the shelving
banks .

I have received the following account of the roll-
wave at Aysgarth from a resident at that place :

" The Aysgarth local name for a flood was
1 spate ' or ' freshet/ I was one evening in the
middle of the river, about 100 yards below .the
lower Force, fishing, when I heard a roar above,
and presently a wall of water some 2 feet or 3 feet
high came dashing over the fall. I, fortunately,
gained the bank in time to see it rush past me,
filling the bed, rushing madly over the boulder
rocks, and spoiling my fishing. The rocks here
are limestone, with great fissures and pot-holes.
Below the Force is the great salmon-hole, the limit
of the up-rushing fish.

" Above the lower Force the stream runs in
reaches over shelving limestones from the second
Force. At the foot of this there is a very deep
hole. . . . Succeeding this Force the water comes
beneath the picturesque bridge from the beautiful
upper Force, a succession of ledges, forming holes
beneath."

AND OTHER WATER WAVES 227

The arrangement of a river in alternating pools
and shallows is a condition theoretically favourable
to the formation of such roll-waves as are de-
scribed by these observers. The wave -velocity
diminishing greatly where the bottom rises at the
lower end of the pool, this section at first receives
far more than it can pass on, so that the wave
face, instead of being of infinitesimal gradient,
becomes quite steep — a " wall " of water in
appearance.

On entering a pool the wave may perhaps lose
this form, commonly called a bore, and become
a group of rounded swells, but on entering
shallow water this will close up, and the front of the
disturbance will be either a cusped wave, like a
wave about to break upon the shore, or a solid
wedge of foaming water — the bore proper — like
those beautiful foaming ridges which come in upon
a flat sandy shore when the great waves of a storm
are breaking far out at sea.

Roll -waves are also reported as occurring in the
Rhondda and the TafT Rivers in Wales. They
are frequent in the rivers among the foothills of
the Himalayas. They are also recorded from time
to time as the result of an exceptional and solitary
cause of flood in various parts of the world. Thus,
during the great typhoon in the autumn of 1902

228 WAVES OF THE SEA

a landslide from Mount Nantaisan in Japan caused
a sudden efflux of water from Lake Chusenzi, which,
combined presumably with the torrential rain,
caused a wall of water many feet high to travel
down the Nikko River, doing great damage to the
celebrated Thousand Statues of Buddha on the
right bank. Its speed was certainly very great,
judging from the account which I received from
the Japanese custodian of a tea-house on the right
bank, which was at once swept away. The man
himself had only just time to scramble up the
hillside, although the situation allowed him a clear
view for a considerable distance up-stream. The
high-water mark of the flood was still visible on
the hillside when I visited the locality a year after-
wards.

In the account which Sir Samuel Baker gives
of the coming down of the waters of the Atbara
(vide " The Nile Tributaries "), the bed of the river
appears to have been dry except for entirely
isolated pools of large extent. The occurrence
was at night, and no details are given of the ap-
pearance of the actual front of the flood as it
advanced over the dry bed. The advance of the
floodhead in such a case is not a simple case of
wave -travel to which a definite speed is allotted
in the theory of long waves, dependent upon the

AND OTHER WATER WAVES 229

depth of water, for there is no water in front of
the advancing wedge. The rate of encroachment
would, in the above case, be somewhat reduced
by the porosity of the soil over which the flood
advanced.

Colonel Gaillard, U.S.A., informs me that he once
saw the wave -front of a flood advancing along
the dry bed of a canyon in Arizona. He estimated
the depth of water at the crest of the wave at
25 feet and the horizontal distance from the ad-
vanced foot of the wave to this crest at about
300 feet. This space presented a series of frothy
ridges. Perhaps these were a series of roll-waves
over -riding one another. The mechanism can be
imagined from that described later for the roll-
waves of the Griinnbach conduit, where the larger
waves, i.e., those which have deepest water at their
crests, continually overtake the smaller ones.

CHAPTER VIII

Tidal bores — Wave-length of the Severn bore — On the want of
concordance between height of tide and height of bore,
and on the conditions which determine the starting-point
of the bore.

On Tidal Bores

THE time during which the tide flows in a river
is less than that during which it ebbs, for during the
flood tide the river quickly gathers an opposing
" head " of water (both on account of the slope
of its bed and of the diminution of its breadth)
which reverses the tidal flow, so to speak, before
its time. Conversely, the form of the channel
as .well as the momentum of the land water, or
true river water, prolong the seaward flow of the
ebbing tide. If the conditions be considered at
different places successively farther up the river,
it will be seen that this difference increases,
the duration of flood tide being less and that of
ebb tide greater at places higher up than at
places lower down the river. When we reach the
limit of tidal influence of the river the duration of

WAVES OF THE SEA 231

flood tide is, of course, zero, and ebb goes
on all the time. The phenomena are too extended
in a horizontal direction., and the surface gradients
of the water are, for the most part, too small for
the eye to see the ebb and flow of the tidal river as
a wave ; but in a diagram, with the vertical scale
much exaggerated, showing in profile the advance
of the tide up the river, it appears in the form of a
travelling wave, which becomes steeper as it
advances up the river. If the course of the ebb
tide down the river be similarly shown on a
diagram, it will be seen that the front of the wave
is never so steep as the front of the flood -tide wave
becomes in the upper reaches of the tidal river.
This is partly because at the commencement of
ebb the river is full and the water deep, instead
of being at its shallowest as at the commencement
of the flood.

In many tidal rivers a visible wave with a very
steep front, travelling up-stream, constitutes the
" first rise " of the flood tide, which is sometimes
referred to by boatmen simply as the " head " of
the flood, but it has also specific names, such as
the "Bore" and the " Aegir " (on the Trent).
This phenomenon has long been accepted in works
which deal with the theory of tides as being the
steep face, or the steep part of the face, of the flood-

232 WAVES OF THE SEA

tide considered as a single wave, although Sir G. H.
Darwin has pointed out that theory serves rather
to explain a rapid rise than an absolutely sudden
one.

In the account which I have now to give of the
tidal bore, as I have seen it in the River Severn,
it will be found that it seems to have a wave -length
insignificant in comparison with that of the tidal
wave considered as a whole.

Wave -Length of the Severn Bore

The River Severn, which is tidal up to and
beyond Gloucester, pursues below this city a
sinuous course, similar to that of a non-tidal river
in an alluvial plain. The gradient is at first slight,
and the chief peculiarity of the bed is the occur-
rence at several places of ledges of rock lying
across the stream, which suddenly reduce its depth.
Thus the depth at ordinary low water over the
" Stonebench " is 3 feet, whereas the depth in the
long pool below is 10 feet. Denny Rock is another
shallow, which has a deep reach above it. The
character of the river changes somewhat near
Priding, where sand-banks begin to be prominent
at low water. Between Gloucester and Priding
is the best part of the river for viewing the bore,

. ..-"4

THE COURSE OF THE RIVER SEVERN FROM GLOUCESTER TO THE
SEVERN TUNNEL.

AND OTHER WATER WAVES 235

if the object be to see an imposing spectacle. The
favourite spot, visited by crowds at the highest
tides of spring and autumn, is Stonebench, and
there are others similar to it, such as Denny
Rock. The phenomenon at Stonebench is very
striking.

The wave slackens in speed when it comes to
the shallowing water, increasing in height the while,
and finally charges over the shoal with a rush of
broken waters. I saw the phenomenon at Denny
" Pill " (or Brook) on April 30, 1900. Here the
wave, when first seen, was already in shoal water,
and, at all events from my low point of sight,
appeared solitary. It had a steep front, in places
overf ailing upon itself with foam (see Plate).
As soon as it passed the place of observation
it presented another appearance, viz., that of
a jgroup of smoothly-rounded waves (see Plate).
Being on this occasion closely occupied with
(obtaining photographs, I did not observe this
part of the phenomenon with undivided attention ;
but on a subsequent occasion (October 30, 1901),
at Priding, I was able to observe carefully, and
to photograph, a similar occurrence. The ap-
proaching bore, whatever wave disturbance may
have been half -concealed behind, presented a face
like the breaker of the seashore, and this was almost

236 WAVES OF THE SEA

all that was noticeable from the front. But when
the bore came opposite to me, the water being
deeper below the part of the bank on which I
stood, the steep, bold front was gone in an instant ;
a rounded wave or swell, followed by others of
the like size and form, being immediately 'sub-
stituted, and the number of these swells rapidly
increased, the group lengthening to leeward, so
that in a few seconds I counted no less than sixteen
of these large swells,1 forming a group of waves
of remarkable appearance, which progressed, as
a whole, with singular slowness, owing, I suppose,
to the well-known circumstance that the speed of
a group of waves (at least in deep water) is only
half that of the individual wave. The above obser-
vation suggests important reflections upon the
nature of the tidal bore. This term is by common
consent employed to designate a steep -fronted
wave, either overf ailing or on the verge of break-
ing, constituting the first rise of the tide in Ja
river or estuary. If it be actually a part of the

1 These are often referred to as " ripples," but the etymology
of the word indicates the propriety of restricting its use to little
waves. Its use for waves of capillary size, as proposed by Lord
Kelvin, may be conveniently extended in the case of other
materials — e.g., sand and snow — to a small class of waves only
affecting superficial strata, co-existing with larger waves capable
of indefinitely great development.

THE BORE ON THE SHALLOWS OF DENNY ROCK, AND AFTER REACHING

DEEPER WATER.

237

AND OTHER WATER WAVES 239

face or front slope of the whole flood tide re-
garded as one wave, then its length is indefinitely
great as compared with the depth of the Severn
at Priding, and the only change on entering slightly
deeper water would be an increase of speed,
accompanied by diminution of height and, perhaps,
of steepness. There would be no resolution into
a group of waves. It appears, on the contrary,
that the greater part of the (no doubt complex)
wave which was seen to approach Priding was
" long," as regarded the shoal water, but " short "
as regarded the deeper water.

From Priding or Framilode to Hock Crib, or
Hock Cliff, as it is also called, is the last great
horseshoe bend of the permanent banks of the
Severn. Below Hock Cliff are the straight diverg-
ing banks, with a straight axis, which indicate the
subordination of fluviatile to estuarine conditions.
Already in the stretch from Framilode, past Newn-
ham at the apex of the horseshoe bend, to Hock
Cliff, we see the near approach of estuarine condi-
tions in the rapid divergence of the banks, and in
the sand-banks, dry before low water, which are
here a feature of the river.

The bore at Newnham is a less imposing wave
than in the narrower river from Denny to Stone-
bench, where the whole width of the channel is

240 WAVES OF THE SEA

filled even at low water, and the bore, besides
being much higher than at Newnham, reaches from
bank to bank, and seems as if it would overwhelm
everything in its course. Nevertheless, con-
venience of access, and the wide prospect of the
river from the lovely Newnham churchyard,
situated on a salient bluff at the bend in the
river's course, combine to make this a favourite
spot for viewing the approach of the bore. The
first appearance of an advancing line of foaming
water far down the river below Awre, at a distance
of some miles, is indeed a most impressive sight.

I first saw the approaching bore from Newn-
ham at the high tide of April 29, 1900. Having
descended to the ferry, I entered a boat and sur-
mounted the wave just outside the projecting cliff,
which makes a kind of harbour at the ferry. There
was no change noticeable in the current when the
boat rose to the bore, in the deep water, but after it
was passed the boatman almost immediately brought
the vessel to land with a few strong strokes, in
order to avoid the tremendous current which
quickly succeeded the passage of the wave.

The wave was not solitary, for after it passed
the water flowed back from the shore, exposing
many yards of tabular rocks which it had covered.
It then surged up again, and during the rapid cur-

AND OTHER WATER WAVES 241

rent above referred to the rise of level was
continuous.

The second occasion on which I saw the bore
from Newnham was on October 29, 1901, after a
summer when the river had been low owing to
small rainfall, and at a time when the usual heavy
rains of autumn had not commenced. Although
the tide was almost the highest of the year, the
bore was a very small one. Stationing myself
first in the churchyard, I noticed that the bore,
which had been visible before entering the pool
near Bullo, disappeared there except for some dis-
turbance of reflection from the surface of the deep
water. I then ran down to the shore. On the
shelving sand-bank which formed the left shore
of the low-water channel the bore advanced as
a crested wave of no great size, rolling over upon
itself. As I watched this, my attention was caught
by the sudden submergence of a stake near me,
which I had noticed as being convenient for
marking if there were any change of level before
the arrival of the bore. I found, however, that
the quick rise of water which covered the stake
was the whole of the " bore " on this, the deeper,
side of the river. There was here no steep-
fronted wave. Moreover, after this rise, there was
a marked subsidence, so that the wave was not

13

242 WAVES OF THE SEA

solitary. I obtained two photographs showing the
level of the water when the bore was passing, and,
a few seconds afterwards, during this subsidence.

On the Want of Concordance between Height of
Tide and Height of Bore, and on the Con-
ditions which Determine the Starting-point
of the Bore

The capricious character of the tidal bore is
one of the most interesting characteristics of this
phenomenon in the Severn, and I suspect that it
is capricious in other rivers also.

The disturbing cause lies in the sand-banks
below Hock Cliff, and we will therefore now
describe the character of the river or estuary
below that point. The change which there com-
mences is not only that which has been mentioned
— the straight, diverging banks of the high-water
channel, in place of winding, nearly parallel banks
— but also a change of gradient. The low- water
slope, which from Gloucester to Framilode is slight,
becomes very steep below Hock Cliff, and con-
tinues of unusual steepness to the Sheperdine
Sands. Below the Severn Bridge, which prac-
tically bounds the view down-stream from Hock
Cliff, the steepness is slightly increased. Below
the Sheperdine Sands to Aust the low-water
gradient is again slight.

V\

THE XOOSE SANDBANK

243

AND OTHER WATER WAVES 245

It is between Hock Cliff and the Severn Bridge
that the bore usually commences, according to all
testimony. The river at low water below Hock
Cliff continues to flow in a single channel, the posi-
tion of which, however, is no longer fairly constant,
as at Newnham, but depends greatly upon the
quantity of land water. After a wet season it hugs
the left bank, cutting a deep trough in the loose
sands, and making as wide a bend as the permanent
bank permits. This is the condition which, accord-
ing to the testimony collected by the late Frank
Buckland l and also by myself, gives rise to a large
bore at Newnham, about four miles farther up.

In dry seasons the channel, which contains all
the water during most of the time* of ebb and
during the commencement of flood, lies much
farther from the eastern shore, taking a straighter
course. Presumably in this as in other cases which
I have noticed elsewhere, the shorter course is due
to the influence of the flood tide, which tends to
flow in a chord of the arc made by the ebb, or
river current.2 After the dry season of the summer
of 1901, the ebb was flowing in such a channel,
far from the eastern shore and between per pen -

1 " Log-Book of a Fisherman and Zoologist," 1875.

2 Geographical Journal, August, 1901 : u On Sand-waves in
Tidal Currents."

246 WAVES OF THE SEA

dicular cliffs of sand. When, at 8 a.m. on Octo-
ber 30, 1901, I stood in the slime at the foot of
Hock Cliff, I saw the bore advancing from beyond
Awre as a line of white breaking water, stretching
quite across the channel, its summit being lower
than the top of the cliffs of sand. The height of
the wave seemed to be about 2 feet or 2| feet.
To the left of where I stood commenced the now
disused channel following the east, or Frampton
shore, which lower down became a deep trench.
At 8.10 a.m. the bore, having reached the upper
entrance to this channel, sent a wave swinging
round to the east into it which travelled down as
a bore, while the main bore passed me at 8.13 a .m .,
much diminished and enfeebled, on its way to
Newnham. That the bore at the latter place would
this morning be a feeble affair, as had been the
case on the preceding evening, I could well believe
when I saw how the " head of the flood " was
squandering itself in driving another wave and
stream of water down the Frampton Channel.
Indeed, the fishermen tell me that sometimes a
bore coming up this channel meets that which I saw
travel down it, and that a boat which finds itself
between them is in a dangerous predicament. At
8.35 a.m. I saw a small bore travelling across the
sandbank which separates the Frampton Channel

AND OTHER WATER WAVES 247

from the present, or Awre, channel travelling
up-stream, and from the Frampton towards
Awre Channel, which was not yet quite full. The
arrival of this reinforcement completed the cover-
ing of the sandbanks, and a broad sheet of water
lay stretched before me from shore to shore . At
8.39 a.m. the water was slack, or nearly so, and
then commenced to flow up-stream towards Newn-
ham, but no longer with a " head." Thus the
first flow was retarded 26 minutes. The total rise
of tide at Newnham would probably be lessened
not at all, or very slightly, by the circulation which
took place between Frampton and Awre.

As has been said, the Severn bore actually com-
mences somewhere between Severn Bridge and
Hock ClifT, according to concurrent testimony.
Below Severn Bridge it is reliably reported that a
bore sometimes makes an appearance in one or other
of the low-water channels between sand-banks, but
it vanishes again . Yet the low-water gradient of the
river is not less, but rather greater, below Severn
Bridge, and the rate of progress of " first rise "
of tide from the Sheperdine Sands to Sharpness
(a little below Severn Bridge) is even slower than
from Sharpness to Hock Cliff. Why, then, does not
the permanent bore originate between Sharpness
and the Sheperdine Sands, especially as it is not

248 WAVES OF THE SEA

far below this that there is the greatest tidal range
(about 40 feet at springs)? It may occur to the
reader that a long run is required under bore-
forming conditions before the bore becomes appre-
ciable ; but both theory and observation show it is
not so. If the conditions for forming a bore be
fulfilled, the wave attains a considerable size in a
very short interval both of time and space.

An answer to the question, Why does
the bore usually originate above and not below
Severn Bridge? — i.e., in the upper, not the lower,
half of the steep slope of the estuary— is afforded
by the following observations made from the com-
manding elevation of the Severn Bridge ( 100 feet
above low -water mark), on April 27, 1900, two
days before the highest of this set of spring tides.
At 3.43 p.m. the approach of the flood tide could
be discerned by a change of appearance of the
water, although there was no actual surface wave.
It was 4.5 p.m. before the level of the water was
rising at the bridge, so slow is the advance of the
first rise. I was stationed near the west end of
the bridge, where the principal low -water channel
of the ebbing water lies. The flood tide did not
force its way up this channel against the strong
stream, but was pressed away towards the east,
filling a swatchway, or blind channel, which led

AND OTHER WATER WAVES 249

away to the east of a sand-bank called the Wave-
ridge, or Waif ridge. After working thus to its
right until 4.30 p.m., with slow current but rapidly
rising level, the flood tide, having filled the swatch-
way brim full, suddenly swept over the Waifridge
Sand in a broad sheet of water, which poured over
to the westward into the main channel.

The sands, which had been drying for several
hours, were covered so suddenly that the im-
prisoned air spouted through the seething water.

It is evident that the presence of an alternative
channel, open from below, prevented the forma-
tion of a bore in this case, just as at Hock Cliff
the alternative channel, open from above, reduced
the bore after it had been formed.

The flood tide goes the way of least resistance,
and if it be free to circulate, it does not stem the
ebbing stream and form a bore. The presence of
alternative channels, which becomes more marked
as we travel down-stream from Severn Bridge to
Sheperdine Sands, is in itself sufficient to explain
the non -formation of a permanent bore in the lower
portion of the steep slope of the estuary.

Near Beachly Point, just below the foot of the
steep slope to which I have so frequently referred,
I watched the commencement of a spring tide on
April 28, 1900. The first rise was perfectly

250 WAVES OF THE SEA

calm, being unaccompanied by any wave or other
commotion.

It remains to explain why the flood tide, at its
first rise, preserves alternative channels in the lower
part of the steep slope below Severn Bridge and
not in the upper, or only to a limited extent, for
on the absence of side channels depends the possi-
bility of forming a bore where the other circum-
stances (shallowness and a fairly steep gradient)
are present.

The sands which encumber the bed of the Severn
from Hock Cliff to the Sheperdine Shoal are sub-
ject to arrangement and redistribution alternately by
the waters which flow seaward and by those which
flow landward. In the upper part of this region
the sands are arranged so as to form a channel
almost like that of a non -tidal river flowing in an
alluvial plain. Particularly is this the case when
the land water much predominates, as during neap
tides and after heavy rains. The ebbing stream,
flowing continuously for many hours in its narrow
winding channels, continually lowers its bed, scour-
ing the sand from beneath and forming a channel
which, at the time of first rise, has high, steep
banks. The first rise of the flood tide has there-
fore, as a rule, to make its way against this ebbing
stream up the normal river channel which has been

AND OTHER WATER WAVES 251

prepared for it. Then the bore is produced, and
it is noteworthy in this connection that, according
to the observation kindly communicated to me by
Mr. D. Wintle, of Newnham -on -Severn, the bore
is more marked there at the commencement of
spring tides than after they have been running
for some days.

In the lower reaches of the steep slope, and
above Beachly Point, the land water forms a
smaller proportion of the total, and the duration
of the ebb is shorter. The sands, as they are at
low water, are therefore not arranged so well to
facilitate the run of the ebbing waters, their dis-
tribution, on the contrary, exhibiting certain
features markedly favourable to the commencement
of an upward flow. This change of conditions
exhibits itself by the presence of swatchways, or
by-channels, such as that above referred to.

How these are formed has been already indi-
cated, and may now be further explained. The
ebbing stream ponds back the flood, which conse-
quently makes another way for itself through and
across the sands. The relation of the two classes
of channel due to ebb and flow respectively has
been described Toy the author elsewhere.1 Briefly,
the low-water ebb channels are narrow, deep, and
1 Geographical Journal, August, 1901.

252 WAVES OF THE SEA

sinuous, those of the flood broader, shallower,
and straighter. Tidal bores appear to be charac-
teristic of rivers where there are drying sand-banks,
and are perhaps only produced there in a part of
the sandy estuary which has not yet settled down
to a permanent form. The bore marks a struggle
between flood or ebb which appears to be a transi-
tory state of things, for in Professor Osborne
Reynolds's model estuaries the bore disappeared in
all cases when the sand-banks had attained their
final form.

From the above it appears, when we study on the
spot the conditions of a tidal bore as exhibited
in the River Severn, that the phenomenon is some-
what more local and less general than the usual
mathematical treatment of the subject would lead
one to expect. The visible wave is not the
steepening of the front of the tide as a whole, but
the steepening of the front of the rising water in a
short reach of the river. The observation above
recorded of the multiplication of the wave on enter-
ing the water of moderate depth supports this view.

The tide presumably does not make its way
steadily up a tortuous channel, its progress, on the
contrary, being alternately checked and hastened.
Even on an open coast the rise of the tide, as
registered on the gauges, is markedly pulsative,

AND OTHER WATER WAVES 253

the curve presenting " notches." These are a
marked and disturbing feature of the records of
tide-gauges, and positions are consequently chosen
for their erection on the coasts where the uninter-
rupted run of the tide shall cause them to be as
slight as possible. This pulsative rise of the tide
is sometimes strikingly visible to the eye in situa-
tions where there is a considerable inflow over
nearly flat sands. Thus, on the Anat sand-bank,
on the left shore of the river mouth at Montrose,
N.B., where I was standing at the turn of the
tide on March 17, 1900, the water came suddenly
rushing in, filling up the hollows and threatening
to cover the whole area. The rush, however, soon
ceased, and the water then receded, leaving the
sands bare once more ; but only for one or two
minutes, when another rush again occurred, and I
do not think that the water subsequently retired.
In subsequent observations on the Severn and
elsewhere it will be well to look out for this pro-
cess, especially at places below the point of starting
of the regular bore. It may be that these con-
siderations help to explain the absolute suddenness
of rise which constitutes the bore, and which,
according to Sir G. H. Darwin, is not quite what
is indicated by theory— that is to say, by the theory
which regards the bore as the face of the tide -wave
considered as a whole.

CHAPTER IX

Cinematographing the Severn bore.

IN 1901 Mr. Charles Urban very kindly lent me a
bioscope camera and the services of an operator for
the purpose of cinematographing the Severn bore.
The photograph was taken under my direction on
September 29, 1901, and was shown at the meeting
of the Royal Geographical Society on Novem-
ber 25th. I believe this is the first cinematograph
of a tidal bore.

The cinematograph picture was taken at Stone-
bench, below Gloucester, which is distant 4 miles
by road, reckoning from the cathedral. The tide
was the third after full moon, and was not quite
so high as that predicted for September 3Oth,
which was one of the four highest predicted tides
of the year. After the dry summer the amount
of land-water in the river was probably below the
average, nevertheless, the low -water level was
ij feet above that given as summer low water in
Admiral Beechey's survey made in 1849. The

254

CINEMATOGRAPHS OF THE BORE APPROACHING STONEBENCH.
255

WAVES OF THE SEA

257

reason, no doubt, is that the spring tides had
already begun to fill up the river. The camera
was placed upon the left bank, as low down as
was consistent with the safety of the instrument,
and about 30 feet back from the submerged
" Stonebench," so as to show the breaking of the
wave where the water suddenly shallows from 6 or
7 to 2% or 3 feet. A boat was engaged to meet the
bore, and was anchored in deeper water at a suit-
able distance ; and to obtain the scale a post near
the left bank was measured, its top being found
to be 58 inches above low water.

The bore was heard at 9 a.m., a few seconds
before its appearance round the bend of the river,
at a distance of 513 yards from the camera. The
resurgings from the concave left bank had a fine
effect, well reproduced when the film is shown upon
the screen. The boat rode easily over the un-
broken wave in about 10 feet of water. The
height of the wave there I estimated at from 3 feet
to 3 feet 6 inches, and the height at the sides of
the river 4 to 5 feet. At the jetty or breakwater,
of which one post already referred to was visible
beyond the osiers, the bore suddenly sent a sheet
of water up to a height of 7 or 8 feet, but, re-
covering itself in a moment, the wave came on
with a front still smooth and unbroken, its inverted

258 WAVES OF THE SEA

image perfectly mirrored by the smooth water
ahead of it. Then, on reaching the hidden Stone -
bench, the wave curled over in a beautiful scroll.
But no stationary photograph can reproduce the
effect which is given on the screen as the dark-
f ronted curling wave rushes out of the picture, which
is then immediately flooded with light, the bright
clouds instead of muddy banks being now reflected
by the smoother waters. The speed of the bore
was about 13^ statute miles per hour. The ex-
posure of film was continued after the bore had
passed in order to illustrate the after-rush of water,
the speed of which was well shown by floating
debris. A boat happened to come by, one of the
occupants of which was gathering flotsam and
jetsam, and the camera was then revolved so as
to follow the boat as it passed. Owing to high
osiers intercepting the view up-stream, it was not
practical to cinematograph the bore from behind,
as had been intended. High water occurred 56
minutes after the passage of the bore, the total
rise being 8 feet 6J inches. The height of the
water then above ordnance datum was several feet
higher than high water of even a 4o-foot tide at
Portishead. The current continued to flow up the
river for 31 minutes after high water.

The tidal bore in nature is not precisely repeated

CINEMATOGRAPHS OF THE BORE ON REACHING STONEBENCH.
259

AND OTHER WATER WAVES 261

at succeeding tides, and in most rivers is not seen
at every tide. The cinematograph representation,
on the contrary, can be repeated on the screen as
often as required, and with a delay of only one or
two minutes while the film is being re-wound. At
each repetition the observer can concentrate his
attention upon one particular feature. In this way
I have seen several things on the picture which
escaped my observation on September 29th.
Measurements can also be made from the film,
either in the hand or from its projection on the
screen.

DESCRIPTION OF PLATES.

(The figures are enlargements from individual pictures upon the
cinematograph film.)

Fig. I shows the bore in the distance as a bright band, where
immediately before had been the dark image of bank and trees.
The 5-foot post is visible on the left, with its reflection below.

Fig. 2 shows the boat rising to the wave. The wave on the
right of the boat cuts into two the reflection of the trees on the
right bank. A comparison with Fig. i shows at once the
turbulence of the water behind the bore. The alternation of
wide bright bands with narrow dark bands parallel to the front
of the bore indicates the character and position of the undula-
tions behind it, whilst the confused reflection of light near the
left bank indicates resurging therefrom. If the apparent heights
of the banks in the two figures be measured, the level of the
water will be found to have risen behind the bore.

Fig. 3 shows the wave as yet unbroken, but with steeper front,
due to its approach to the shoal ; the inverted image is plainly
visible. Measurement of the post from the picture shows that

262 WAVES OF THE SEA

the water there is 2 feet 5 inches above the level of the river in
front of the bore.

Fig. 4 shows the bore rushing over the Stonebench. The
mean level of water at the post is 2. feet n inches above low
water, but there is a noticeable difference of level at front and
back of the post, indicated by a dark shadow on the picture.
This shows that the current, which, shortly before the bore
arrived, I found to be ebbing seawards at O'8 mile per hour,
is now making in the opposite direction with considerable
strength. The boat remains in position, being anchored.

.-

263

CHAPTER X

Stationary or standing waves — Cross-stream progressive
waves : observations in Niagara River.

Stationary or Standing Waves

ONE who observes the well-known waves of rapid,
or rock -encumbered, rivers from the bank cannot
fail to notice that whereas the shape of the corru-
gated surface is not very different from that of an
agitated sea, yet there is this great difference, viz.,
that the river-waves maintain their position un-
changed ; and, partly for this reason, they are
called stationary or standing waves. If a piece
of stick be tossed upon the stream, its down-
stream motion over the corrugated surface will be
seen to be alternately checked and accelerated as
it reaches the crests and troughs respectively.
Mathematically, this undulated river is regarded
as a steady stream, flowing, say, to the right, with
a train of waves travelling to the left at a speed

14 «

266 WAVES OF THE SEA

equal to that of the stream.1 This conception will
be found very helpful to a proper understanding
of the subject ; and that it is no mere subtlety of
thought is realised immediately by one who shall
drift in a boat through such a train of waves.
Dropping down-stream in this way on the ebbing
tide between the piers of the Severn Bridge opposite
Sharpness, my eyes were fixed upon the waves
which combed over towards me. Almost at once
the sense of drifting vanished, the boat seemed no
longer to progress through rough water, but, on
the contrary, to be at a standstill, whilst wave
after wave charged past her.

In small streams it is not difficult to produce
stationary waves by introducing a stone or
boulder, or, better still, a transverse barrier which
rises above the bottom sufficiently near to the

1 An excellent illustration of a wave with a motion equal and
opposite to that of the current is seen when one pours water
into the centre of a flat-bottomed circular sitz-bath. The
current flows outwards in all directions with diminishing
velocity, and the water, resurging from the circumference, makes
a breaking wave with a circular front facing the centre of the
bath. As the depth of water behind the wave increases the
velocity of the wave also increases, so that its front closes in
towards the centre where the outflowing current is more rapid.
The circle is presently reduced, at first slowly, afterwards
more rapidly, so that only a small hole is left, and finally the
wave closes in completely upon the down-pouring column of
water.

AND OTHER WATER WAVES 267

surface. A mound of water forms in the neigh-
bourhood of the obstruction (its precise position
relatively thereto depending upon the circumstances
of depth and speed), and a hollow and a second
crest, and then a third, a fourth, and so on, appear
farther down-stream, a train of waves speedily
being formed. If the obstruction be now dragged
up-stream, the whole train of waves moves up-
stream with it, preserving their position relatively
to one another (which is the second connotion of
the epithet " stationary " as applied to them). In
performing this simple experiment the close re-
semblance between the ordinary waves of rivers
and ship-waves becomes at once apparent. The
analogy is yet further brought home when one
notices the waves formed by a model or toy vessel
moored in a rapid stream. The familiar train of
waves shown by a ship steaming through still water
is here reproduced in the water which flows past
the stationary vessel.

There are, however, considerable differences in
the appearances usually presented by ship-waves
and river -waves, which are due partly to the fact
that the latter are produced by disturbances which
affect the water throughout its whole depth, and
the former are generally only superficial. Again,
river -waves, when caused by a weir, extend in

268 WAVES OF THE SEA

straight parallel ridges at right angles to the
current, quite across the stream, a form very
different from the wave-track of a ship.

A solitary boulder in mid-stream does, however,
reproduce, very roughly, the wave-track of a ship,
a series of waves being formed on either side,
each wave inclined at an angle which appears to
be about the same as in the case of ship-waves,
viz., 19^° to the current, each succeeding wave
projecting somewhat farther into the stream than
its predecessor. There is generally but little
indication visible of any system of transverse waves
like the thwart -ship waves which are comprised
between the diverging, or " echelon," waves of a
ship's track.

When river-waves arise from the retardation
caused by a rough bank, or where a stream
narrows, or where it enters upon a different
gradient, the wave-front is inclined to the bank.
If the stream be wide, the oblique standing waves
are of greater elevation near the bank, the height
diminishing farther out, the centre of the river
being smooth. If, however, the stream be narrow,
the standing waves originating from the opposite
banks are superposed in the centre of the stream,
and the combined crests there have a greater ampli-
tude than either separately. Thus the highest wave

STATIONARY WAVES CAUSED BY A WEIR ON THE RIVER AARE, SWITZERLAND.

269

AND OTHER WATER WAVES 271

is in this case found in the centre of the stream,
as may be seen, for example, near the spot, called
Bloody Run, opposite Foster's Flats, in the rapids
between Niagara Whirlpool and Lewiston.

In 1896 I noticed some facts relating to waves
in rivers of which I found no published explana-
tion. The first was that the water of rivers, per-
ticularly rapid mountain streams — e.g., at Meran,
in the Tyrol — does not maintain a constant level
at any fixed spot, but, on the contrary, oscillates
perceptibly with a motion sufficiently rapid and
short in period to be readily perceived by the eye.
This indicated that there was something of the
character of a progressive wave, but I could not
at that time see any travelling wave.

The second observation was that the so-called
stationary waves (e.g., on the Eisah, above Botzen,
and at the Bingen Rapids, on the Rhine) were not
perfectly stationary, but oscillated somewhat about
a mean position. Their most noticeable movement
was that, from time to time, they charged some-
what rapidly a foot or two up-stream ; and in
this case the cusped waves broke as waves break
on a sea-beach. It appeared to me that the second
phenomenon was related to the first in the follow-
ing way : granting that the '" stationary " waves
are travelling up-stream as fast as the current

272 WAVES OF THE SEA

flows, then if the speed of the current be suddenly
diminished, the speed of the waves will be too
great, and they will charge up-stream. Thus, if
the current be subject to fluctuation, as the first
observation seemed to indicate, we should expect
the " standing " waves to fluctuate about a mean
position .

A third fact, also, best observed in mountain
streams — e.g., the Lutschine, at Grindelwald, in
Switzerland — was that in the shallows of little bays
there was always a succession of progressive waves
rushing towards the shore, as waves come in on
a sloping sea-beach. These " rollers " in the little
bays were evidently connected with the oscillation
or throbbing of the stream. A long series of these
" rollers " was timed just below Speybridge, near
Grantown, N.B., when the " Galloping Spey " was
swollen by melting snow and ice, in February,
1900. They were only roughly periodic. They
rolled in upon the shore in a direction about at
right angles to the current — their direction being,
of course, conditioned by the shallowing of the
water ; and it was of interest to observe that these
waves rippled the sand at right angles to their
motion, although the current drifted the sand-
grains parallel to the ripple ridges.

Beyond the frequent repetition of these three

AND OTHER WATER WAVES 273

observations in different rivers, I was not able to
progress in this matter for some time. I deter-
mined, however, to see what I could learn of wave
phenomena in rivers, particularly those connected
with the pulsation or throbbing which I had
noticed, by a visit to the River Niagara, where
I thought I could see such things in their full and
free development.

Cross-stream Progressive Waves. Observations in
Niagara River

I arrived at Niagara Falls, N.Y., on July 8,
1903, accompanied by my wife, who has shared
in all my travels in search of wave phenomena. The
next three weeks were spent in observation between
Niagara Falls and Lewiston, after which a voyage
was made from Kingston, Ontario, to Montreal,
passing through numerous falls and rapids on the
St . Lawrence .

Above the Falls of Niagara the river is wide and
generally shallow, flowing very swiftly on a con-
siderable gradient over an uneven, rocky bottom.
Between the American shore and Goat Island the
water is shallowest. Above the bridge connecting
them I was able to see waves progressing down-
stream which I thought " faced"— i.e., had their
steeper face — turned down -stream and towards the

274 WAVES OF THE SEA

shore, instead of up-stream and away from the
shore, as the stationary waves are. The travelling
waves were not conspicuous, however, and I was
not able to detect similar ones (facing down-
stream) in the deep waters of the Whirlpool
Rapids .

In the upper rapids of Niagara regular trains
of waves are not prominent. The most noticeable
waves are such as that beyond the last '" Sister
Island," where a huge mass of water surmounts
a rocky protuberance, to leeward of which the
water curls back in a fine cusp.

In a little sheltered channel among the islands,
where the water flowed less tumultuously, much
better examples could be seen of a regular train
of waves. From Lunar Island I saw one of the
cusped waves near the brink of the American Falls
break periodically, thus :

In 57 seconds the wave broke 7 times ;

» 62 » i> ji D ° 11

corresponding to periods of 8.14 and 7.77 seconds
respectively. This is in the same part of the river
where I observed the progressive waves. I post-
pone until another section the account of certain
phenomena of the actual falls, and, passing by
without remark the 2 -mile stretch of deep water

„. .

BIRD'S-EYE VIEW OF WAVES IN WHIRLPOOL RAPIDS, NIAGARA.
275

AND OTHER WATER WAVES 277

(160 feet to 190 feet), with scarcely any fall of
level, which succeeds them, I come to the second
rapids of the Niagara River, called the Whirlpool
Rapids, from the pool at their lower end. The fall
is 50 feet per mile, nearly i in 100. The width of
the Rapids is only about 350 feet, the depth is stated
to be 35 feet to 50 feet, and the reputed velocity
is 30 miles per hour.1 The course of the river
here is curved, the apex of the curve being ap-
proximately at the " Whirlpool Rapids " station of
the Niagara Gorge Light Railway, situated on the
right bank . A very fine general view of these rapids
is obtained from the footpath of the high level rail-
way bridge at their upper end, and an excellent
view of the waves near the railway station
is obtained from the cliffs of the left bank opposite
thereto. Waves commence a little above the
bridge, where the gradient of the bottom increases
and the water begins to flow more swiftly. There
are two sets of waves originating from the right
and left bank respectively. The first few waves
are smoothly rounded in form and practically
steady in position. Lower down, where sets of
waves originating from the opposite banks extend
sufficiently far out to meet each other, they are

1 G. K. Gilbert : " Explanation of United States Geological
Survey Map of Niagara River."

278 WAVES OF THE SEA

often cusped and foaming, and they shift some-
what rapidly for a short distance up and down
about a mean position.

Numerous standing waves originate from
successive positions on the banks, the position
being determined doubtless by changes of pres-
sure and, consequently, of velocity. Such change
of pressure and velocity is obviously produced in
some places by rocky obstructions, but in some
instances, particularly opposite the railway station,
the change of direction of the current probably
contributes to the effect. No long and regular
trains of waves can be observed, except just at
the commencement, but the positions of the prin-
cipal mounds of water are perfectly definite, so
that (as long as the river remains at a certain
level) these waves are recognisable individuals.
Nevertheless, I noticed from my elevated stations
on the bridge and the cliffs that in this terrible
rapid (where the combined depth, speed, and
volume are so unusually great) the throbbing,
which is so slight a feature in most wavy streams,
had developed to a remarkable extent. The sta-
tionary waves of the river differed from those
of quieter streams in the same way that the bow-
wave of a steamer in a heavy sea differs from the
bow -wave in smooth water. In the latter the bow-

279

AND OTHER WATER WAVES 281

wave is constant in size and steady in position, but
in a heavy sea the vessel throws off from her bows
a succession of waves. Similarly, I saw the stand-
ing waves near each shore periodically wax and
wane (though never waning to less than, say,
three -fourths of their maximum), and as each
passed its maximum it disengaged a conspicuous
and considerable travelling wave, which surged for-
ward (facing diagonally up-stream) towards the
centre of the stream. The waves travelling out-
wards from each bank met in the middle of the
stream with much commotion and throwing up of
spray, after which they could be clearly seen to
have passed right through each other, and to con-
tinue each its course towards the opposite shore.
The wave, however, is drifting down -stream all
the time ; the resulting motion of the mound of
foaming water being more down -stream than across
stream, for the current velocity is greater than the
wave velocity relatively to the bank.

Viewed from the edge of the torrent at Whirl-
pool Rapids Station, the great standing mounds of
water in the centre of the stream towered up above
the line of sight. They are formed (as I knew
from my bird's-eye reconnaissance) where the
standing waves, diverging from the banks, cross
one another. They fluctuated continually in height

282 WAVES OF THE SEA

(from 15 feet to 20 feet I estimated) ' and also in
position, but the amount of shifting was not great
—perhaps one -half of the length of the mound
of water. This staggering and heaving conveys
the notion of efforts so great that some breakdown
must soon occur. And while I watched enthralled
the breathless heavings of the standing waves, a
surge came rushing upon the shore where I stood,
as if the river would suddenly rise and overwhelm
me. I drew back, realising that my post of
observation was unsafe. Acting on the ordinary
experience of rivers as flowing with practically
steady motion, I had not sufficiently allowed for
the amount of throbbing in the Niagara Rapids.
Of course, the rush of water which drove me back
was not the commencement of a continuous rise,
but merely the discharge of a wave, and the water
receded again with a somewhat more deliberate
motion, only to make way for another dashing
surge. The surge was timed by the covering and
exposure of a rock :

Number of Times Rock Covered.

First Second Third Fourth Fifth

Minute. Minute. Minute. Minute. Minute.

35445
Average period, 14*3 seconds.

1 The late Mr. T. V. Welch, formerly Superintendent of the
New York State Reservation at Niagara, informed me that they
are estimated at 30 feet when at their highest.

AND OTHER WATER WAVES 283

Such a surge is well shown in cinematograph
views of the Rapids. The vertical rise and fall
of this surge upon the shore was about 2 feet. It
is easy to realise that it is connected with the sway
and heave of the standing waves, and recollecting
what I had seen from above, I naturally connected
it with the travelling waves which come from near
the opposite shore.

My feeling that the standing waves were
heaving and swaying too much for permanence
was presently justified. After watching for a time
the seething and roaring waters, the great billow
before me suddenly leaped into the air, scat-
tering its waters in showers of spray, which fell
to leeward upon the river with a " swish," whilst
a much diminished mound was seen where the ex-
plosion occurred. It was, however, only a matter
of seconds for the standing wave to grow again
to its normal dimensions. I have called this phe-
nomenon the " leaping wave." Doubtless it may
be seen in many places on Niagara, and in other
such tumultuous waters, but the best place, as far
as I know, for observing the phenomenon is at
the Whirlpool Rapids Station. Presumably, the
spot for the station was selected on account of its
being opposite the place of greatest turbulence.

I was, fortunately, able by actual observation to

284 WAVES OF THE SEA

trace the phenomenon to its cause ; for, returning
to the cliffs on the Canadian side directly above
the spot, I saw travelling waves buffeting their
way to mid-stream from either side (but swept
down-stream, so that their resulting course was
inclined at an acute angle with the current) meet
together just where the crossing of the standing
waves made one of the great mounds of water
opposite the railway station. When the two travel-
ling waves met each other and the great standing
wave, the water leaped high into the air, shattering
and scattering all regularity of form or structure.
After seeing the thing from this point of vantage,
I was able on another occasion to recognise the
process from the nearer but lower point of view
close to the railway station. My eye having become
accustomed to the maze of motion (acquiring thus
a temporary efficiency far beyond one's ordinary
powers of seeing), I actually saw several waves con-
verge at the same time to produce a leaping wave.

I may add that I never noticed any great leaping
up of the water except the leaping of a standing
wave when progressive waves converged upon it.

In the voyage from Kingston, Ontario, to
Montreal, passing through many rapids, including
those of Lachine, I was able to make my observa-
tions under another set of conditions — viz., while

WAVES IN WHIRLPOOL RAPIDS, NIAGARA.

285

AND OTHER WATER WAVES 287

sharing the motion of the current, so that the only
movement of the water which the eye had to follow
was its periodic or wave motion. The changed
conditions of vision are well indicated by the
photographs then taken, in which there is no indica-
tion of the shutter being too slow, for the particles
of foam, &c., travelled along at the same speed as
the camera. As we passed through one after
another of the St. Lawrence rapids, I noticed re-
peatedly that the first few waves were rounded in
form, unbroken in surface, constant in size, and
practically fixed in position. Lower down, how-
ever, where two or more trains of waves inter-
sected one another, they became cusped and foam-
ing, breaking also and sometimes fluctuating.

Some part of this difference may be due to in-
creased speed in the lower part of the rapid, but
it was fairly evident that the changed character
of the waves was mainly due to superposition.

The most conspicuous billows, or apparent waves,
in torrents are usually of small lateral extension, for
they are produced where two standing waves cross,
and each standing wave is usually inclined at about
20° to the direction of the current. In the Niagara
Rapids below the Whirlpool, opposite Foster's Flats
(Devil's Hole Station), there is a splendid series of
such combination standing waves. The course of

288 WAVES OF THE

the river being here straight, there is less irregu-
larity than at the bend of the Whirlpool Rapids.
The distance from crest to crest in the direction of
the current was 100 feet, but this is not a true
"wave-length" in the physical sense.

It is now incumbent to explain the co -existence
of the ordinary diagonal standing waves of rivers
with travelling waves facing diagonally up-stream
in the rapids of Niagara and the St. Lawrence.

The absolute steadiness of standing waves can
only be secured by absolute steadiness of current.
In a river with a rough bed and a crooked course
it is impossible that the motion should be perfectly
steady if the current be even moderately swift,
for (to take the principal and most evident cause
of fluctuation) eddies are alternately formed and
released. By this means a standing wave is caused
to fluctuate as the " unwinding scrolls " and other
irregularities follow one another down the stream.
Generally speaking, the fluctuations so produced in
a wave near the right bank will not synchronise
with those of a wave near the left bank, for such
irregularities of flow of the river are generally
partial, not affecting simultaneously the whole
cross -section of the stream.

Wave -motion is essentially differential, and if
the rate of change of motion be slow, the effect

289

AND OTHER WATER WAVES 291

on a wave is slight. Thus, such fluctuations of
current generally only produce a flicker in the
stationary waves, as described in the earliest obser-
vations recorded above. But if wave be super-
imposed upon wave, the effect of such fluctuation
is intensified in a very high ratio. The combination
wave may be regarded as a " higher power " of
the original quantity, and the effect of an inequality
of current as affecting the fluctuation of the com-
bined system will increase in a rapid ratio. The
fluctuation of a waved wave (as I may term it)
is much more sharp and sudden than that of a
simple wave. The effect will also be more marked
when the standing waves are themselves steep and
high relatively to their wave-length.

Thus the fluctuation of the standing waves of the
Whirlpool Rapids becomes sufficiently great for the
disengagement of visible travelling waves. The
independence of various causes of unequal flow
in different parts of the stream makes the travel-
ling waves arise independently in different places,
and their synchronisms are, therefore, irregularly
timed. Great leaping waves are only caused when
a number of them (in their resultant drift) converge
simultaneously upon a combination standing wave.

These cross -stream progressive waves do not,
however, exhaust the possibilities of progressive

15

292 WAVES OF THE SEA

waves in rivers, and I was on the look-out more
particularly for waves facing down -stream and pro-
gressing through the water in a down -stream direc-
tion. Such waves would, of course, pass the bank
more rapidly than the water itself, for their apparent
velocity would be that of the current plus the
proper motion of the wave.

Near Devil's Hole Station, opposite to Foster's
Elats, on the rapids below the Whirlpool, I observed
that from time to time freshets came down the
river, raising the level of the water on the bank for
as much as 90 seconds. Thus at 1 1 hours
26 minutes 5 seconds a large freshet arrived, rais-
ing the general level of the water about 12 inches.
Duration of high water, ij minutes.

1 1 hours 32 minutes 5 seconds, another freshet ;
high water, i£ minutes.

1 1 hours 37 minutes 5 seconds, a small freshet.

1 1 hours 42 minutes 5 seconds, a small freshet.

I could not, however, perceive any visible travel-
ling wave, nor was there anything to indicate that
these freshets travelled faster than the current. If
they had been due to " long waves " progressing
in the direction of the stream, they would have been
travelling at some much greater velocity, perhaps
twice as fast, for the depth here is very consider-
able. I am inclined to think, therefore, that this

AND OTHER WATER WAVES 293

kind of swelling of the river, which co -existed with
the shorter period waves which were coming in on
the shore all the time, is due to the intermittent
disengagement of masses of swirling water from
the great whirlpool up above. Some confirmation
of this view is afforded — first, by watching the up-
wellings which take place in the whirlpool near the
exit, and also by the appearances of such masses
of swirling water lower down the Foster's Flats
Rapids, where there are fewer standing waves. It
is not uncommon here to see a cyclone and an
anticyclone of water drifting down -stream side by
side with a difference of level (reckoned from the
crown of the anticyclone to the pit of the cyclone)
of probably 5 feet or 6 feet. In these there is
horizontal circulation of water about vertical axes.

Thus in the deeper waters of Niagara I never
saw any repetition of down-stream progressive
waves such as I believed I had detected in the
shallow water above the American Falls. This
might be explained either by their non-existence
or by their being too flat to be visible in deep
water .

In the next chapter I shall give an account of
the circumstances under which a stream of water
flows in a series of down -stream bores.

CHAPTER XI

On streams which flow as a series of roll-waves — Observations
on a conduit from Territet to Glion — Observations on the
conduit of the Grunnbach (Merlingen, Thunersee) — Obser-
vations on the conduit of the Guntenbach (Gunten,
Thunersee).

On Streams which flow as a Series of Roll-waves

ON June n, 1904, I walked from Grindelwald to
view the Apbach Waterfall. Alongside the sheet
of water which leaped from the overhanging part of
the rock was a small body of water sliding down
the precipitous, but not vertical, part of the rock.
The water here would have been only a small frac-
tion of an inch in depth if it had been uniformly
spread, but it was, on the contrary, flowing in
detached/ portions, having the form of small, wedge-
shaped, progressive " solitary " waves, miniature
bores, about J- inch in amplitude, separated by
portions of rock which were covered by a film of
merely capillary thickness.

The same phenomenon was seen on another occa-

20i

WAVES OF THE SEA 295

sion, on a slightly larger scale, where the water of
the little Pfanenbach flows down a precipitous rock-
face near Gunten, on the Thunersee. Here, again,
the runnels of water were not wide, and the wave-
front of the progressive waves was V-shaped.

Water flowing in a broad, thin sheet upon a
sloping platform goes in progressive wavelets,
which have a widely extended wave -front, present-
ing a series of parallel ridges, which recall the
typical form of surface waves more forcibly than
the V-shaped wavelets of a film flowing in a narrow
runnel. I have detected the progressive -wavelet
form of flow on the face of a vertical slab of
smooth stone down which water flowed, but have
seen it better upon the sloping, polished marble
slab of a fishmonger's shop when being washed
down with water flowing from a pipe. The out-
flow from the pipe may not have been absolutely
steady ; but any unsteadiness there may have been
was certainly slight, whereas the flow of the sheet
of water rapidly formed itself into a procession
of progressive wavelets, which were both con-
spicuous and regular. The ridges were about
9 inches apart. The same thing can be seen where
the street pavement or a ship's deck is flushed from
a large hose.

296 WAVES OF THE SEA

Observations on a Conduit from Territet to Glion

- .r

From Territet (on the Lake of Geneva) to Glion,
about 800 feet above, there runs a funicular rail-
way, with an average ascent of nearly i in 2. On
the east of the line is a cement conduit, 14 inches
wide, with flat bottom and nearly vertical sides,
which carries off small quantities of water over-
flowing from the machinery, as well as, perhaps,
a little drainage water. The regularity of the con-
duit is interrupted above the bridge which crosses
it on a level with the Church of Les Planches,
and the water there flows in the ordinary manner.
It is only from the place where the cement floor
commences that the waves become noticeable. The
slight, rapid, and confused inequalities of the
flickering flow here become regularised into trans-
verse progressive waves in the course of a few
yards, and these waves dash past the bridge and
go foaming on as far as the railway station ;n
an orderly and regular procession, dozens of frothy
crests being simultaneously visible.

On February 9, 1905, I measured the depth at the
crests of the waves and found it to be 0.2 inches,
and at the troughs o.i inch. The apparent period
(that is to say, the interval of time separating the
passage of two succeeding crests past the observer

AND OTHER WATER WAVES 297

on the bank) was 0.4 second on one occasion and
0.7 second on another. The wave-length attains
a maximum of about 18 inches or 2 feet before
the end of the run is nearly reached. The reason
why the waves soon attain a uniform maximum
size is that the increase of depth at the crests is
accompanied by a corresponding diminution of
depth at the troughs where the water becomes too
far reduced for further growth. On one occasion
I have seen the sudden accession of a little more
water (from the passing train) greatly increase the
size of the waves. On another occasion, however,
near the Glion Station, when much water was
poured into the conduit at the end of the journey,
the progressive waves vanished altogether. There
appeared instead diagonal stationary waves,
originating from both sides of the conduit. When
the excess of water ran off, the shallower stream
ceased to be steady, and again ran in a series of
progressive waves.

The cement floor and sides of the conduit are
not, of course, nearly so smooth as the polished
marble slab above referred to, but their surface
is plain, uniform, and free from palpable excres-
cences. The course is straight, and of uniform
gradient for considerable distances. The steepness
of the gradient is immensely greater than in rivers.

298 WAVES OF THE SEA

The wave phenomena in the conduit are abso-
lutely different from those normal to rapid rivers
of considerable depth. In the latter, any cause
which retards the flow gives rise to waves stationary
as regards the bank, with their steeper face up-
stream, and travelling through the water in a direc-
tion more or less directly up-stream. In the con-
duit, on the contrary, the waves, which have their
steep face down -stream, travel through the water
down-stream, as I proved by measurements, to be
quoted later. In rivers of moderate depths where
standing waves arise, the dominant factor in
wave-making is pressure, the effects of friction
being relatively very small. Thus, where pres-
sure is increased, the stream-lines open out and
the level of the surface rises, in the manner
and for the reasons which have been set forth by
many authors who have dealt with the theory of
ship -waves.

The total depth is greater at the crest of the
waves, and here the flow is slower ; less at the
troughs where the flow is quicker ; and a state
of continuous flow is thus maintained, an equal
quantity of water passing each cross -section of the
river in each unit of time.

But in the conduit, where the depth is initially
very small, the frictional resistance of the bed be-

AND OTHER WATER WAV7ES 299

comes the dominant factor in determining the rate
of flow. If this small depth be increased, the rate
of flow is at once greatly accelerated, for the upper
layers flow with considerable freedom upon a couch
of water, whereas the lowest layer clings to the
bed. Thus a momentary retardation of flow at
any spot, by increasing the depth there, enables
the water which then arrives to flow with much
greater speed. The excrescence caused by any
momentary check therefore dashes down-stream.
Thus every retardation quickly causes acceleration.
This condition necessitates the substitution of a
gushing for a continuous flow. The more highly
developed are the down -stream progressive waves,
or roll -waves, the more gushy is the stream.

I shall now give some account of observations
of these spontaneous roll-waves in shallow streams
(generally artificial conduits) which I made in
Switzerland during 1904 and 1905. The waves in
the conduits, which are much easier to observe
than the corresponding waves in natural channels,
throw some light upon occurrences which are con-
fused and obscured under natural conditions.

When looking at water flowing past in a shallow
channel, I find that the eye is generally fixed by
stationary features of the surface, such as diagonal
standing waves originating from the banks. When

300 WAVES OF THE SEA

the gaze is thus fixed, the surface of the flowing
water has either a smoothed-out appearance or that
of stationary streaks or stripes. If, however, the
eye can be trained to follow the water in its flow,
it will be seen that its surface is usually covered
with travelling inequalities. This habit of vision
is somewhat difficult to acquire, and the movement
of the eye is always liable to be arrested involun-
tarily by some fixed object. If, however, a small
dead leaf, or a short piece of straw, or some such
light thing, be cast upon the stream, the eye follows
it in its drift naturally and with ease ; and then,
in shallow channels with a steep gradient, the
surface of the water, instead of having a smoothed-
out or striped look, is found to be covered with
rounded excrescences travelling at about the
speed of the stream. The smoothed surface is,
in fact, an optical illusion. An excellent oppor-
tunity of following up this observation was afforded
me by journeying up and down on the funicular
cars from Territet to Glion, and from Vevey to
Mont P61erin. The appearance of the water when
coming down (the car sometimes travelling at
almost exactly the speed of the current) was very
different from that when going up, or when standing
on the banks. On the Mont P61erin funicular,
when going up, the only surface inequalities visible

AND OTHER WATER WAVES 301

were diagonal standing waves. Coming down, a
knobbly surface travelled along with us, one of
the knobs of water occasionally bursting. There
were no regular roll-waves in this case, but in
that of the Territet-Glion conduit I was able from
the car, which travelled down at nearly the same
speed as the roll-waves, to observe that, in addi-
tion to the larger waves with front extending the
whole breadth of the stream, there were innumer-
able embryo waves, which seemed to be in continual
course of production. How embryo waves become
united into relatively large roll -waves, regular in
form and travelling in orderly procession, can be
better explained from the phenomena observed in
the conduit of the Griinnbach, at Merlingen, on
the Thunersee, Switzerland, during 1904 and
1905.

Observations on the Conduit of the Griinnbach
( M erlingen, Thunersee )

The Griinnbach is the torrent flowing through
the great gorge of the Justisthal to the Thunersee.
The lower portions are first controlled by a series
of weirs causing waterfalls, and, finally, for the last
1,360 feet, the stream is carried in a straight, paved
conduit about 7 feet deep and 15 feet wide, with
nearly vertical sides, the form and structure being

302 WAVES OF THE SEA

shown on the Plate . The lip of the conduit is several
feet above the highest level of the lake, and the
water leaps the outflow as a waterfall. The object
of a structure so considerable as this conduit is,
not the accommodation of the usual flow of water,
but the provision for the great rush which takes
place when a thunderstorm bursts over the Justis-
thal, especially in springtime before the snows are
melted. Under ordinary conditions, even in wet
weather, the average depth of water in the conduit
is seldom more than 3 inches. The speed is so
great, however, on a slope nowhere less than
i in 14, that the discharge is not insignificant.
With a depth of about 2 inches, the speed is about
i o feet per second ; but if the depth were increased
to 3 feet or 4 feet, the speed would, no doubt,
be very much greater.

The last of the series of waterfalls above the
conduit discharges the stream into a pool, whence
it flows over a piece of slightly hollowed pavement
for 5 i feet, when it enters the rectangular channel .
The discharge of the upper waterfall is steady, in
the sense that there is no cadence, the minor
flickerings of one part neutralising those of
another. The pool is of irregular depth, and the
discharge from it has no regular pulsation. Never-
theless, as the water rushes over the slightly

ROLL-WAVES IN THE GRUNNBACH CONDUIT, LOOKING UP-STREAM,
303

AND OTHER WATER WAVES 305

hollowed piece of pavement, it can be seen to flow
gushingly, for the greater regularity of cross -
section to some extent co-ordinates the flickerings,
and the smaller depth tends to increase the gushi-
ness of flow, as has already been explained.

At the entrance to, and for the first few yards
of, the rectangular, flat-bottomed, paved channel
these embryo roll -waves pass the eye in too rapid
succession to be accurately counted, but there are
about 1 20 per minute. They are here little more
than ripples, and the fronts, which face down-
stream, are free from white froth. As we walk
down the bank of the conduit, we observe that a
regularising process is at work, which, in a short
distance, produces from this hurried and con-
fused crowd of progressive wavelets an ordered
series of roll -waves of greater amplitude, with
foaming fronts facing down -stream, extending
across the channel in a straight line at right angles
to its axis. On June 6, 1904, at 465 feet from,
the entrance to the paved channel, there were
notable larger waves ; but there were many minor
ones also, and the appearance was still somewhat
confused. At a distance of 567 feet from the
entrance to the paved channel there was no more
confusion, a distinct series of waves, 33 per
minute, passing the observer ; whilst after travel-

306 WAVES OF THE SEA

ling another 554 feet (or 1,121 feet in all), there
were 20 waves passing every second ; the height
and length of the waves having increased propor-
tionately, and the depths at the troughs being
correspondingly diminished. The current is much
accelerated at and near the crests, and considerably
diminished in speed at the troughs, as is readily
seen by watching the progress of small floating
bodies.

At the outfall into the lake, a further dis-
tance of 240 feet, or 1,361 feet in all, the waves
were 1 7 per minute . The outfall of water is often
twice or three times as great when a roll -wave crest
arrives as at other times. The fall of the roll-wave
is accompanied by a booming noise, and the flash
of the outflowing water is sometimes visible at a
distance of 2 miles.

On September 16, 1904, with a uniform depth
in the upper part of the channel of 3 inches to
3^ inches, as nearly as could be determined, the
water at the outflow had a depth of 8 inches at
the crests and i J inches at the troughs of the waves .
The time of flow of the water from entrance to exit
of the paved channel was 90.2 seconds — a short
time indeed for the evolution of such a cadence
from a mere flicker, and for the development of a
wave amplitude from, say, ^o inch to at least 6

ROLL-WAVE LEAPING THE OUTFALL OF THE GRUNNBACH CONDUIT.

307

AND OTHER WATER WAVES 309

inches. The distance between the wave-crests in
the lower part of the channel was on this day
66 feet.

The process of growth is easily observed, the
larger wave -crests catching up the smaller and
incorporating them, the wave -velocity being greater
where the depth is greatest. As soon as the differ-
ence of depth between troughs and crests of the
larger waves becomes considerable, the process of
incorporation of the smaller wave -crests is much
hastened ; for when they are situated in the troughs
of the larger waves their total speed is much
diminished.

On several days the speed of the current and
the rate at which the waves travelled past the
observer were determined. The latter, which may
be called the apparent speed of the waves, is the
velocity of the current plus the rate at which
the wave travels through the water in a down-
stream direction. Deducting the velocity of the
current from the apparent velocity of the wave,
we obtain the true velocity of the wave. If this
should be found to be nearly the same as the calcu-
lated velocity of a long wave (viz., V = >/ g h,
where V = velocity, g = acceleration of gravity,
and h = depth, all expressed in feet and seconds),
it may be safely concluded that these roll -waves

310 WAVES OF THE SEA

progress by gravitational transmission of pressure
in the manner postulated in the theory of long
waves. The conditions are so different from those
usually contemplated for long waves that such a
test is far from superfluous.

True Velocity of Roll-Waves in the Grunnbach Conduit.

Calcu-

Observed

Observed

Observed

lated

Date.

Depth

Depth

Speed

Speed

at Crest.

at Trough,

(F.P.S.).

(F.P.S.;

Aug. 26, 1904

... 2-5 in.

i in.

2'06

2-58

Sept. 8, 1904

... 4-0 „

i „

3^75

3'27

June 15, 1905

••• 4'5 „

2 „

3'54

3'47

There was, however, one observation which did
not agree with the theoretical numbers, and was
also out of accord with the other three observa-
tions, viz. :

Date.
Sept. 16, 1904

Observed
Depth
at Crest.

... 8 in.

Observed
Depth
at Trough.

1*5 in.

Observed
Speed
(F.P.S.).

3

Calcu-
lated
Speed
(F.P.S.).

4 '60

Or, putting it the other way, the calculated depth
at crest for the observed speed is only 4.6 inches,
the difference from the observed depth of 8 inches
being too great for error of observation. This
was the occasion of greatest observed wave de-
velopment on the Grunnbach, the depth of
1.5 inches at trough being certainly small for the

AND OTHER WATER WAVES 311

transmission of a wave with an amplitude from
trough to crest of 6.5 inches. I think the dis-
crepancy, however, is to be explained not so much
by this circumstance as by an error introduced by
the determination of the velocity of the current.
I made a note at the time that the floating objects
which I was observing were several times caught
and pushed along by the foaming front of the
waves . Thus their speed was probably greater than
the average velocity of the current, making the
wave-velocity come out too low.

On some occasions the failure of the stream
just before the arrival of the crest was distinctly
noticeable — a fact in itself, and apart from the
measurements, indicating that the waves differ more
in appearance than in essence from ordinary waves.
The waves had not completed their growth when
they reached the outflow; but if the length of
the conduit could be much increased, we should
doubtless see the last part of the course traversed
by a series of waves of uniform height, length, and
speed, as occurred after a short run in the
shallower, but smoother, conduit of the Territet-
Glion Funicular Railway.

The following table shows the number of wave-
crests passing per minute at different distances from;
the entrance of the channel, taken on several days,

16

312

WAVES OF THE SEA

with the depth of water in the upper portion of
the channel varying from i . 5 inches to 3 inches
or 3.5 inches.

Date.

Distance in
Feet from
Origin.

Period in
Seconds.

Distance —
Period.

Ratio of
Period to that
at Outfall.

June 24, 1904

465

2-14

2173

0-458

M

567

—

—

II2I

4-00

280-2

0-856

,,

1361

4-67

291-4

I'OOO

June 25, 1904

465 '

—

„

567

2-OO

283-5

0-467

„

II2I

3-16

3547

0-737

„

1361

4-29

317-2

I'OOO

June 26, 1904

465

—

—

„

567

1-82

311-15

0-513

n

II2I

3-00

3737

0-851

..

1361

3'53

385-6

I'OOO

June 28, 1904

465

1-97

236-0

0-414

„

567

—

—

—

M

II2I

—

—

—

5>

1361

4-76

285-9

rooo

Sept. 1 6, 1904

465

1-50

310-0

0-411

„

567

—

—

—

II2I

—

—

—

»

1361

3-65

370-0

I'OOO

The period on any one occasion — i.e., for
a particular depth of water— is proportional to the
wave-length. If the wave-lengths were propor-
tional to the distance run, for a particular depth
of water, then the distance run divided by the
period in seconds would be a constant .quantity.

AND OTHER WATER WAVES 313

for any one day. The figures show a less simple
relationship, the period increasing somewhat slowly
at first, although towards the end of the course the
increase is more nearly proportional to distance
run.

It will be seen from the tables that the rate of
increase of period is nearly the same on different
days when the depths differed by moderate
amounts. In order to make a thoroughly satis-
factory examination of such relationship it would
be necessary to know, not only the distance run
by the wave relatively to the bank, but also the
distance travelled through the water, which was
not determined on every occasion.

The following figures show the degree of irregu-
larity in the intervals between successive wave-
crests at the outfall. This measurement, made
with a stop-watch, is very easily taken, and is free
from the uncertainties which attended the measure-
ment of depth, and, to some extent, of the velocity
of current.

The intervals between Successive Wave-crests at Outfall of the
Griinnbach. In Seconds.

5, 3, 4, 8, 4, 7, 4, 4, 2, i,

5, 4, 5, 6, 4, 5, 3, 3, 4, i,

6, 3> 4) 2, 4, 4) 3, if 7, 2,

7, 9, 2, 9, 8, i, 10, i, 5, 6,
i, 4, 9> J> 6, *i 2> 6> 7, 4,

314

WAVES OF THE SEA

6 waves had a period of i second
„ „ 2 seconds

> » M 3 »

» » v 4 11

11

wave

7
"

9

10

Reverting from figures to the description of
appearance, I may note the following additional
circumstances observed in the Griinnbach conduit,
which tend to elucidate the origin and mode of
growth of the train, or series, of roll-waves.

The first noticeable agency of growth is the
catching up of the smaller waves by the larger,
due to more rapid motion of the latter ; but &
new factor (not possible on the cement floor of
the Glion conduit) is the increase of amplitude
as the front passes over each transverse ridge of
the flag pavement. It appears, therefore, that we
have here a case of a progressive wave increased,
not merely by friction with a flat bed, but also by
passing over perceptible transverse inequalities.
The depths being small, the reasoning previously
employed to explain discontinuous flow as result-
ing from local increase of depth still holds
good.

ROLL-WAVES IN THE GRUNXBACH CONDUIT, LOOKING DOWN-STREAM.

315 -

AND OTHER WATER WAVES 317

There is one portion of the conduit paved more
smoothly, in larger and better trimmed blocks, than
the rest. Here, when there was little water, the
wave development proceeded best ; afterwards, on
entering the rougher part, the wave was somewhat
broken up. But when the depth of water was
greater, there was but little growth of the wave in
passing over the smoother pavement, the growth
becoming more rapid when the wave began to ride
over the transverse joints of the rougher pavement.
Thus, for the best development of the wave, there
should exist a certain proportionality between the
amplitude of the transverse corrugation and the
depth of the water.

The longitudinal joints of the pavement tended
somewhat to destroy the transverse wave, especi-
ally when any irregularity of channel caused
the wave to pass somewhat obliquely across
them.

There was a good deal of lateral wave motion,
which sent a considerable wash against the sides
of the channel ; but these, being nearly vertical,
reflected the wave back again, and thus tended
to keep the front transversal. About half-way
down the conduit the slope is somewhat abruptly
diminished, remaining thereafter less than in the
upper half. It was always a matter of surprise to

'
318 WAVES OF THE SEA

me that no obvious change in the waves occurred
when the gradient diminished.

The uniformity of depth in this conduit is, of
course, a most important factor in preserving the
transverse waves, and the unequal depth (in cross-
section) in natural streams equally tends to prevent
their development. I saw an excellent example
of this at St. Maurice, in the Rhone Valley, where
a paved conduit terminated in a channel encum-
bered by gravel, through which the stream had
made for itself the usual winding course, with
unequal depths on the two sides. The conduit
delivered strong transverse roll-waves at intervals
of a few seconds, each of which vanished almost
instantaneously upon entering the winding channel
of unequal depths in cross -section.

Since the velocity of the wave relatively to the
banks is that of the current plus the true wave-
velocity, and the latter is greater for deep water,
it follows that the wave -front loses its trans -
versality when the cross -section of the stream is
not uniform, and this is more marked in down-
stream roll -waves than in up-stream bores (where
current and wave oppose one another). This is
one reason why down -stream progressive waves are
so much less familiar than up-stream bores.

AND OTHER WATER WAVES 319

Observation of Roll-waves in the Conduit of the
Guntenbach, Gunten, Thunersee, Switzerland

The Guntenbach, which drains a smaller valley
than the Griinnbach, runs for the last 1,000 feet
of its course in a paved conduit, with a practically
uniform gradient of i in 22, as measured with a
small Abney level. The sides of this conduit are
sloping, not vertical, as in the Griinnbach ; the
paving -stones are more irregular in form, and
the depressions at their joints are deeper, as well
as less regular. No roll-waves were ever seen
in the upper part of the conduit ; ! they originated
suddenly lower down, generally at or below the
lowest bridge, which was 370 feet from the outfall.
Thus the course of events differed considerably
from that in the Griinnbach, where the waves could
be watched through all their stages of development.
On the roughly-paved Guntenbach it took much
watching to discover the origin of the roll-waves.
I would stand near by where they generally com-
menced, watching the water closely ; then, to the
right or to left of where I was looking, I would hear
a sudden sound like that of the word " flop," and,

1 The upper part of the conduit has in many places deep
longitudinal grooves in the central paving-stones. The cross-
section of the lower part is more nearly uniform.

320 WAVES OF THE SEA

on turning quickly, there would be a fully-formed
roll-wave extending transversely across the whole
channel. Once formed, they were never subse-
quently dissipated, but, on the contrary, grew
quickly as they travelled through the water. The
reason for their growth was not evident from mere
observation. The outfall into the lake was in fairly
regular cadence, the phenomenon being similar to
that of the Griinnbach, though not so crisp. This
want of crispness was evidently due partly to the
sloping sides, which did not keep the wave -front so
perfectly transverse as the Griinnbach. The Plate
is from photographs taken at intervals of a few
seconds, the first photograph showing the outfall of
the Guntenbach at a wave -trough, the second at
a wave -crest.

After watching for three months, I came to the
conclusion that the mode of origin of the waves
in the Guntenbach was entirely different from that
in the Griinnbach. In the former there were some
slight, long depressions extending the whole width
of the pavement which were almost masked by its
general roughness. The most marked depression
was under the lowest bridge, and somewhat con-
cealed thereby. I found that the roll-wave started
here more often than at any other point, and I
noticed that up-standing edges of the pavement

OUTFALL OF THE GUNTENBACH AT THE WAVE-
TROUGH, AND (A FEW SECONDS LATER) AT
THE WAVE-CREST.

321

AND OTHER WATER WAVES 323

stones made something resembling a dam at
the lower end of what was, in fact, a pool.
Here the wave seemed to originate by the sudden
emptying of the pool. The depth being very small
(generally not more than ij inches or 2 inches
on the sill), and the pool being several yards
long, there was great sensitiveness to the slight
flicker always perceptible in this and similar
streams. Wherever in the course of these irregu-
lar flickerings a slight deficiency was followed
suddenly by a slight excess, the latter would have
to burst a way across the shallow sill as a small
wave with a steep front ; and this, clearing the
way before it, drained the pool considerably, thus
preparing for the formation of a second wave.
This reasoning, I repeat, is only valid for a certain
scale of things. If the dimensions be greatly
changed, the relative importance of the factors
would also be changed. This origin of the wave
by the filling and emptying of a sort of pool
accounts for the fact that the interval between
successive waves on the Guntenbach was never less
than several seconds, whereas on the Griinnbach
the period at first was much less than a second.
When the Guntenbach was flowing sluggishly, with
less water than usual, the period was always a long
one, for it took a long time to fill and empty the

324 WAVES OF THE SEA

pool When there was very little water, the
formation of the waves appeared to be capricious,
a long interval occurring, during which the stream
flowed steadily, to be succeeded by a fairly regular
series of waves. On the small conduit of St.
Maurice,1 already referred to, this capriciousness
was still more marked, and more obviously de-
pended upon some slight variations in the strength
of the stream, caused one knows not how. It is
evident that in this case we have something rather
like the roll-waves of the Tees on a minute scale.

The average depth in the conduit of the
Guntenbach was difficult to determine on account
of the inequalities of the pavement, but 2 inches
was a usual amount. The speed of the current
was determined at 8.5 feet per second, and the
true speed of the wave at approximately 2.25 feet
per second. On one occasion the depth at crest
at outflow was estimated at 3.5 inches, and at the
trough 2 inches.

On more than one occasion a thunderstorm filled
the conduit to a depth of from 5 inches to 9 inches,
and then there was absolutely no roll -wave or

1 Average period of waves, 13-5 seconds. The conduit was
only 3 feet wide, and paved with blocks extending the whole
width, so that there were no longitudinal joints, which in the
Guntenbach tend to spoil the wave by making unequal depths in
cross-section.

THE GUNTENBACH WITH TWO ROLL-WAVES.

325

AND BOTHER WATER WAVES 327

cadence in the outflow. The depth was, therefore,
apparently too great for the effect of frictional re-
sistance to produce an intermittent flow, and the
pools of the pavement were now too insignifi-
cant to act as they did with a smaller depth of
water .

I have never seen a stream with a uniform
depth of more than 4 inches adopt spontaneously
the intermittent flow in a series of roll-waves. The
conduit of the Chauderon River at Montreux, with
a depth of 6 inches, did not flow thus ; neither did
the much larger Veveyse River, in its conduit at
Vevey, flowing swiftly at the time of snow-
melting, with a depth of 48 inches.

Nevertheless, I found (after my eyes had been
trained by watching well-marked roll -waves for
some months) that waves progressing down-stream
through the water co -exist with stationary waves
in shallow streams, and may even be detected in
deep ones, although they do not (except if caused
by floods) there develop or grow so as to become
conspicuous or important relatively to the other
phenomena of flow. Thus (commencing with the
Guntenbach ), on looking closely at a standing wave
(in which the depth of water was only about
2 inches) I noticed that the water here flowed
gushily — i.e., the excrescence of the bottom, which

328 WAVES OF THE SEA

caused a stationary wave, also caused progressive
waves. Close to Schloss Ralligen (between Gunten
and Merlingen) is a short and very steep conduit,
3 feet wide, with a pavement of ribbed form, each
rib extending quite across the conduit. The
distance from the summit of one rib to that of
the next is 6 inches, and the line of the crest of
the ribs is about 0.3 inches above the line of their
troughs. The depth of water covering the crests
of the ribs was 0.5 inch. The appearance of
the whole is that of a cascade with transverse
bars of white foaming water, situated at the
summit of each rib, these transverse bars showing
(as is usual in cascades and waterfalls of small
dimensions) a longitudinal striping, so that the
form of the standing waves caused by each
rib is that of a comb, the back of the comb
representing the principal transverse line of white
water, and the teeth the smaller longitudinal lines
of white water. This, with a slight flicker, was all
that I saw in 1904. But in 1905, being now aware
how stationary objects fix the eye so that it cannot
distinctly see moving things,1 I tried the expedient,

1 Conversely when moving bodies are many and conspicious
the attention is distracted from stationary objects. A good
example of this may be obtained by visiting the vicinity of the
Mansion House in the City of London early on a Sunday
morning. Those who think that they are familiar with the sur-

AND OTHER WATER WAVES 329

which I had often found useful, of half-closing
the eyes, so as to render the outlines of the
stationary objects indistinct. I saw immediately
that roll -waves extending the whole breadth of the
conduit were dashing down the channel all the
time with great speed, and at intervals of not more
than half a second. Thus by varying the method
of looking, it became possible to appreciate clearly
the dual aspect of the phenomena of the flow. The
roll -waves were no insignificant part of the whole
flow, the apparent predominance of the stationary
waves being due more to optical advantage than
physical superiority. I made a similar observation
in the roughly-paved steep conduit which carries
the Verraye torrent at Veytaux (Switzerland) in
the lower part of the course below the lower road.
In deep streams the down-stream progressive
waves are difficult to observe, but I have no
doubt that they are normally present wherever
waves exist at all. If the eye be allowed
to follow the stream, it is often easy to see
some travelling inequalities of surface in the
deep water, especially when the light is low, but
it is not always clear whether they are truly waves ;

rounding buildings from frequent, or even daily, visits will
probably notice many architectural features which escaped their
attention during the hours of busy traffic.

330 WAVES OF THE SEA

still less is it usually possible to know if they are
travelling through the current down -stream. If,
however, the streams have gently shelving shores,
and especially if these be smooth, the direction of
the waves which come in upon them facing
diagonally, but on the whole down-stream, indicates
clearly that there are in the deep water progressive
down -stream waves invisible only on account pf
their flatness.

Should I have the opportunity to revisit the
Niagara Whirlpool Rapids, I might perhaps detect
the existence of down -stream waves there, although
I could not do so before I had daily practice in
their detection. The fact that waves which have
not a length great as compared to the depth con-
tinually multiply themselves, would of itself account
for the fact that such waves tend to die out rather
than to increase in deep streams. Unequal depth
of cross -section, as has already been mentioned,
also tends to do away with them, causing them
to discharge themselves upon the banks.

UPPER PART OF FALLS AT NIAGARA, SHOWING UNBROKEN WATER.

331

CHAPTER XII

The sounds of running water — The gushing motion of cataracts
— Conical structures produced by the break-up of a water-
fall— The wave-track of a ship.

On the Sounds of Running Water

WHEN we watch the standing waves of a shallow
stream and think, perhaps, of the steady state
to which it is supposed to have attained, the
pleasant but irregular sounds which greet the ear
are evidence of momentary variations in this state,
and of disturbances passing down -stream. The
sound of the foaming cusped wave, if continuous,
would, indeed, indicate a steady condition, although
the motion at that spot is " discontinuous " in the
sense that the thread of the stream is there broken ;
but the breaking of the cusped wave is, as a rule,
intermittent. From time to time also a pretty tinkle
catches the ear, a single sound, presently repeated
in another place. A careful study of these sounds
will greatly assist the eye in discovering the details
of the stream's motion. It is upon the sounds as

334 WAVES OF THE SEA

much as the appearance that the poetical student
of Nature has relied for conveying his impressions
of these scenes. Tennyson's phrase to " babble
on the pebbles " is a familiar example. When he
speaks of the " drumming thunder " of a great
waterfall, he records by ear the partial intermittence
superimposed upon a steady motion, which will
be dealt with in the next section of this paper.

On Gushing Motion in Cataracts and on the
Conical Structures produced by the Break-
up of a Waterfall

We have seen how in a swift shallow stream the
frictional retardation of the layers next to the
bed imparts a gushing motion to the water, which,
when the channel is straight and of uniform cross -
section, produces a train of long waves of the
bore form with foaming fronts transverse to
the current, following one another in regular suc-
cession down the stream. In cataracts and water-
falls there is also a gushing motion, but it is
irregular. In hilly or mountainous districts the
noisy cataract of white water replaces the clear
babbling brook with standing waves which is
characteristic of undulating country, or the silent
stream of the plain with its curling currents and

NIAGARA FALLS, SHOWING FLEECY APPEARANCE PRODUCED BY THE BREAKING OF THE

FALLING WATER.

335

AND OTHER WATER WAVES 337

smooth surface. The broken water of the cataract
passes too swiftly for the eye to follow its motion,
and the streaky appearance is evidently due to
this circumstance . On thrusting my hand into the
flying water of a small cascade which comes foam-
ing down through the Forest of Chillon I found
that the real intermittence of the optically con-
tinuous motion was at once apparent, for instead
of being subjected to a pressure, as from a
current, the hand experienced a succession of
sharp buffets .

In a cataract descending the right bank of the
Gorge of the Chauderon, at Montreux, I saw well
the transition from the rush of the cataract to the
leap of the waterfall. Along reaches of lessor
steepness the water kept to its bed, yet all whitely
foaming, being tofn to drops by friction with its
bed ; but steeper reaches were leaped by the shower
of water, the leap being what one calls a waterfall.
By a cataract I mean that extreme case of a torrent
in which the water is all foamingi.

A low waterfall of i foot or 2 feet in height,
unless delivering water already in violent motion,
generally presents to the eye a number of brilliant
vertical stripes, having a lustre as of polished metal,
continuous from top to bottom, and practically
steady in position.

17

338 WAVES OF THE SEA

The appearance of the water in a high waterfall
is quite different, for the water is more opaque or
milky, there are none of these brilliant stripes, and
( especially if the eye be allowed to follow the water
in its fall) it is seen to be patchy, the patches being
more or less conical or V-shaped. Photographs
of waterfalls sometimes show them, when the
shutter of the camera works with sufficient rapidity.
Livingstone thus describes these characteristic
bodies as he saw them at the Victoria Falls of the
Zambesi : ' " On the left side of the island we
have a good view of the mass of water ... as
it leaps quite clear of the rock, and forms a thick,
unbroken fleece all the way to the bottom. Its
whiteness gave the idea of snow, a sight I had
not seen for many a day. As it broke into (if I
may use the term) pieces of water, all rushing on
in the same direction, each gave off several rays
of foam, exactly as bits of steel, when burned in
oxygen gas, give off rays of sparks. The snow-like
sheet seemed like myriads of small comets rush-
ing in one direction, each of which left behind
its nucleus rays of foam. I never saw the ap-
pearance referred to noticed elsewhere. It seemed
to be the effect of the mass of water leaping at once

1 " Missionary Travels in South Africa."

I

THE BREAKING WATER OF NIAGARA FALLS, TAKEN FROM S.S. MAID-OF-THE-MIST.

339

AND OTHER WATER WAVES 341

clear of the rock, and but slowly breaking up into
spray."

The phenomenon is very noticeable in the com-
paratively thin sheet of water which forms the
American Falls at Niagara, but the 2o-feet-thick
green water at the " Horse-shoe " retains its
homogeneity much better. This fact indicates
that the partial break-up of a waterfall is not
due so much to friction with the air as to other
causes, chief among which is, presumably, the
dynamically unstable condition of a sheet of water
falling under the constant acceleration of gravity.
This partial breaking up, which, as Livingstone
well indicates, is an early stage of the process by
which the water will, if it falls far enough, be
finally resolved into spray, must be greatly hastened
in the case of a waterfall fed by a stream already
markedly intermittent in its motion. I have already
described (p. 273) the unsteady motion of the shal-
low water in the rapids above the American Falls.
The late Professor J . Tyndall says « of the Falls :
" The descent finally resolves itself into a rhythm,
the water reaches the bottom of the fall in periodic
gushes." And Captain Basil Hall, in the Cave

1 u Niagara," a discourse delivered at the Royal Institution of
Great Britain, April 4, 1873, published in the Fragments of Science
(p. 178).

342 WAVES OF THE SEA

of the Winds, behind the falling sheet of water,
found that the barometer pulsated. The cones in
the American Falls appeared to follow one an-
other in swift succession, but in watching the fall
of the water of the Tschingelbach, at Burglauenen,
near Grindelwald, Switzerland, May 22, 1904,
where the cones were very perfect, but the
volume of water small, I concluded that the
apparent swiftness at Niagara was due to the great
number of cones passing confusedly. So also do
snow-flakes seem to pass the eye rapidly when
we look through a long column of air, standing out
of doors, but if we watch from the interior of a
room, so that no flakes pass close to the eye, it is
seen that for the most part they are subsiding
slowly through the air.

The conclusion was confirmed when I next
viewed the Tschingelbach Fall. The amount of
water was then much diminished, and the fall was
coming down in several separate threads of water
instead of in a broad sheet. The cones in each
of these threads of falling water followed one
another in an orderly and unhurried manner,1 the

jjjfa: iwu.

1 In a narrow waterfall at Isetwald, on the Lake of Brienz, I
saw the cones, which were close together near the commence-
ment, become widely separated as their velocity increased under
the action of gravity.

FALLS OF THE TSCHINGELBACH, BURGLAUENEX.
343

AND OTHER WATER WAVES 345

speed of each individual cone increasing as it fell,
the pointed shape sometimes becoming more pro-
nounced, until at last the forces making for
disintegration dissipated the structure in spray.

This appearance is closely paralleled in the case
of the snow avalanches seen from Grindelwald
when they leap the edge of precipices on the Eiger
or the Mettenberg. There is the same appearance
of cones amidst the white clouds of snow, the cones
increasing in speed, with sharpening points, and
finally bursting in dust. The drawing out to finer
lines as the cone descends is easily understood
if we remember the acceleration of gravity, and
the air -resistance at the edges, and the greater
retardation of the finer particles. In water it is
the same. When jets are thrown upwards, as from
the " Horse-Shoe " at Niagara, the sharpening of
a cone proceeds still more quickly.

On visiting the Tschingelbach in June, 1905,
I saw the water -cones in very fine development,
and they were even united into roughly transverse
bands. Between these the veil of misty spray was
thin and semi-transparent. I then perceived that
there was a local cause for their unusually fine
development in the last big leap of the fall, for
the water above slides over a steep, face of rock,
where it g;oes into fairly well defined roll -waves.

346 WAVES OF THE SEA

The ranging of the water -cones in roughly trans-
verse bands is due to this cause ; they gradually
lose their transversality as they descend.

Below a waterfall near Matten, Grindelwald, the
waters flow steeply over a bed of rock, which gives
a uniform, small depth to the stream, which flows
in roll -waves owing largely to the initially dis-
continuous character of the motion of the falling
water.

Below one of the principal leaps of the Giessbach
Falls (Lake of Brienz) I also saw down-stream
waves, which, however, soon lost their transver-
sality on entering the swift channel of exit from the
pool.

When any waterfall or cascade discharges into
still, deep water, progressive trochoidal waves pro-
ceed outwards in all directions, as may be prettily
seen, for instance, in the ornamental waters of the
public gardens at Buxton.

On the Wave -track of a Ship as seen on the Swiss

Lakes

The late Lord Kelvin described l the dual system
of waves which originates at the bow of a ship.
They are the diverging series, the fronts of which
1 " Popular:Lectures and Addresses/'

347

AND OTHER WATER WAVES 349

make an angle with the ship's course, and the
transverse series which lie across her course, travel-
ling in the same direction. Leaving out of account
the first two or three diverging bow-waves, every
wave of this series has a front concave to the
direction of advance. The transverse series have
fronts convex to the direction of their advance.
They are flatter than the diverging waves, and
therefore less conspicuous if the water be ruffled.
This whole system of waves is bounded on the
right and left by two imaginary straight lines, each
making an angle of 19^° with the ship's course.
A similar dual series of waves originates from the
stern. The pattern of waves originating from the
bow or from the stern, as deduced mathematically,
satisfies all that is usually visible at sea.

Being anxious to see ship-waves undisturbed
by the waves of swell or wind, I decided to make
observations on the placid waters of Swiss lakes.
I began on the Thunersee during the fine summer
weather of 1904, and continued the observations
at Montreux, on the Lake of Geneva, in the spring
of 1905. On still mornings the surface of the
Thunersee was frequently as smooth as plate -glass,
without any ruffle or darkening by even the gentlest
breeze.

Under these conditions I found that the thwart

»
350 WAVES OF THE SEA

waves are more conspicuous relatively to the
diverging waves than in rougher water, and that
their relative prominence is further increased when
the wave -track is viewed from a height. At alti-
tudes of from 300 to 800 feet on the steep slope
above Gunten, opposite to Spiez, the number of
visible thwart -ship waves in a single series must
have amounted to hundreds, the water looking like
corded silk. Unfortunately, the condition of glassy
water is often accompanied by a slight haze, which
makes it impossible then to obtain a strong photo-
graph.

I saw nothing in the appearance of the train of
thwart waves different from that indicated by Lord
Kelvin's diagram, and nothing different from what
is seen at sea, except their greater distinctness.
The case of the diverging waves, however, was
very different. Only the outer edge of the group
presents the uninterrupted concave fronts of the
diagram. Behind this comes a row of notches in
the wave -fronts, which row appears from a dis-
tance as a strongly marked band, light or dark
according to the circumstances of reflection.
Standing near the stern of a steamer, I was able to
see distinctly that the first notch occurred where
a diverging wave of the bow series was crossed
by the first diverging wave of the series which

AND OTHER WATER WAVES 353

originates at the stern. The steamer which showed
this best was the Spiez, a small screw vessel, the
others being paddle steamers. Behind this row
of notches (i.e., nearer to the line of the ship's
course) were many other rows. I have counted
in a good light as many as eighteen of these
" interference bands " as I term them. When the
water is quite glassy they are sometimes more con-
spicuous than the individual waves. The photo-
graph reproduced in the Plate on page 361
was taken on Coniston Water. It shows, not only
the notches in the wave fronts, but, on the right,
the vertical inflection on the crests of the diverging
waves caused by interference. This causes the
crest of the diverging waves to appear as a pair
of dark stripes separated by a broader bright
stripe. The circumstance under which the photo-
graph was obtained was peculiar. There was a
fine drizzling rain when I started for a tour down
the lake by the steam gondola, so I left my camera
behind out of concern for its welfare. I found
that the whole surface of the lake was covered
with a thin scum, which appeared to consist of
a very slight film of oily soot, possibly from the
smoke of the furnaces and factories which are some
miles distant at Ulverston and Barrow. The surface
being in this condition, the vessel left a wonderful

354 WAVES OF THE SEA

train of waves behind. This suggests that by drip-
ping oil out behind a vessel one might succeed
in showing the detailed pattern of the ship-waves
even when there is a slight breeze on a lake. I
had to do the double journey before I could get
my camera, and the photographs were taken on
the second journey down the lake.

The effect of interference between the diverg-
ing waves from bow and stern was noticeable in
the series of breakers which came in upon the
beaches near Gunten after the passage of a steamer
on the Thunersee. The surf was found to be inter-
rupted by lulls during which the breakers were
much smaller.

When observing from the ship, or from a posi-
tion near her, the strong curvature of the fronts
of the individual diverging waves is a marked
feature of the wave -track. When, however, I went
to a considerable height upon the hillsides in order
to obtain a bird's-eye view of the wave -track I
often passed the distance where the waves were
individually distinct or even discernible. Curved
lines then ceased to be seen and were entirely re-
placed by lines which were of rigid straightness
whenever the ship was running a straight course.
When we are near, the case is similar to that de-
scribed in the phrase " one cannot see the wood

w

g co

w S

OH OS

w w

g

Bo

g

355

AND OTHER WATER WAVES 359

for the trees " — i.e., one cannot see the group for
the waves. At a distance, when the trees are no
longer individually discernible, one makes out the
size and shape of the wood. Similarly, when one
can no longer distinguish individual curved waves
one sees at once in startling distinctness Lord
Kelvin's straight -lined boundary, marking the limit
to which the waves appreciably extend. In
addition to this group-line there is another, also
originating at the ship, which marks the rear of the
diverging series of waves. Thus the wave-track
of the ship is generally reduced at a distance to
four straight lines, radiating from the ship, two
on either side.

When this is the appearance presented to the
naked eye a pair of field-glasses reveals the
individual diverging waves. Sometimes also,
especially when the ship is directly receding, the
space between the inner boundaries of the diverging
waves is seen to be filled up by a cross -barring
of the flatter and broader thwart waves.

The visibility of the waves depends upon cir-
cumstances of reflection, and these vary much with
the direction of the ship's course relatively to the
observer and to the bright and dark parts of the
sky and land. Thus, it sometimes occurs that the
straight line forming the outer boundary of the

360 WAVES OF THE SEA

visible diverging disturbance is not the outer edge
of the bow-waves, but the first interference band
of these and the stern-waves. On the approach
of the vessel to Gunten on her way from Spiez
I have noticed individual curved bow-waves come
into view beyond the straight line which had
formed the visible boundary at a greater distance.
On examining the line of the inner boundary pf
diverging disturbance with the field-glasses I have
seen it as a band, skew-barred by the individual
diverging waves. These, I presume, are the rear
members of the stern -waves, which ought to
extend within the limits of the bow-waves. They
here make a somewhat small angle with the ship's
course and are consequently much crowded, with
a very small wave-length.

I have never detected any rearward boundary-
line to the system of transverse waves, nor have
I seen light or dark bands indicative of interference
between those originating from the fore -part and
after -part of the ship respectively.

Ship -waves, which maintain their form un-
changed and keep the same positions relatively
to the moving agent which produces them,
are classed as stationary or standing waves. A
curious progressive condition is, however, seen
among them when two steamers pass one another

w

C5 >

2 ^

i

^

361

363

aa w
H >

§1

§>

=» P

365

AND OTHER WATER WAVES 367

on opposite courses at such a distance that the
outer boundaries of their wave -tracks meet at a
small angle. On the glassy waters of the
Thunersee, and on a bright day, the new disturb-
ances of reflection run along the line of meeting in
short bars of light which flash across the water at
almost lightning speed, by which I mean a speed
much greater than that of any railway train or of
any bird in flight.

INDEX

ABERCROMBY, the Hon. Ralph, observations by, 77
Abernethy, Mr. G. A., on littoral drift, 187
Atlantic Ocean, North, 42, et seq.
Atlantic Ocean, South, 68
Avalanche, conical structures in, 345

BAILLIE, Captain C. W., 114

Bertin, M., on the period of swells, 120

Bore —

In shallow water of seashore, 165

Tidal, 230-262

Tidal, cinematograph of, 254

Bournemouth, observation of period of breakers near, 87-93
Brodie, Mr. F. J., on gales on the coasts of the British Isles, 119
Buckland, Mr. Frank, on the Severn Bore, 245

CATARACTS, gushing motion of, 334-346

Cheret, Captain T. G. K., observations by, 138 note

Chesil Beach, 186-206

China Sea, 40

Coniston Water, waves on, 28

Coode, Sir John, on the Chesil Beach, 204

Currents, vertical and horizontal —

Of waves, 146-154

Of tides, 1 80, et seq.

Curtis, Mr. R. H., on velocities of wind, 109
Cyclones, rate of advance as influencing the character of
waves, 121-128

370 INDEX

DARWIN, Sir G. H., on the theory of tidal bores, 232
Darwin, Major Leonard, observations by, 72
David, Captain Hugh F., observations by, 73
Depth—

To which wave-agitation extends, 141-146

In which waves break, 170

Of water as affecting speed of waves, 85
Duluth, waves in canal at, 34

EDDY of air between wave-crests, 105

FLOOD, mode of advance over dry ground, 229
Forel, Dr. F. A., observations by, 31
Formulae for calculations relating to waves, 25, 86, 309
" Fulls," or beach ridges—

Of shingle, 158

Of sand, 161

GAILLARD, Colonel D. D., U.S.A.—

On the height of waves on Lake Superior, 33
On the depth in which waves break, 171
On the wave-front of a flood, 229

Geneva, Lake of, size of waves, 31

Glyn, Mr. F. R., observations by, 223

Groynes, note on, 199

Griinnbach, roll-waves in conduit of, 301-318

Guntenbach, roll-waves in conduit of, 319-330

HAMIL, Mr., observations by, 29
Helmholtz, H. von, on the steepest wave, 136
Hepworth, Captain Campbell, 114
Howe, Captain Percy, observations by, 75

INDIAN Ocean, South, 68

INDEX 371

KELVIN, Lord —

Observations by, 24, 60

On use of the word u ripples," 236 note

On ship- waves, 346

LAMB, Prof. Horace, on waves of permanent type, 136
Langmaid, Captain C. P., observations by, 138 note
Lions, Gulf of, height of waves, 40

MEDITERRANEAN, Western, size of waves, 35
Montrose, N.B., pulsative rise of tide at, 253
Mud, transport of by waves, 141-146

NIAGARA Falls, break up of water in, 341

Niagara, River, cross-stream progressive waves in, 273-293

OGILVIE, Mr. G. T., observations by, 76
Owens, Dr., 184

PACIFIC Ocean —

North, waves in, 61

South, waves in, 76-78
Paris, Lieut, observations by, 24, 41, 68
Percolation, effect ]of, to promote the building of beaches,

157

Ponds, size of waves on, 25
Portland, tides at, 208
Prestwich, Sir J., on the Chesil Beach, 192

REYNOLDS, Prof. Osborne—
On group-velocity, 94 note
Model estuaries, 252
Richardson, Mr. Nelson B., an experiment on the movement

of shingle, 190

Russell, Mr. J. Scott, on group-velocity, 95 note

18

372 INDEX

ST. LAWRENCE River, waves on, 284

St. Maurice, Rhone Valley, roll-waves in conduit, 318

Sand, movement of, by waves, 158-166

Sand-bank —

The Shambles, 206-210

The Skerries, 211

Sand-banks, shifting of, effect on tidal bores. Sec Severn River
Scoresby, the Rev. William, observations by, 42
Severn River, tidal bore in, 232-262
Shingle —

Action of waves to drive shorewards, 144

Effect of undertow on, 166

'Longshore transport of, 178
Ship-waves, 346

Possible effect on apparent wave-length of waves observed

at sea, 72
Sounds —

Of running water, 333

Of waterfalls, 334
South wold, drift of shingle at, 184
Stevenson, Mr. Thos., table of height of waves as related to

length of fetch of wind, 32
Stokes, Sir G. G.—

Observations on swell by, 93

On the symmetry of waves of permanent type, 135

On the steepest wave, 136
Swell. See Waves

TEES, River, roll-waves in, 223
Territet-Glion, roll-waves in conduit, 296
Tides—

In relation to transport of shingle, 180

At Portland, 208
Tschingelbach, falls of the, 342
Tyndall, Prof. J., 341

UNDERTOW, effect on transport of shingle, 166
Ure, River, roll-wave in, 225

INDEX 373

WATERFALL —

Sounds of, 334

Breaking of water in, 334-346
Waves of the sea —

Height of, in relation to length of fetch of wind, 67

Height of " swell " during storms, 96

Average height in relation to velocity of wind, no. See

also under localities, as " Atlantic," " Pacific," &c.
Length of, discrepancy between wave-lengths determined

by simultaneous and by successive observations of

wave-crests, 78

Length of swell which reaches the shore after storms, 85
Co-existence of waves of different lengths, 101
Calculation of wave-length. See under Formulae. See also

under localities, as " Atlantic," " Pacific," &c.
Mountainous appearance of, 137
Number of, in a single series. See under localities, also

pp. 88-96, 126-127

Period of, mathematical relation to wave-length, 25
Periods of swells observed from near Bournemouth,

87-93

Periods of swells observed from north coast of Ireland,
93-96. See also under localities, as u Atlantic,"
"Pacific," &c.

Undertow of, 166

Velocity of storm waves in relation to average velocity
of wind, in

Velocity of swiftest swells in relation to highest wind-
velocity, 119

Velocity of waves and swell in relation to rate of
advance of a cyclone, 121

Velocity in relation to depth of water, 85

On group-velocity, 94, 119

Action of, to transport mud, 141

Action of, to transport sand, 158

Action of, to transport shingle, 146, 176

374 INDEX

Waves of the sea (continued) —

Action of, to arrange shingle according to size. See

Chesil Beach
Action of, to form patches of shingle upon a sandy

beach, 211

Vertical and horizontal currents of, 146
Waves of rivers —

The flood- wave in, 221-229
Tidal bores in, 230-262
Stationary waves in, 265-273
Cross-stream progressive, 273-293
Leaping waves of Niagara rapids, 283
Down-stream progressive waves, or roll-waves, other
than those caused by flood, 294-330. Sec also Tees,
Ure, Nikko torrent, Severn, Niagara, St. Lawrence,
Griinnbach, and Guntenbach
Velocity of long- wave in, 221
Waves, of ships. See Ship-waves
Wheeler, Mr. W. H., on littoral drift, 188
Wind-
Effective length of fetch of, in North Atlantic, 63
Relation of length of fetch to height of waves, 67
Table of velocities of, 109

Relation of velocity of, to average height of waves, no
Relation of velocity of, to velocity of waves, in
Velocity of, in gales on coasts of British Isles, 119
Velocity of, in gusts, 119

Direction in cyclones, 122. See also Squalls, also under
the different localities, as " Atlantic," " Pacific/' &c.
Veering of, effect on waves, 132
On- and off-shore, effect on breakers and on undertow,

175

Eddies of between wave-crests, 105

UN WIN BROTHERS, LIMITED, THE QBE SHAM FREBB, WOKJKG AND LONDON.

Large Crown 82/0, cloth, 8/- net.

The Age of the Earth, and
other Geological Studies

BY W. J. SOLLAS, LL.D., D.Sc., F.R.S.

Professor of Geology in the University of Oxford.

Illustrated.

THIS volume, while written by one of the foremost of
English geologists, will be found interesting and attractive
by the reader who has no special knowledge of the science.
The essay which gives the book its title sets forth the bearing of
the doctrine of evolution on geological speculation, and par-
ticularly on the vexed question of our planet's antiquity. The
subjects of the other studies include the following : The Figure
of the Earth, and the Origin of the Ocean ; Geologies and
Deluges ; the Volcanoes of the Lipari Isles ; the History and
Structure of a Coral Reef ; the Origin and Formation of Flints;
the Evolution of Freshwater Animals ; and the Influence of
Oxford on Geology.

" They range over a great variety of subjects, including many which are
of sufficiently wide interest to bring the geologist into sympathetic touch with
the general reader. What educated man can fail to be interested in such
subjects, for instance, as the age of the earth, the building of coral islands,
the cause of volcanic action, or the Deluge ? Of all these matters the
Professor discourses pleasantly and well, writing with command of much
scientific learning, yet always readably, sometimes with brilliancy of diction,
and occasionally with a touch of humour." — Athenaeum,

LONDON : T. FISHER UNWIN.

(THE SOUTH AMERICAN SERIES, Vol. II.)

PERU

Its Former and Present Civilization, History and Political

Conditions, Topography and Natural Resources,

Commerce and General Development.

BY C. REGINALD ENOCK, F.R.G.S., Author of "The Andes

and the Amazon."

With an Introduction by MARTIN HUME, a Map, and Numerous
Illustrations. Demy 8vo, cloth, 10s. 6d. net.

OPINIONS OF THE PRESS

"An important work. . . . The writer possesses a quick eye and a
keen intelligence ; is many-sided in his interests, and on certain subjects
speaks as an expert. The volume deals fully with the development of the
country, and is written in the same facile and graphic style as before.
Illustrated by a large number of excellent photographs." — The Times.

" Mr. C. Reginald Enock's elaborate and well-studied descriptive
treatise would be sure of a welcome even were it less well done than
it is. The work unites in the happiest way the best qualities of an official
manual and a personal description. Plentifully illustrated, well informed,
and written throughout in an agreeable style, the book will prove
interesting reading."— Scotsman.

"Mr. Enock's book contains much material necessary for our en-
lightenment of Peru. In every part of his book one finds the evidences
of independent personal observation directed by a mind trained for such
work. The book may be commended to all students, not only of the
West, but of the East."— Morning Post.

"The author treats of Peru as a political and commercial entity, and we
find it even more interesting than his previous work." — The Economist.

" An able and exhaustive study of Peru ; its past, its present, and in-
teresting matter upon which to estimate its future. As one reads through
page after page of clear, concise, graphic description, one feels that one
has actually travelled with Mr. Enock. All will find in this charming
volume matter of interest."— New York Herald.

" The book is a valuable contribution to the literature of Peru, and a
trustworthy summary of our knowledge of the country. The illustrations
are excellent, and give an admirable idea of the scenery." — Manchester
Guardian.

"Mr. Enock's admirable book will certainly direct attention to the
country. No one can read this able and delightful volume without
acquiring much information and great interest in a country of which so
little is known." — Aberdeen Free Press.

" We have read the present book from cover to cover, and it seems to
tell just what is wanted about one of the most interesting countries in the
world. Mr. Enock's ways as a traveller commend him to us." — Country
Gentleman.

(THE SOUTH AMERICAN SERIES, Vol. II.)

PERU

Its Former and Present Civilization, History and Political

Conditions, Topography and Natural Resources,

Commerce and General Development.

BY C. REGINALD ENOCK, F.RG.S., Author of "The Andes

and the Amazon."

With an Introduction by MARTIN HUME, a Map, and Numerous
Illustrations. Demy 8vo, cloth, 10s. 6d. net.

OPINIONS OF THE PRESS.

•' Mr. Enock's work is of the highest value as a careful account of the
existing conditions of Peru. The book is as interesting as it is in-
structive."— Truth.

"A magnificent collection of information on this interesting country.
The author's vivid and eloquent description invests it for us with some of
the glamour it possessed for the Conquistadores of the sixteenth century.
And on closing the book the reader feels tempted to set out at once for
Peru." — Yorkshire Observer.

" A glowing and detailed account, with a mass of information which
will prove of immense service alike to students, travellers, and traders." —
Daily Graphic.

" Mr. Enock's former work was so good that any new effort of his was
bound to attract notice. In the present volume we find all his best
qualities — picturesqueness, literary skill, a dexterous combination of fact
and suggestiveness, a succinct historical survey, and a clearly-drawn
picture of existing social conditions — a book of unusual excellence." —
Birmingham Post.

" The author is already favourably known, and he writes with the same
thoroughness about Peru. One rises from the perusal of so lucid and
exhaustive a survey with a vivid impression. Many fine illustrations
heighten the appeal of this thoroughly practical and welcome volume." —
Standard.

"Mr. Enock has turned out an admirable addition to 'The South
American Series.' Many will welcome his admirable rtsume' of the story
of the Inca Empire and the history of the Spanish Conquest and
occupation of this wonderful country." — Glasgow Herald.

BY THE SAME AUTHOR
THIRD IMPRESSION

THE ANDES AND THE AMAZON

Life and Travel in Peru
With a Map and Numerous Illustrations. Medium 8vo, cloth, 5s.

I

With Photogravure Frontispiece. Each vol., cloth, 12$. 6d. net.

A Literary History of the
English People

BY J. J. JUSSERAND.
VOLUMES I., II. & HI. NOW READY.

OPINIONS OF THE PRESS.

" The execution of the task so far as it has proceeded at present is
masterly. M. Jusserand's erudition is vast, but it does not overwhelm his
sense of proportion nor distort his fine critical sense. . . . M. Jusserand
has many advantages over Taine. His learning and his industry are
certainly not less conspicuous, his critical method is less rigid and
mechanical, his English sympathies are stronger and based on a much
more familiar knowledge of English habits and English modes of thought ;
at the same time, like Taine, he is independent of purely English pre-
judices, and his literary judgments are those of a citizen of the great
republic of letters which knows nothing of national or political boundaries.
Altogether, the work is full of a rare attraction." — Times.

"I envy this man his style, his subtlety, his lightness of touch, his
thoroughness. ... At last we have— or rather shall have when the
«vork is complete — a real History of literature." — Dr. AUGUSTUS JESSOPP
m the Illustrated London News.

" M. Jusserand's qualifications for the task which he has undertaken
are of a high order. . . . We cordially commend both to English and
French readers this brilliant and thoughtful book, and shall look forward
with high expectation to the appearance of its successor." — Athenceum.

" We may say, without contradiction, that the marvellous story of our
literature in its vital connection with the origin and growth of the English
people has never been treated with a greater union of conscientious
research, minute scholarship, pleasantness of humour, picturesqueness of
style, and sympathetic intimacy." — Daily Chronicle.

"The success which has been attained by M. Jusserand, one of the
most accomplished of modern French students of this country, in his
latest enterprise is exceedingly remarkable. He brings to the task which
he has undertaken not merely a deep erudition, but an extraordinary
insight into and sympathy with our national modes of thought and
expression." — Daily Telegraph.

'' We have no work at once so trustworthy and so captivating. . . . M.
Jusserand knows, in a judicial way, what is and what is not evidence
and authority ; he is fresh, animated, eager, yet he never speculates with-
out a warrant. It is his method that is practically an innovation. ... As
we follow his skilful guidance, we see almost in action the making of
England, of English character, and of English literature."

LONDON: T. FISHER UNWIN.

Illustrated. Large crown &vo, cloth, ?s. 6d.

The English Novel in the Time
of Shakespeare

BY J. J. JUSSERAND.
Translated by ELIZABETH LEE.

OPINIONS OF THE PRESS.

" All lovers of Elizabethan literature will welcome M. Jusserand's new
book. ... No Englishman who has written on the period has shown
himself more completely in touch with his subject, or more fully and
widely read in the authors with whom he deals. Want of accuracy or of
literary insight is never apparent, and it is very rarely that even the
smallest feature is missed because of a ' foreigner's standpoint.' . . . M.
Jusserand's book and its exquisite engravings form a most valuable con-
tribution to the study of English literature." — Standard.

" The handling has all the traditional (and sometimes rather imaginary)
Gallic lightness, combined with an accuracy and precision of fact and
reference which is traditionally (there is some, though less, of the
courtesy of imagination here also) German. And in particular M.
Jusserand is very happy in his historical citations serving as parallels to
the novel. In short, it is an excellent book in all ways for the student."
— Manchester Guardian.

"A contribution of permanent value to the history of Elizabethan
literature. The points of interest about this book are so numerous that it
would be impossible to deal with them in detail here. But those who
read for amusement only may be as safely recommended to procure it as
the smaller class who seek to extend their knowledge of the Elizabethan
epoch." — A theneeum.

" We hasten to invite the attention of the reader to one of the brightest,
most scholarly, and most interesting volumes of literary history which it
has been our good fortune to meet with for many a long day."— -Speaker.

" M. Jusserand's book is scientific in the best sense of the word ; it
shows that he has thoroughly explored the literary province he sets
forth to describe, and that he possesses in a high degree the faculty of
critical co-ordination. Yet so lucid is his style, so happy his power of
seizing upon the salient and characteristic features of his subject, that he
never becomes tedious or needlessly discursive. To the general reader,
and even to many who would call themselves students of our literary
renascence, his work will prove a valuable corrective of false preconcep-
tions."— Pall Mall Gazette.

"A work of solid value. The book is full of suggestiveness, and shows
by a variety of incidental remarks the author's mastery of the subject." —
Spectator.

LONDON: T. FISHER UNWIN,

Crown 800, limp cloth, silk sewn, 35. 6d.

The Coming of the Friars

And other Mediaeval Sketches

BY AUGUSTUS JESSOPP, D.D.

Fourteenth Impression.

OPINIONS OF THE PRESS.

M The papers which show Dr. Jessopp at his best are, without doubt
that on 'Village Life Six Hundred Years Ago' and the two on 'The
Black Death in East Anglia.' These reveal that historic imagination, that
power of making the past live again, of taking one beyond the record of
the court roll to the man who signed the deed or the suitors who formed
the court, and finding out how they lived and what they did, which Dr.
Jessopp possesses, perhaps, in a unique degree. Nothing can be more
telling than these essays, with their light touches of humour." — Athenaeum.

" The antiquarian information is conveyed in the most attractive form
by a writer who has nothing of a dry-as-dust in his composition except
the zeal and the patience of investigation, while the East Anglian colouring
gives that individuality and precision to the descriptions which materially
assist the imagination to realise with distinctness the required pictures.
Another peculiar charm of Dr. Jessppp's writings is the freshness of his
sympathies. . . . Always lively, picturesque, and suggestive, he is in
living touch with existing realities, and uses his historic gleanings to
illustrate by contrast or by resemblance some present condition of modern
society." — Guardian.

"In the present volume Dr. Jessopp has developed a power almost
equal to that of the author of ' John Inglesant,' of catching the tone of a
generation that has passed away, and of depicting the condition of Eng-
land in the Middle Ages, unhidden by a veneer of modern conventionalism.
... It would be difficult to find a more graphic picture of old English
life, or one in which even the driest facts of history are presented in a
more attractive garb." — Morning Post.

"It is delightful to have them thus collected, for few writers have
Dr. Jessopp's gift of painting to the life. His ' Village Life Six Hundred
Years Ago' is as graphic and as truthful as one of Richard Jefferies's
sketches of to-day. His papers on 'The Black Death' and on 'The
Building of a University ' are full of teaching ; and no one has ever
discassed with more intelligent appreciation that mediaeval Salvation
Army of which Franciscans and Dominicans were the two main corps."
— Graphic.

" The glimpses into the social life of the past afforded by these essays
will impress all who reflect for a moment upon the marvellous growth of
England." — Daily Chronicle.

LONDON: T. FISHER UN WIN,

By J. CAMPBELL OMAN, D.Lit.

THE MYSTICS, ASCETICS, AND
SAINTS OF INDIA

Fully Illustrated. Cheaper Edition. Demy 8vo, cloth, 7s. 6d. net.

"A work of the first importance. ... In the work of analysis and
description Mr. Campbell Oman has no superior in authority, at least as
far as the races of the Punjab are concerned." — Daily Chronicle.

" A volume of peculiar, almost painful interest." — Observer.

" The able and learned monograph before us will certainly add to his
reputation." — Glasgow Herald.

"A most uncommon and fascinating book." — Birmingham Daily Post.
" A book of genuine value." — Times.

"The fullest study of Indian asceticism from the most modern and
recent aspect which has appeared." — Academy.

" A monumental work." — Civil and Military Gazette.

THE BRAHMANS, THEISTS AND
MUSLIMS OF INDIA

Fully Illustrated. Demy 8vo, cloth, 7/6 net.

This book deals with interesting phases of Indian religious and social
life at the present time. The religion (goddess- worship) of the Bengalis,
who have of late been so much before the world, has a chapter to itself in
which some strange facts in respect to esoteric rites practised by these
people are narrated. The dominant position of the Brakmans is brought
into prominence in a careful study of the Hindu caste system ; while
Religious and Social Reformers, as well as the results achieved by them,
are reviewed in some detail. Descriptive sketches of some curious
festivals and ceremonies are included in this volume. Muslim India has
two chapters devoted to it. As in his previous books the Author has
incorporated in this one various stories and legends, and has drawn
largely upon his own somewhat exceptional experiences. The photo-
graphs and the illustrations supplied by Mr. W. Campbell Oman are
designed specially to elucidate the text.

LONDON : T. FISHER UN WIN, ADELPHI TERRACE.

The Modern Travel Series.

CHEAP EDITIONS OF STANDARD WORKS
OF TRAVEL AND ADVENTURE.

ILLUSTRATED WITH PHOTOGRAPHS OF THE PLACES AND
SCENES DESCRIBED.

Large Crown 8vo, cloth, 55. per volume.

LIST OF VOLUMES.

Through Savage Europe. By HARRY DE WINDT.
In Dwarf Land and Cannibal Country. By ALBERT B.

LLOYD.

In the Land of the Blue Gown. By Mrs. ARCHIBALD LITTLE.
Links in My Life on Land and Sea. By Commander J. W.

GAMBIER, R.N.

The Andes and the Amazon. Life and Travel in Peru.

By C. REGINALD ENOCK.

In Search of El Dorado. A Wanderer's Experiences.

By ALEXANDER MACDONALD, F.R.G.S.
Adventures on the Roof of the World. By Mrs. AUBREY

LE BLOND (Mrs. Main).

Present- Day Japan. By A. M. CAMPBELL DAVIDSON.
John Chinaman at Home. By the Rev. E. J. HARDY, Author

of " How to be Happy though Married."

Other Volumes in Preparation. Please Write for Complete List.
ON SALE AT ALL BOOKSELLERS.

T. FISHER UN WIN, i, Adelphi Terrace, London.

A

CLASSIFIED CATALOGUE

OF

T. FISHER UNWIN'S

PUBLICATIONS.

CONTENTS.

PAGES

I.— INDEX of Authors, some Illustrators and Editors iii— vii

II.— INDEX in order of Titles, including a list of Mr. Unwin's various series

of books ... viii — xv

III. — CATALOGUE, classified under the following subject-headings : —

1. Literary History I — 2

2. Poetry and the Drama 3 — 7

3. Novels, Humorous Works, Short Stories, &c 8—32

4. Essays, Criticisms, Philosophy, &c 33— 34

5. Art and Music 35 — 37

6. Biography, Memoirs, Correspondence, &c 38—46

7. History and Historical Literature 47 — 59

8. Politics, Economics, Free Trade, &c. 59—66

9. Geography, Travel, Mountaineering, &c. ... ... 66 — 74

10. Natural History, &c 74— 77

ir. Religion and Education 77 — 80

12. Domestic Literature 81 — 82

13. Books for Children ... 82—85

14. Varia 85—87

15. " The New Irish Library " " The Welsh Library " and " The

International Review " ... 87

Book Buyers are requested to order any volumes th*.y
may require from their bookseller. On receipt of a post-
card, Mr. Fisher Unwin wi'.l be pleased to furnish the
address of the nearest local bookseller where the works
detailed in this list may be inspected.

Should any difficulty arise, the Publisher will be happy
to forward any book in the list to any country in the Postal
Union, on receipt of the price marked and a sufficient sum
to cover postage, together with full Postal Address. Any
amount forwarded in excess will be returned to the sender.

Remittances may be made by Cheque, draft on London^
Money Orders, or Stamps.

After reading this Catalogue, kindly pass it on to some
book-buying friend, or send an address to which this or
future editions may be sent.

1909.

INDEX of AUTHORS, some ILLUSTRATORS, and EDITORS. iii

INDEX of AUTHORS, some
ILLUSTRATORS, and EDITORS.

Abrahams, Israel i, 79

Adam, Mme. Edmond
Adams, Arthur H/ ,

PAGE

Adams, Francis 66 j Besant, Annie

de Benyowsky, Count 46

Bernhard, Oscar 85

Berry, T. W 77, 85

Adams, W. Augusta

Aesop

Aho, Juhani

Albright, Mrs. W. A
Alexander, Mrs. . . .
Alien

59

Allardyce, Paul 77

Amber, Miles 8

Andreief , Leonidas 8

Andrews, Katherine 8

Arbuthnot, Sir A. J 39

Archer, Laura M. Palmer 8

Archer, T. A 47

Archer, William 5

Bigelow, John 33

Bindloss, Harold 66

Birch, Walter de Gray 47

Blacker, J.F 35

Blake, Bass 1 1

Blake, B.C. n

Blind, Mathilde 3, 74

Bliss, Rev. Edwin M 47

Blond (Set Le Blond).

Bloom, J. Harvey 35

Blount, Mrs. George n

Blunt, Wilfrid Scawen 48, 59

Blyth, Edmond Kell 77

Bodkin, M. McDonnell n

Armstrong, I. J 8 Boissier, Gaston

Arnold, A. S 39 | Boland, Mary A.

Aronson, V. R.

Askew, Alice and Claude . .8, 87

Austin, Mrs. Sarah 43

Axon, William E. A 60

Bacheller, Irving 9

Badham, F. P 77

Bolsche, Wilhelm 41

Bolt, Ben n

Bon (Sff Le Bon):

Bond, J. A. Walpole- 77

Bonner, Hypathia Bradlaugh 38

Booth, Eva Gore 65

Boulger, Demetrius C 40

Bailey, E. E. J r | Bourget, Paul n

Baillie-Saunders, Margaret. . . 9

Baker, Ernest, A 66

Baker, H. Barton 9

Baker, J ames 9

Bamford 59

Banfield, E. J 66

j Baring-Gould, S 47

Barlow, J ane 9

Barnett, Canon 59

Barr, Amelia E 9, 85

Barr, Walter 10

Barry, William 10, 47

Barth, Dr. Theodor 60

Bartram, George 10

Basile, Giambattista 82

Bastian, H. Charlton 74

Bateson, Mary 47

Batey, John 85

Bealby, J. T 10

Bearne, Catherine A 47

Beauclerk, Lady Diana 35

Beaumont, Francis 5

Beavan, Arthur Hr 74

Beazley, C. Raymond 39

Becke, Louis 10, 43

Beckman, Ernest 82, 83

Beckworth. James P 46

Beers. Henry A i

Bell, Robert.

Bourinot, Sir John G 48

Bousset, W 77

Boutmy, Emile 33

Bowack, William Mitchell ... 59

Bowen, Ivor 59

Bowen-Rowlands, Lilian .... n

Bowles, Thomas Gibson

59

Boxall. G. E ......... 74, 48, 59

Boyesen, Prof. Hjalmar H. . . . 48

Bradley, Henry ..... . ...... 48

Brainerd, E. H ............. n

Bray, Reginald A ......... 60, 77

Breda, G. H ............... ii.

Bren tano .................. 82

Brereton, Austin .......... 48

Bridgett, T. E ............. 77

Bright, Allan H ............. 60

Brightwen.Mrs ......... 38, 74

Broda, Rodolphe .......... 87

Bromley, A. W ............. 85

Brooke, Magdalene

Brooke. Rev. Stopford A .....

Brookes, L. Elliott ..........

Brookfield, Arthur

Brooks, Geraldine 4?

Brown, Charles Reynolds 60, 77
Brown, Francis . . 60

PAGE

Bruckner, A r

Brunetiere, Ferdinand i

Buchanan, A. J 67

Buchanan, Alfred n

Buchanan, Robert 1 1

Buckmaster, J. C 60

Buel, Clarence C 48

Bulfin, W 67

Bullen, Frank T n

Burne-Jones, Edward 5

Burns, John 63

Burns, Robert 3

Burrard, W. Dutton n

Burton, E. de Witt 77

Butler, Lewis 48

Butler, W. F 48

Byles, Rev. John 82

Byrde, Margaretta n

Byron, Lord 70

Cable, G. W 46

Cadbury, Edward 60

Caddick, Helen 67

Caird, Lindsay H 85

Caird, Mona 67

Callahan, James Horton 60

Cameron, V. Lovett 46

Campbell, R. J 77

Campbell, Mrs. Vere 12

Canning, Albert S. G; i

Capes, Bernard 4

Capuana, Luigi 83

Carey, Charles 12

Carducci, Giosu6 4

Carlile, W. and Victor W 60

Carroll, Lewis 35

Carse, Roland 48, 53

Cartwright, Mrs. Edward .... 12

Caryl, Valentine 12

Cayley, George John 67

Cayley-Webster, H 72

de Cervantes, Miguel 13

Cesaresco, Countess Mar tin -

engo 34, 39, 49, 67, 75

Chamberlain, Charles J 75

Chambers, R. W 12

Chapman, George 5

Chesson, Nora 12

Chevalier, Albert 39

Chomley, C. H 12

Choyce, James 46

Chrichfield, George W 49

Christy, Robert 33

Church, Prof. Alfred J 49

Clare, Austin 12

Brown, Madox '....'. 83 ! Clark., H. A 7

j_,v.., *x»i»,i. /^ Browne, Prof. Edw. G i | Clayden, P.'W 49

Bellermann, Ludwig 7 j Browne, Gordon 84 ! Cleeve, Lucas 12

Benjamin, S. G. W 47 I Browne, Haji A 48 ; Clerigh, Arthur 49

Benson, Robert Hugh 77 Browne, H. Morgan 60 ' Clifford, Hugh 67

Bentley, Arthur F 59 Bruce, Mary L 44 ! Clifford, Mrs. W. K 13

T. FISHER UNWIN'S PUBLICATIONS.

iv INDEX of AUTHORS, some ILLUSTRATORS, and EDITORS.— contd.

PAGE

[ Clyde, Constance 13

! Cobbleigh, Tom 13

Cobden, Richard 39. 60

Cole, Timothy 35

Coleridge, Lord 39, 49

Collet, Collet Dobson 60

Collingwood, S. D 35, 39

Collodi, C 82, 83

Compton, Henry 46

Congdon, Charles T 40

Congreve, William 5

Conrad, Joseph 13

Conway, Sir William Martin . . 67

Cooke, Frances E 83

Coolidge, W. A. B 67

Copinger, W. A 49

Corkran, Henriette 13

Cornaby, W. A 67

Cornish, Vaughan 67

Costelloe, Ray 13

Cotterell, Constance 13

Courlandcr, Alphonse 13

Courtney, Leonard 60

Cowper, William 4

Cox, Harold 60, 61

Cox, Palmer 83

Cox, Rev. Samuel 77

Crampton, George 13

Crawford, F. Marion 13

de Crespigny, Mrs. Philip

Champion 13

Crockett, S. R 13

Crompton, Henry 61

Crottie.JuliaM 14

Cruikshank, George 82

Cruso, H. A. A 4

Dale.T.F

Dalin, Talmage

Dalton, Moray

Dalziel, James

Dana, Chas. A

Danson, John Towne

Daudet, Alphonse 82,

Davenport, Arthur

Davenport, Herbert Joseph..

Davids, T. W. Rhys

Davidson, Augusta M. Camp-
bell

Davidson, Lillias Campbell. . .

Davies, Mary

Davis, Richard Harding

Davis, Thomas 49,

Dawson, W. Harbutt

Dean, Mrs. Andrew

Deasy, H. H. P

Defoe, Daniel 82,

von Degen

Degener, Herman A. L

Dekker, Thomas

De la.Rey, Mrs. General

Dethridge, G. Olivia

Dew-Smith, Mrs

Dewsnup, Ernest R

Dickeson, Alfred

Dietrich, Max

Dietzel, H

Dieulafoy, Marcel Auguste . . .

Digby, William

Dillon, E. J

Dittrich, Hermann 35,

Dodge, Walter Phelps 39, 49,

Douglas, Sir George

Douglas, Prof. R. K

liowie, Menie Muriel

Drachman, Holger

Drosines, Georgios. . . .14, 82,
Drury, Robert

PAGE

>ryden, John 5

Dubi, H 67

Duff, J. Wight i

}uffy, Bella 49

Duffy, Sir Chas. Gavan

33, 39, 40, 49- 37

Duhamel, H 67

)u Maurier 36

)umillo, Alice 14

Dunckley, Henry 60

Dundas, Christian 14

Diintzer, Heinrich 40

Dutt. Romesh 14

Dutt, W. A 68

Dyer, John 4

van Dyke, John C 35

Dyke, Watson 14

Eastwick, Robert W 46

von Ebner-Eschenbach, Marie 14

chegaray, Don Jos6 4

Sckenstein, Oscar 68

Edwards, Owen M 49, 87

van Eeden, F 14

Egerton, Hugh E 43

Sivind, R 83

Elias, Frank 6r

Eliot, George 68

Elizabeth of England, Prin-

ess 40

Ellenberger, Professor 35

Elliott, Ebenezer 61

BHis, Havelock 56

Elphinstone, Lady 78

Elster, Ernst 4

Emerson, Ralph Waldo 40

Enock, C. Reginald 68

Erskine, Mrs. Steuart 35

Escott. T. H.S 49, 61

Evans, Howard 42

Evans, S. Hope 83

Evans, Thomas W 40

Evans, W. Sandford 8

Ewald, Alex.C 5

Eyre-Todd, George 44

Faguet, Emile

Falconer, Lanoe

Farge (See La Farge).

Farquhar, George

Farrer. J. A

Farrow, G. E

Fawcett, Mrs. Henry

Fegan, Bertie

Ferguson, Sir Samuel 14,

Ferri, Prof. Enrico

Field, Michael

Findlay, Frederick R. N

Fisher, Harrison

Fisher, Lala

Fitz-Gerald, E. A

Fitzgerald, Percy . . 15, 35, 4 1,

Fitzmaurice- Kelly, J

Flammarion, Camille .......

Fletcher, J.S

Fletcher. John

Flowerdew, Herbert

Fogazzaro, Antonio

Ford, Douglas

Ford, John

Ford, Mary

Foreman, John

Forrest, J. Dorsey

Forrest, R. E

Forster, L. M

Foster, George Burman

Foster, J. J 35,

Foster, Sir Michael

PAGE
rapan, He 15

Fraser, John 15

razer, H. W I, 50

7rederic, Harold 15

7reeman, Prof. E. A 50

rench, Henry Willard 15

Tuller, Margaret 40

rurness, Annette 15

Furniss, Harry 36

Gaggin, John 68

Gambier, J. W 40

anconagh (W. B. Yeats) 24

iannon, John P 50

Gardiner, A. G 62

rardiner, J. H 78

rardner, W. J 50

Garnett, Richard 4, 45

Gebuza 61

Seen, Philip 85

George, E. A 78

Gertrude, Aunt 82

Gibb, E. J. W 52

Gil" 13

Gilman, Arthur 50, 52

Gilman, Daniel Coit 78

Gissing, George 13

Glover, John R 42

Goethe, W 4

Gornme, G. Lawrence ....50, 61

Goodenough, Rev. G 86

Gordon, Charles 50

Gordon, H. Laing 44

Gordon, Lady Duff 43

Gordon, William Clark 33

Gorky, Maxim 15

Gosse, Edmund 6

Gould, F.Carruthers 61,84

Gould, G. M 40

Grace, R. W 84

Graham, R. B. Cunninghame . 68

Grant, Daniel 62

Graves, Alfred Perceval. . .43, 87

Gray, E. Conder 40

Gray, Thomas 50, 73

Greeley, Horace 40

Green, Anna Katherine 16

Greene, Robert 5

Gregory, Lady 34

Gribble, Francis 68

Grieve, Ed. B 86

Griffiths, D. R 16

Griffiths, Arthur 16, 50

Guarracino, Beatrice 81

Guest, Lady Charlotte 16, 87

Guyer, Michael F 75

Gwvnn, Stephen 36

Gyp 16

Hackwood, F. W 86

Haldane, Richrad Burton 62

Hale, Susan 50

Hales, A. G 16

Hall, Charles Cuthbert 78

Hall, Moreton 4

Hall, R. N 68

Ha!p6rine-Kaminski, H 46

Hamilton, Cosmo 15

Hamilton, Lord Ernest 14

Hannah, J. E 50

Hardie, J. Keir 65

Harding, Ellison 15

Hardy, Rev. E. J.

16, 41, 68, 78, 81, 87

Harland, Marian 81

Harper, S. Eccleston 32

Harper, William Rainy 78

Harrison, Mrs. Burton 16

T. FISHER UNWIN'S PUBLICATIONS.

INDEX of AUTHORS, some ILLUSTRATORS, and EDITORS,-*™ Id. v

Harrison, Mrs. Darent 16

Harrison, Jane E 36

Harting, J.E 75

Harvie- Brown, J. A 75

Hasen, Ch. Downer 50

Hasler, G 67

Hatfield, Henry Rand 86

Hauff, Wilhelm 83

Hawkesworth, Alfred 69

Hay, J ohn 42

Hay, William 16

Hayden, Arthur 36

Heine, Heinrich 4

Heinemann, Karl 4

Hemans, Mrs 87

Hennessey, J . W 83

Henshaw, Julia W 16

Henson, H. Hensley 78

Henty, G. A 16, 85

Herbert, George 4, 78, 87

Herford, C. H 5

Herrick, Christine Terhune ... 81

Herring, Frances E 69

Hertz, Gerald Berkeley 50

Hertz-Garten, Theodor 16

Heywood, Thomas 5

Heywood, William 69

Hicks, John W 86

Hill, Edmund L 4

Hill, Geoffry 7«

Hill, George Birkbeck 43

Hill/Robert T 69

Hindlip, Lord 69

Hinkson, H. A 17

Hirst, Francis W 62

Hobbes, John Oliver ..4, 17, 69

Hobhouse, L. T 62

Hobson, J. A 63, 69

Hocking, Silas K 1 7

Hodgson, W. B 62

Hoffmann, E. T. A 83

Hogan, James Francis 62

Holdsworth. Annie E 17

Holmes, Timothy 38

Holyoake, George Jacob 41 , 62, 86
Honeyman, C. van Doren .... 69

Hornby, F. M 33

Horne.H.P 6

Horniman, Roy 18

Horridge, Frank 41

Horrwitz, Ernest i

Horton, R. F 78

Hosmer, Prof. James K 50

Houghton, Louis Seymore. ... 50
Howard, George Elliott.. 51, 78

Howe, Frederic C 62

Howell, George 62

Hueffer, Ford H 62,83

Hudson, W. H 18

Hug, Lina 51

Hugessen, Knatchbull 83

Hulbert, H.B 73

Hulme, F. E 75

Hume, Martin A. S. ..43,51,72

Humphrey, Frank Pope 18

Humphrey, Mrs 18, 81

Hungerford, Mrs 18

Hyde, Douglas 2, 5, 78, 87

Ibsen, Henrik 5

Indicus 69

Ingersoll, Ernest 75

Iron, Ralph (Olive Schreiner). 26

Irving, Edward 75

Irving, Fanny Belle 18. 85

Irwin, H. C 18

James, David H 51

PAGE

Jane, L. Cecil 51

Japp, Alex. H 41

Javelle.Emile 69

Jay, Harriett 38

Jebb, Louisa 69

Jeffery, Walter u, 18, 43

Jenkins, Rhys 86

'enks, Edward 51

ennings, Edward W 18

ephson, Henry 02

ephson, Julie 38

epspn, Edgar 18, 84, 87

ernigan, T. R 62

erningham, Sir Hubert 18

essopp, Augustus 18. 33, 51

ewett, Sarah Orne 51

ohnson. Robert U 51

ohnson, T. Broadwood 69

ones, David Brynmor 51

ones, H. Stuart 51

ones, W. Lewis 2

onson, Ben 5

usserand, J.J 2, 33, 52

de Kantzow, Alfred 3

Keary, C. F 18

Keene, Charles 37

Keller, Gottfried 18

Kelly, J.D.J 52

Kempster, Aquila 18

Kerr, S. Parnell 69

Kettle, Rose Mackenzie ..19, 85

Kiesow, E. L 85

Kildare, Owen 19

King, Clarence 69

King, Irving 78

King, Joseph 62

King, Richard Ashe ....44, 87

Kingsford, C. L 47

Kinross, Albert 19

Kitson, Arthur 63

Knight, William 39

Ko, TaSein 78

Kolokorones, Theodore 46

Korolenko, V 19

Kroeker, Kate Freiligrath . . 83

Kruger, Paul 41

Kruger, Gustav 78

Kurz, Louis 67

La Farge 69

Lambe, J. Lawrence 19

Landon, Mary 19

Lane, Ralph 63

Lane-Poole, Stanley 52

Langbridge, Rosamond 19

Langland, William 2

Latane, John H 52, 63

Lanyon, H. St. Martin 19

Laurenson, Arthur 41

Laverton, Mrs. H. S 19

Law, Alice 3

Lawless, Emily 53

Lawson, Sir Wilfrid 61

Lawton, Frederick 36 42

Lear. Edward 45

Le Blond , Mrs. Aubrey .... 69, 70

Lebon, Andr6 52

Le Bon, Gustave 33

Lee, Vernon 19, 33, 52

Lee-Hamilton, Eugene 19

Legge, Helen Edith 36

Leigh, M. Cordelia 79

Leland Ch. G. (" Breitmann •") 19

Lentheric, Charles 70

Leroy-Beaulieu, P 60

Levasseur, R 63

Levy, Amy 5

Lewis, Frank C; 20

PAGE.

Leyds, W. J 52

Lidddl, Arthur R 85

Lilly, W. S 52

Litta, Duke 20

Little, A. G 52

Little, Mrs. Archibald 20, 70

Lloyd, Albert B 70

Lloyd, H. D 63

Lloyd, Wallace 20

Locke, James 20

Loeb, J acques 75

Lombroso, Prof. C 34

Lonergan, W. F 52

Lord, Walter Frewen 42

Lorraine, Rupert 20

Low, Sidney 63

Lowes, Mrs 36

Lucas, Alice 79

Lumsden, James 70

Lunn, Henry S 63

Lynch, B. M 20, 87

Lyons, A. Neil 20

Lyons, Albert E 20

Lyttelton, Edith 5

Mac, J ?o

McAulay, Allan 20

MacBride, MacKenzie 20

McCarthy, Justin 42,52

McClelland, J 63

McCormick, A. D 67

MacDermott, Martin 34, 87

MacDonagh, Michael ..39, 40, 87

Macdonald, Alexander 70

Macdonald, George 20

Macdonald, Leila 5

Macdonald, Robert 84

von Mach, Richard 63

Mcllraith, J. R 5»

Mcllwraith, J. N 83

McKendrick, John G 41

Mackintosh, C. W 39

Mackintosh, John 53

McMahan, A. Benneson jo

McManus, Blanche 84

MacManus, James 20

McManus, L 20

Macpbail, Andrew 79

Macy, J esse 63

Maddison, F 4*

Magnay, Sir William 20

Mahaffy, Prof. J. P 53

Malet, Lucas 34

Mallet, Sir Louis 60, 63 66

Mallik, Manmath C 34, 7<>

Mann, Mary E 21,87

Marble, Annie Russell 2

Mario, Jessie White 44, 53

Mark, H. Thiselton 79

Marlowe, Christopher 6

Marquis, T. G 21

Marsh, Richard 21

Marshall, Thomas 34

Martin, Alfred J 79

Martyn, Edward 21

Martyn, Ethel K 33

Mason, Eugen 5

Maspero, G 53

Massey, Gerald 53

Massinger, Philip 6

Massingham, H. W 63

Masson, Gustave 53

Masterman, C. F. G 34. 62

Mathews, Shailer 77, 79

Maude, Edwin 42

Maugham, W. Somerset 21

Maurice, C. Edmund 53

du Maurier, G 36

T. FISHER UNWIN'S PUBLICATIONS.

vi INDEX of AUTHORS, some ILLUSTRATORS, and EDITORS.— contd.

PAGE

Mayne Ethel Colbura 21

PACK

Oman, John Campbell 79

PAGE

Rogers Thorold 55 64

Mazzanti C 83

Omond, G. W. T 22

Roosevelt Florence

Meade Mrs L T . 21 85

Orczy, Baroness 22

Roosevelt Theodore

Meakin Budgett 63

Meirion Ellinor 21

Otway, Thomas 6

Rosegger Peter

Outhwaite R M 12

Rossetti Dante Gabriel

Mikoulitch V 21

Owen, Charles . . . . . 22

Rowbotham, F. Jameson 25,55,84
Rowlands, Lilian Bowen .... 25
Rowsell Mary

Milford L. S 53

Page, H. A 43

Millar J H 2

Miller' Frank Justus 6

Paget, Stephen 41

Roxby Percy M 40

Miller William 53 70

Mills E J 2

Pais, Ettore 54

Russell, Charies E 64

Mills Wesley . . • 75

Russell Sir Edward

Russell George WE 34

Milyoukov Paul • . 63

Parker, Theodore 79

Russell T Baron

Minns Ellis H . i

Parsons, John Deuham 76

Russell W Clark 25

Mistral Fr6d6ric 6

Paulsen, Friedrich 79

Rutherford Mark 25

Mitchell S Weir ..21 45

Payne, J . F 44

Ryley J Horton 40

Pennell, Charles 37

Ryves K C 26

Molesworth Mrs 83

Pennell, Elizabeth Robins.... 36
Pennell, Joseph 36

de Molinari G 63

de Pentheny, S 22

St Hilaire Philippe ' 26

Montagu Lily H ... 21

Perrin, F 67

St John Sir Spencer 38

de Montalban D. J. P 40

Pfleiderer, Otto 79

Saiutsbury George.. . . 65

Montgomery K L 21

Phelps, William Lyon 5

Moore AW 53

Philpott, Hugh B 80

Moore George . ..6, 21, 34

Pidgin, Charles F 22

Santayana George 7

Morel, E. D 63

Pike, G. Holden 39, 43, 45

Sarnia 26

Morfill W. R 34

Pike, Oliver G 76

Scaife, A. H

Pink, Alfred 82

Schallenberger V 26

Morris Mrs Frank 83

Schiller Friedrich 7

Morrison, W. Douglas. ... 34, 54
Moscheles Felix 36

Pinto, Ferd. Mendez 46

Pitt-Lewis, G 41

Schmidt Rudolph 76

Schreiner, C. S. Cronwright . . 65

Mottram William 2

Plowden, A. C 43

Miigge MA. . . . 34

Schuller Leo Sarkadi 7

Porter, C 7

Scidmore, Eliza Ruhamah. .. 72

Murray David 54

Pott, F. L. Hawks 54

Scott Sir Walter 26

Scott-Elliott G F 72

Myron *A Kiel 6

Praed, Mrs. Campbell . . . .23, 43
Presland, John 6

Scully WC* 26

Needham Raymond 54

Prichard, K. and Hesketh. ... 23

Seccombe Thomas 43

Negri, Gaetano 79. 4*. 54

Pryce, G 23

Newman Edward 75

Pusey, S. E. Bouverie 54

Selleck, W. C . , . . 80

Pyle, Howard 46

Sellon B Mildred 84

Nicholson Brinsley 6

de Quevedo, Francisco 37

Nicholson! F. C 5

Service, Robert W 7

Nicholson, L 6
Nicholson R. A 2

Ragozin Zenaide A 54

Seymour, Frederick H. A 37
Seymour, Major-General .... 72

Nicolson, Arch K 83

Ravenshear, A. F 64

Shadwell, Thomas 6

Nietzsche Friedrich 34

Ravenste'n G E 80

Shakespeare, William 7

Nieuwenkamp WOT" 3'

Rawlinson, Professor George . 55
Rea, Thomas 3

Shaw Albert 65

Noble M. A- 86

Sheehan. Rev. P. A 26

Noel Roden . . . 6 64

Read C Stanford 82

Sheehy-Skeffington F 43

Nordau, Max 36

Reeth, Allan 25

Shelley, Percy" 70

Norman Henry 71

Reid Forrest 25

Shenstone Mildred 26

Sheppard Arthur 86

Normyx 22

Rey, Guido 71

Norris WE: 22

Rhead G Woolliscroft 37

Sherwood A Curtis 26

Rhys, Ernest 5

Ober FA 71

Shirley James 6

Richardson, Mrs. Aubrey .... 25
Richardson E. . . 6

O'Brien, R; Barry 54, 64, 83

Shuckburgh, B. S 55
Shuddick, R 86

Richmond, Mrs 76

Sibley, N. W 65

O'Donn^ll C J 64

Offilvie Will H

Rita 25

O'Grady, Standish. . .22, 83, 87

Sillard, Robert M 44

Roche, James Jeffrey 46

Simpson, Wm. (Crimean S.) . . 24
Small, Alb'on W 65

Oman C W C

Smith.F. Clifford 26

T. FISHER UNWIN'S PUBLICATIONS.

INDEX of AUTHORS, some ILLUSTRATORS and EDITORS.— contd. vii

PAGE

Smith, F. E 65

Smith, Goldwin 3, 40

Smith, Isabella 26

Smith, John 27

Smith, Mrs. S. H 44

Smith, T. Berkeley 72

Smyth, Eleanor C 41

Snell, F. C 76

Snow, Isabel 27

Sollas, W.T 76

Somerset, Lady Henry 86

Spelling, T. C 65

Spence, Catherine 21

Spicer, Howard 86

Spinner, Alice 27

Stacpoole. H. de Vere 27, 87

Stanley, Edward 55

Stead, Alfred 72

Stead, Richard 51

Stead, W. T 65

Steele, Richard 6

Stein, M. Aurel 72

Stephens, H. Morse 55

Stevens. Nina 27

Steveni, William Barnes 65

Stillman, W. J 37

Stokes Sir William 44

Stopes, Mrs. C. C 63

Stott, Beatrice 27

Strachey, John St. Loe 5, 76

Strain, E. H 27

Strasburger, Eduard 72

Stratilesco, Tereza 72

Street, Eugene E 72

Stuart, C. Douglas 37

Stubbs, Chas. William 80

Sturgis, Russell 37

Stuttard, John 76

Summers, Dorothy 27

Sutcliffe, Halliwell 27, 72

Svenske, Anders 65

Swain, A. B. H 6

Swift, Dean 44

Swift, Benjamin 27

Swinburne, Algernon Charles. 6
Syinonds, John Addington . . 6

Symonds, Margaret 72

Symons, Arthur 6

Synge, Mrs. Hamilton 27

Tadema, L. Alma 59

Taine, Adolphe Hippoly te .... 72

Tayler, F. Jenner 28

Taylor, Austin 65

Taylor, Charles M 72

Taylor, Ellen 28

Taylor, J. F 43, 87

Taylor, Mrs. John 43

Tetley, J. George 44

Theal. Dr. G. McCall 57

Thomas, Edward 87

Thomas, Emile 58

Thomas, W. Jenkyn 84

PACK

Thomas, William J 34

Thompson, Helen Bradford . . 76

Thompson, H. Gordon 85

Thring, Rev. Edward 34

Thynne, R ... 28

Tirebuck, William 44

Todhunter, Dr. John 43, 87

Tomson, Graham R 4

Tourneur, Cvril 6

Townsend, C. W 72

Townshend, Dorothea 43

Tregarthen, Greville 58

Treherne, Philip 28, 44

Trelawny, Edward J 46

Troubridge, Lady 28

Trowbridge, W. R. H..28, 49, 58

Truscott, L. Parry 28

Tucker, G6nevieve 82

Tuin, W. J 37

Tunison, Joseph S 7

Turnbull, A. R. R 73

Turner, Ethel 28, 84

Turner, Samuel 73

Turguan, Joseph 58

Twain, Mark 65

Tweeddale, John 28

Tynan, Katherine 7

Tyrrell, George 80

Unwin, A. Harold 76

Unwin, Mrs. Cobden 62

Usher, Sir Thomas 42

Valentine, E. U 32

Vambery, Arminius 44, 46, 58

Vanbrugh, Sir John 6

Vanderlip, Washington B 73

Vaughan, Henry 87

Veldheer.J.G 37

Verga, Giovanni 32

Verity, A. W 5

Viele, Herman K 32

Vierge, Daniel 37

Villari, Luigi 37, 65, 73

Villari, Pasquale 42, 43, 58

Villars.P 46

Villiers, Brougham 65

Villiers, Chas. Pelham 60,66

Vincent, Arthur 4

Voigt.J.C 5

Volkhovsky, Felix 8

Wagner, Charles 80

Wallis, Braithwaite 73

Walpole, Sir Spencer 45

Walpole-Bond, J. A 77

Walsh, C. M 7

Ward, Mrs. Humphry 85

Ward, W. C 6

Warden, Florence 32

Waring, Henry F

Warren, Algernon 86

PAGF.

Warry, C. King 32

Watson, Aaron 45

Watson, John 77

Watson, John Reay 32

Watson, Margaret 32

Watson, R. Spence ...... 45 66

Watson, William. ........ .7, 46

Watts, Henry Edw 58

Webster, Alexander. .. >.*. .. 58

Webster, H. Cayley 73

Webster, John 6

Welby, Lord 60, 66

Wellby.M.S 73

Wells, H. G 32, 34

Wendell, Barrett 3

Werner, A 73

Westell, W. Percival 77

Whadcoat, Gordon Cuming . . 82

Whistler, J . McNeill 35

Whi taker, Samuel F. G 7

White, Hester 32

White, William 66

Whitechurch, Victor L 32, 87

Whitehouse, H. Remsen 38

Whitman, Sidney 58

Whitty, E. M 59

Wiel, Alathea 59

Wilberforce, William 45

Wilkens, Mary E 32

Wilkinson, Kosmo 45

Williams, Leonard 83

Williams, Meta 83

Williams, Rowland 80

Willamson, C. N 32, 87

Williamson, W. H 32

Willmore, Edward 7

Wilson, Claude 73

Wilton, Jos 32

de Windt, Harry 73

Witchell, Charles A 7?

Witt, Paul 32

Wood, Katharine B 82

Woods, H. C. 73

Worsley, A 80

Workman, Fanny Bullock .... 73
Workman, William Hunter. .. 73

Wright, Arnold 86

Wright, H. K 35

Wright, H. M 73

Wycherley, William 6

Wylwynne, Kythe 32

Yeats, Jack B 83

Yeats, W.B 7,32,34

Yeigh, Kate Westlake 32

Yeld, George 67, 73

Ystridde, G 32

Zimmermann, Jeremiah 73

Zimmern, Alice 59, 83, 85

Zimmern, Helen 59, 85

Zurbriggen, Mattias. 73

T. FISHER UN WIN'S PUBLICATIONS.

INDEX IN ORDER OF TITLES.

INDEX in order of Titles.

PACK

Abbot (The) 26

Abyssinia (Sport and Travel). 69

Adam (Robert) Artist 35

Addresses 34

Adelphi Library (The) U

Admiral Phillip 43

AdmiralVernon and the Navy 44
Adula Alps of the Leopu'itine

Range (The) 67

Adventure Series (The) .... 46
Adventures of a "Bloc kade

Runner 46

Adventures of a Supercargo. . 10
Adventures of a Younger Son 46

Adventures of a Dodo 84

Adventures of James Sher-

vington 10

Adventures on the Roof of the

World 69

jEsop's Fables 83

Aga Mirza (The Adventures of) 18

Age of the Earth (The) 76

Alexander's Empire 53

Alfred the Great 4

Almayer's Folly 13

Along the Labrador Coast . . 72

Alpine Memories 69

Alps (My Climbs in the) 71

Alps to the Andes (From the) 73

Amazing Duke (The) 20

Amaranthus 4

Amaryllis 14

Ambassador (The) 4

America (Literary History of) 3
American Civil War (Battles

and Leaders of the) 51

American Commerce 86

American Literature (Heralds

of) 2

American Literature (Short

History of) i

American Opinion of the

French Revolution 50

American Railway Organiza-
tion 61

American Scholar (The) 79

American Workman (The) ... 63

Among the Man-Eaters 68

Among the People of British

Columbia 69

Among the Syringas 21

Andes and the Amazon (The) 68

Anglo-Americans 12

Anglo-Italian Library (The) . 66

Anglo-Saxon (The) 48

Animal Micrology 75

Animals I Have Known 74

Anne of Geiersteiu 26

Another Englishwoman's Love

Letters 22

Another View of Industrialism 39

Another Wicked Woman .... 22

Anthony Jasper n

Antiquary (The) 26

Appreciation of the Bible

(The New) 80

Arabs (LiteraryHistory of the) 3

Arcacly : for Better for Worse 51

Arden Massiter 10

Aristotle's Theory of Conduct 34

Armaments (The Burden of). 60

Army Reform 62

Art aud Artists (On) 36

Artist's Letters from Japan 69

FACE

Artist Songs 6

Arts of Design (The) 37

As a Tree Falls 28

Ascent of M.in (The) 74

As Others See Us 14

Aspirate (The) 78

Assisi (Golden Sayings of

Giles of) 80

Assyria 54

Astronomy for Amateurs .... 75
Atrocities of Justice under

British Rule 59

Augustus (Life and Times of). 55

Australia (The Real) 67

Australian Bushrangers (His-
tory of) 48

Australian Commonwealth

(The) 58

Australian Girlhood (My) 43

Australian Sheep and Wool. . 69

Austria 38

Autumn Leaves 19

Avocat Patelin (Lf) 7

Awakening of a Race (The) . 59

Baboo English 86

Bachelor in Atcady (A) a7

Bachelor Maid (A) 16

Baile's Strand (On) 7

Baldwin 33

Balfour's Pamphlet (A Reply) 61

Balfourism 60

Balkans (The) 53

Bamford's Passages 39

Barbara Cunline 27

Barbarian Invasions in Italy. . 58

Barbary Corsairs (The; 52

Bards of Gael and Gall 3

Battles and Leaders of the

American Civil War 51

Beach and Bogland (By) .... 9

Beaconsfield (Lord) 38

Beauclerk (Lady Diana) 33

Beauty Adorned 18

Beckwourth (James P., Life

and Adventures of) 46

Beetle (The) 21

Before I Forget 39

Begliojoso : A Revolutionary

Princess 38

Behind the Arras (From) 13

Belcaro 33

Belle Marie (La) 19

Belle Niveruaise (La) 83

Bending of the Bough (The) . . 6
Benyowsky (Memoirs and

Travels of) 46

Bergen Worth 20

Bernard (Claude) 38

Bernese Oberland (The) 67

Besant (Anne) 38

Betrothed (The) 26

Bible as English Literature

(The) 78

Big Game Shooting in South

Africa 68

Birdland (In) 76

Bird Life (British) 77

Bird Life in Wild Wales 77

Birds I Have Known 74

Bird Skinning and Bird

Stuffing 75

Bird's Nest (The) 77

Bishop Doyle 40, 87

1 Black Dwarf 26

PAGE

Bl.:ck Mary 20

Black Shilling (Tbc) 9

Blue Gown (In tlic Land of

the) 70

Blue Lagoon (The) 27, ?7

BlueLilies 12

Bog of Stars (The) 22, 87

Bohemia 53

Bohemia with Du Maurier (In) 36

Bonaparte in Egypt 48

Bond of Blood (The) 15

Bossism and Monopoly .... 65

Bourgeois (The) 27

Boy and the Angel (The) 82

Bradlaugh (Charles) 38

Brahmans (The) 79

Brand 5

Breachly (Black Sheep) 10

Breakfast, Dinner, and Supper

(Quickest Guide to) 82

Breitmann in Germany-Tyrol 19
Bride of Lammermoor (The) . . 26
Bright Days in Merrie Eng-
land 69

Brightwcn, Mrs. (Life and

Thoughts) 38

Brightwen Series (The) 76

Britain (Early) 49

British Bird Life 77

British City (The) 62

British Columbia (Among the

People of) 09

British Diplomacy (The Story

of) 61

British East Africa 69

British History (Literary In-
fluence in) i

British India 50

British Industries under Free

Trade 60

British Political Leaders 42

British Regiments (Famous) . . 50
British Writers on Classic

Lands i |

Brodie (Sir Benjamin) 38 j

Brooke (Rajah) 38

Brown (Captain John) 38

Brown Owl (The) 83

Brown, V.C 8, 85

Brownies in the Philippines . . 83
Buccaneers and Marooners of

America (The) 46

Buchanan (Robert) 38

Budapest 72

Buddhist India 49

Builders of Greater Britain . . 38
Bulgarian Exarcha^ "(Tne). . 63

Bundle of Life (A) 17

Burden of Armaments (The), bo

Buried City of Kenfig 50

Burmese Language (Hand-
book of the) 78

Burton(The Real Sir Richard) 39

Bush Honeymoon (A) 8

Business of Life (The) 81

Butterfly (The) ?6

Bygones Worth Remembering 41

Byron in Italy 70

Byzantine Empire (The) 54

Cabot (John and Sebastian).. 39

Cameo Series (The) 3

Camera in the Fields (The) . . 76
Canada (Children's Study) .. 83
Canada (Story of the Nations) 48

INDEX IN ORDER OF TITLES.— continued.

Ca-ia l.i in Harvest
(Through)

PAGP

ng in the Karakoram-
alavas 67

lime Climbin

70 Him.

Canada To-day 69 ! Climbs in the Alps (My) 71

Canadian Contingent (The).. 85 j Climbs in New Zealand Alps. 68
Canal System of England. ... 36 j Climbs of Norman-Nermia 71

Canon in Residence(The) . . T, 2, 87 ' dive (Lord) 39

Cape Colony (Everyday Life). 68 Cobden and Jubilee of Free

Captain of the Locusts (The) . . 73 I Trade 60

Captain Sheen 12 Cobden as a Citizen 39, 60

ii ! Cobden, Richard (Life of) ... 39
21 Cobden (The Political Writings

of) 60

Capture of Paul Beck (The).

Cardinal's Pawn (The)

Carding Mill Valley 19

Carlyle (Thomas) . '. 39

Carpathian to Pindus (From) 72

Carroll, Lewis (Life of) 39

Carroll Picture Book (The

Lewis) 35

Carthage . 49

Cartoons in Rhyme and Line. . 63

Case of Miss Elliott (The) 22

Case of Wagner (The) 34

Castle Dangerous 26

Cat and Bird Stories 76

Catharine Furze 25

Caucasus (Fire and Sword in

the) 73

Cause and Effect 21

Cause of Discontents in India 64
Cause of IndustrialDepression 63

Cavalleria Rasticana 32

Cecilia's Lover 9

Celtic Twilight (The) 7

Century Cook- Book (The) 82

Century In valid Cookery Book 81

Century Library (The) 12

Century Scott (The) 26

Certain Personal Matters 32

Chaldea 54

Charing Cross to Delhi(From) 69

Chats on Book-Plates

Chats on Costume

Chats on Earthenware 36

Chats on English China 36

Chats on Old Furniture 36

Chats on Old Lace 36

Chats on Old Miniatures .... 35

Chats on Old Prints 36

Chats on Oriental China 33

Chats Series (The) 33

Chaucer's Maytime (In) 25

Chelsea Window Gardening . . 81
Children of Endurance (The) , . 12
Children's^ Library (The) 82, 83

ChUdre^'s Study Tine) . 83

Chile 72

Chillagoe Charlie 84

China (Story of the Nations) ..49

China Cup (The) 83

China from Within 67

Chinaman (John) at Home . . 68
China under the Searchlight. . 6?
China's Business Methods. ... 62
Chinese History (A Sketcli of) 54

Chinkie's Flat 10

Christ and the Nation 78

Christian Belief 78

Christian Democracy 78

Christian Origins 79

Christianity and the Bible . . 80

Cobden 's Work and Opinions. 66

Cogne (The Mountains of) 67

Coillard of the Zambesi 39

Colette 26

Colonise England (To) 62

Comedy of Three (A) 26

Coming of Friars (The) 51

Coming of Parliament (The). . 51

Coming of Sonia (The) 27

Command of the Prince (By). 19

Commerce (American) P6

Commercial Travelling 86

Commissioner Kerr 41

Concerning Cats 4

Concerning Himself 32

Confessions of a Beachcomber 66
Confessions of a Caricaturist 36
Confessions of a Match-Making

Mother 14

Congo (The) 68

Continental Outcast (The) . . 60

Convict Days (Old) 10

Co-operation (The History of) 62

Corner of Asia (A ) 23

Cornish Whiddles 83

Corn Law Rhvmes 6 1

Counsels of the Night (The) . . 13

Count Robert of Paris 26

Countess Kathleen (The) 7

Country of Horace and Virgil 66
Country Parson (Trials of a) 51

Courage 80

Court Beauties of Old White-
hall 38

Court Cards 12

Creek and Gully (By) n

Cremer (The Life of W.

Randall) 4*

Crete (The Palaces of) 36

Cricket 86

Cricket on the Brain 13

Crimean Simpson's Autobio-
graphy 44

Criminal Appeal 65

Criminal Justice (Our) 61

Criminal Sociology 33

Criminology Series (The) 33

Crimson Azaleas (The) . . .... 27

Cromwell and His Times 39

Crowd (The) 33

Cruise of the Wild Duck (The) 14

Crusades (The) 47

Crystal Age (A) 18

Cuba and International Re-

lations

Cuba and Porto Rica 69

Cults of India 79

Curiosities 33

Christmas Berries .......... 19 Curzon (Lord). The Failure of . 61

Churches and the Liquor Cut off from the World ...... n

Traffic (The) ............ 59

Cinderella ................. 13

City (The) ................. 63

Civilisation (The History of) . 55

ood

25

Clara Hopg

Clearer Vision (The) ......... 21

Cliff Days ................. 25

Climbers' Guides ............ 67

Climber's Note Book (The). . 73

Diugnter ol Patricians (A). . . 26

Daughter of the Fen (A) 10

Dauphin y (The Central Alps of

the) . i 67

Dauphiny (Mnps of the) 67

David the King 49

Davidson (Memorials of

Thomas) 39

PAGE
Davis (Thomas) A Short Life

of 39, 87

Davitt (Michael) 40

Dawn of Day (The) 34

Dawn of the igth Century in

England (The) 47

Days Spent on a Doge'sFarm 72
Dazzling Miss Davison (The) . 32

Dazzling Reprobate (A) 28

Death, The Showman 15

Deeps of Deliverance (The).. 14

Deidre 7

Democracy and Reaction. ... 62

Derwent (Sir Frederick) 19

Desert Ways to Baghdad(By) 69

Desmonde, M.D 13

Destroyer (The) 37

Development of Christianity. 79
Development of Western

Civilization 30

Devil's Half Acre (The) 8

Devonshire House (The Story

of a) 39, 49

Diana's Hunting 1 1

Diarv of a Dreamer 14

Diplomatic Relations of the

U S.A. and Spanish America 52

Disciple (The) n

Discourse of Matters (A) 79

Discovery of the Future (The) 34
Disdainful Maiden (The).... 83
Disestablishment in France. . 64

Divine Presence (The) 79

Divorce : i r

Doctor (The) 27

Doctor Gordon 33

Dog Book (The) 73

Dog Stories 76

Don Quichote 12, 37

Double Choice (A) 9

Double Marriage (A) 12

Doubt and Faith 78

Drama of Sunshine (A) . . 25

Dramatic Traditions of the

Dark Ages 7

Dream and the Business (The) 17
Dream Life and Real Life. ... 26

Dream Woman , . 32

Dreams 26

Driven 32

Dutch and Fleirish Masters

(Old) 35

Dutch Towns (Old) 37

Dwarf-land and Cannibal

Country (In) 70

Dyer, John (Works of) 87

Earl's Cedars 19

Early Mountaineers (The) .... 68

East Africa (British) 69

East Africa (Sport and Travel) 69
Eastern Asia (A Brief History

of) 30

Ebbing of the Tide (Th«) 10

Eben Holden - 9

Economic and Statistical

Studies 61

Economic Interpretation of

History 64

Editor's Sermons (An) 34

Education (Trend in Higher). 78

Edward Barry 10

Erne Hetherington n

Egypt (Ancient) 33, 55

Egypt (Bonaparte in) 48

Egypt (The New) 66

Egypt (New Light on Ancient) 53
Egypt (Secret History of the

English Occupation of) .... 48
Eighteenth Century Painter

(Memorials of an) 36

INDEX IN ORDER OF TITLES.- -continued.

84
. 83
. 23

83

PAGE

El Dorado (In Search of) .... 70
Eleanor Lambert (The Story

of) '. ii

Electoral Reform 62

Elgivia, Daughter of the Thegn 16
Eliot, George (True Story of) 2
Elizabeth (Grandmother's ad-
vice to) 16

Elizabeth (Letters of her Mother

to) 16

Elizabeth of England (Prin-
cess) Correspondence of . . . 40
Enchanted Castle (The) . .
Enchanted Garden (An) . . .
Ending of My Day (The). . .
England (Children's Study)
England (Bright Days in

Merrie) 69

England (Dawn of the igth

Century in) 47

England (The Governance of) 63
England (The Industrial His-
tory of) 55

England's Title in Ireland . . 64

England (Mediaeval) 47

England (Modern) 52

England (The Monarchs of

Merry) 48

England (Parliamentary)

(1660-1832) 51

England (Socialist Movement

in) 65

England under the Coalition. . 48

English Cathedrals 37

English Cathedrals (Hand-
book of) 37

English China (Chats on) ... 35
English Essays from a French

Pen V 33

English Novel in the Time of

Shakespeare (The) a

English People (The) 33

English People (Literary His-
tory of the) 2

English Public Opinion 50

English Sports (Old) 86

English Wayfaring Life 52

Epistles of Atkins (The) 21

Epoch in Irish History (An) . . 53
Escalades dans les Alps (Mes) 71
Escapes of Latude and

Casanova (The) 46

Essays in Puritanism 79

Essays Political and Bio-
graphical 45

Ethiopia in Exile 7i

Buphorion 33

European Military Adventures

of Hindustan 46

European Relations 14

Evans (Memoirs of Dr.

Thomas) 40

Evelyn Innes 21

Bvery Dav Life in Cape Colony 68

Bve's Apple 13

Evolutions of World and Man 74
Expositions • 77

Fabian's Tower 19

Face and How to Read it (The) 75

Facing the Future 28

Failure of Lord Curzon (The) . 61

Fair Maid of Perth (The) 26

Fairy Tales (Irish) 83

Fairy Tales from Brentano

(New) 82

Faith of a Modern Protestant

(The) < 77

Falls of the Loder (The) 19

Fanny Lambert 27

Far East (Peoples and Politics

in the) 71

PAGE

Far in the Forest 21

Fast Miss Blount (That) 18

Father Alphonsus 17

Father Felix's Chronicles . . 12

Father of Six (A) 23

Feather (The) 83

Female Offender (The) 34

Filibusters (The Story of the) 46

Filigree Ball (The) 16

Finality of Christian; Religion 78

Finn and His Companions 83

Finnish Legends 83

Fire to Fortune (Through) .... 8

First Aid to the Injured 85

First Fleet Family 11

First Folio Shakespeare(The) 7

First Novel Library (The) 15

First Watch (In the) . . 14

Fiscal Problem (The) 63

Fiscal Reform Sixty Years

Ago 66

Fisher Book (The Harrison) . 35

Fishes I Have Known 74

Fishing in Ireland 85

Fishing in Scotland 85

Fishing (What I have Seen

While) 75, 85

Fitch (Ralph) 40

Five Children and It 84

Five LittleJPeppers 84

Five Talents of Women (The) 81
Flame and the Flood (The).. 19

Flamma Vestalis 5

Florence (The History of) ... 58

Flute ofJPan (The) 17

Foma Gordyeeff 15

Fool- Killer (TJie) 12

Fool's Tax (The) 12

Football, Hockey, and Lacrosse 86
For Better ? For Worse ? . . 34

Forest Trees (Future) 76

Fortunes of Nigel (The) 26

Four Philanthropists (The) . . 18

France (Children's Study) 83

France (Journeys Through).. 72
France (Literary History of), i

France (Mediaeval) 53

France (Modern) 52

Franks (The) 55

Free Food and Free Trade .... 62

French Ambassador (A) 52

French Court (Dames and

Daughters of the) 48

French Court (Pictures of the

Old) 47

French Literature (Essays in) i
French Literature (Manual of) i
French Masters (Modern) .... 33
French Society (Heroines of) 47

Frivola 18, 33

Froissart (The Modern Chroni-
cles of) 61

Froissart in 1002-03-06 61

From One Man's Hand to

Another n

Fuller (Margaret) Love Let-
ters of) 40

Furniss (Harry) at Home.... 36
Furee Blossoms 19

Gael and Gall (Bards of the) . * 3
Gaelic Literature (Story of

Early) 2, 87

Game of Consequences (A) ... 19

Gardening for the Million 82

Genealogy of Morals (A) 34

General's Daughter (The) 25

Generation of a Norfolk House

(One) 51

Gentleman Upcqtt's Daughter 13
German Education 76

PAGE
German-English Conversation

Book So

German Love Songs (Old) . . 6
Germany (Children's Study). . 83
Germany (Story of the Na-
tions) 47

Germany (The Evolution of

Modern)'^ 68

Ginette's Happinefs 16

Girl of the Multitude (A). . . . 28

Gladstone Colony (The) 62

Gladstone (My Memory of) . . 40
jlimpses into Plant Life. ... 74

Sod and the People 80

Sod's Scourge 4

Gods, Some Mortals, and

Lord Wickenham 17

God's Will 15

Goethe's Werke 4

Goethe (Life of) 40

Gogmagogs (On the) 14

Golden Sayings (The) 80

Good Men and True 41

Good Reading about Many

Books 33

Gordon (General) The Life of. 40

Gospels of Anarchy 33

Goths (The) 48

Gould-en Treasury (The) . . 62
Governance of England (The) 63
Sovernace of London (The) . 50

Grain or Chaff 43

Grand Old Hills (Under

the) 19, 85

Grand Relations 15

Grandmother's Advice to

Elizabeth 16

Grattan (Henry) 40

Great Minds at One 33

Great Minds in Art 44

Great Noodleshire Election . . 14

Great Pillage (Before the) 51

Greater Love (The) 26

Greece (Story of the Nations) 55

Greece (Old Tales from) 83

Greek Anthology (A Chaplet

from the) 4

Greek Art (Introductory

Studies in) 36

Greek Sculptors (Ancient) .... 36
Green Cloth Library 28

Green Tea 26

Grey Man (The) 13

Guiana Wilds (In) 72

Guy Mannering. . , 26

Gwilym (Dafydd ap) 2

Haeckel, Ernst (Life of) 41

Haileybury College 53

Halls (The) 37

Handbook of the Philippines. 73
Handy-Man Afloat and Ashore 86

Hansa Towns (The) 59

Happy-go-Lucky Land 34

Harvey (William) 41

Haunts of Men (The) 12

Hawaii and Japan (Vacation

Days in) 72

Health at its Best v. Cancer 74

Hearn (Concerning Lafcadio) 40

Heart of the Empire (The) . . 62

Heart of Midlothian (The) 26

Heavy Laden 15

Hebrew Lesson Book (A) 79

Hebrew Life and Thought.. 50

Heine's Werke 4

Helen Adair 10

Hellenism (The Progress of) . . 53

von Helmholtz (Hermann) . . 41
Hemans' Welsh Melodies

(Mrs.) 87

Herb Moon (The) 17

INDEX IN ORDER OF TITLES.— continued,

PAGE

Herb of Love (The) 14

Herbert (TheWorks of George) 87

Hermit of Carinel (A) 7

Heroic Adventure 42

Heroic Tales 59, 85

Herridge of Reality Swamp. 16
He that had received the

Five Talents 22

High Life in the Far East . . 14

High Policy 18

Highland Sister's Promise 19

Highland Widow 26

Hill (Sir Rowland) 41

Hillesden on the Moor ro

Himalaya (In the IceWorld of) 73

Historic Americans 79

History in Scott's Novels .. i
History of Co-operation

(The) 62

History of Jamaica 50

History of the Holy Eucharist 77

Holland 55

Holland House (The Pope of) 43
Home of the Dragon (The) ... 24

Hon. Stanbury (The) 24

Honour of the Flag (The) 25

Hookey 20

Horse (The) 35, 75

Horse (Psychology and Train-
ing of the) 75

Hotel d'Angleterre (The) 14

Hour Glass (The) 7

House by the River (The) 28

House of Arden (The) 84

House of Commons (Inner

Life of the) 66

Housewife's What's What . . . 81
How to Arrange with your

Creditors 86

How to become a Commercial

Traveller 86

How to become a Private Secre-
tary 86

How to become a Teacher 77

How to be Happy Though

Married 81

How to Buy a Business 85

How to get Married 81

How to Know the Starry

Heavens 75

How to Punctuate (Stops) 77

How to Study the Stars 76

Hugh Wynne 21

Humours of Donegal (The). . . 20
Humorous Rhymes of Histori-
cal Times 53

Hundred Riddles of the Fairy

Bellaria 19

Hundred Years Hence (A) ... 34
Hungary(StoryoftheNations) 58

Hungary: Its People 51

Hungry Forties (The) 62

Hunter (John) 41

Husband of no Importance . . 25
Ideas of Good and Evil .... 7

Idle Hour Series (The) 18

Illustration of Books (The) ... 36

Impossible Person (An) 13

Impressions of a Wanderer. . 70
Increase of the Suburbs (The) 63
India (The Brahmans of) . . 79

India (British) 50

India (Buddhist) 49

India (Cults of) 79

India (Imperial) 69

India (Literary History of). .. i

India, Mediaeval. . . .'. 52

India (The Mystics, Ascetics,

and Saints of 79

India (" Prosperous " Brit-
ish) 68

PAGE

India (Vedic) 55

India (Winter) 72

Indian Literature (Short His-
tory of) i

Industrial Influence of English

Patent System 64

Industrial Depression (Cause

of) 63

Industrial History of England 64
Industrial Rivers of the U.K. 86
Inmates of my House and

Garden 74

Inner Life of the House of

Commons 66

Innocent of a Crime 32

Insane Root (The) 23

Inspiration and the Bible ... 78

International (The) 87

International Law 65

Interpreters (The) n

Ipane (The) 68

Iphigenia in Delphi 4

Ireland (Children's Study) . . 83
Ireland (England's Title in) . . 64
Ireland (St9ry of the Nations) 52

Ireland (History of) 49

Ireland (Literary History of). 2

Ireland (Love Songs of) 7

Ireland (the Past History of). 54
Ireland : The Patriotic Par-
liament 49

Ireland (Young) 49

Irish Fairy Tales 83

Irish History (A Review of) . . 50

Irish Library (The New) 87

Irish Literature into the Eng-
lish Tongue 33

Irish Literature (The Revival

of) 33

Irish Memories 54

Irish Poems of Perceval Graves 4
Irish Song Book (The) . . 36, 87

Iron Gates (The) 17

Irving (Sir Henry) 41

Isle of Man (The Story of the) . 53

Is Liberty Asleep ? 60

Italian Characters 39

Italian Masters (Old) 37

Italians (Lives of Great) 41

Italy (Ancient) 54

Italy (The Birth of Modern) . 53

Italy (Modern) 54

Italy (Studies in the i8th Cen-
tury in) 52

Italy (The Barbarian Inva-
sions of ) 58

I, Thou, and the Other One . . 9
Ivanhoe - 26

Jamaica as It Is 71

Jamaica (A History of) 50

James Shervington 10

Japan (Story of the Nations) . 54
Japan (An Artist's Letters

from) 69

apan, Our New Ally 72

apan (Present-Day) 68

apan (The Real) 71

ava, the Garden of the East . 72

ews (The) 50

ews under Roman Rule (The) 54
ewish Literature (Short His-
tory of) i

ilt's Journal (A) 25

ob (The Original Poem of) . . 78

ohn Jones, Curate 23

ohn Sherman 32

ohnson Club Papers 86

osephine's Troubles 15

Journeys of Antonia (The) ... 14

Julian the Apostate 41, 54

J uvenile Offenders 34

PAGE

Juvenilia 33

Kafir Stories 26

Karakoram-Himalayas(Climb-

ing, &c., in the) 67

Karakorams and Kashmir ... 68
Keene (Charles), The Work of 37

Keith's Crime (Mrs.) 13

Kenfig (Buried City of) 50

Keuilworth 26

Kho tan (Sand- Buried Ruins of) 72
King Leopold's Soliloquy. . 65

King's Threshold (The) 7

Kingdom of Twilight 25

Kit Kennedy 13

Kitty Costello 8 85

Kolokotrones : Klepht and

Warrior 46

Kruger (Paul), The Memoirs of 4 1
Labour and Other Questions

in South Africa 69

Labour and Protection 63

Labour and Victory 41

Labour Legislation 62

Labour Movement (The) 62

Labour Party (The) 64

Lady from the Sea (The) 5

Lady Jean 50

Lady Killer (The) 27

Lady Mary of the Dark

House 32, 87

Lady Noggs, Peeress (The)

18, 84, 87

Lady's Honour (A) n

Lake of Palms (The) 14

Lally of the Brigade 20

Land of the Blue Gown (la

the) 70

Lang land's Vision of Plowman 2

Last Hours with Nature 75

Last Mackenzie of Redcastle 19
Last Step to Religious Equality

(The)F f 77

Latter-day Sweethearts 16

Laura's Legacy 27

Laurenson (Arthur) The Me-
moirs of 41

Law of God (The) 79

Lays of the Red Branch ..14, 87

Leader of Society (A) 47

Leaders of Men 43

Lear (Letters of Edward) ... 41
Leaves from the Life of an

Eminent Fossil n

Legend of Montrose (The). ... 26

Legend of St. Mark (The) 82

Legions of the Dawn (The). 25

Leithay's Banks (On) 19

Leopontine Alps (The) 67

Lessor's Daughter 14

Lessons from the World .... 79
Letters of Her Mother to Eliza-
beth 28

Lewell Pastures 19

Library of Literary History 2

Life and To-morrow 17

Life in a Crack Regiment 26

Life in the Open 71

Life in Two Hemispheres (My) %

(Duffy) 40

Life of an Empire ( The) 63

Life of Man on the High Alps . . 70

Life of Christ (The) 77

Light Eternal (The) 25

Lilac Sunbonnet (The) 13

Lincoln (Abraham) 42

Lindsay o' the Dale (A). ... 16
Links in My Life (Gambier) . 40

Lion's Whelp (The) 9

Literary History of America 3
Literary History of France. . . i
Literary History of India (A), i

INDEX IN ORDER OF TITLES.— continued.

PACK

Literary History of Ireland (A) 2
Literary History of Persia (A) . i
Literature History of Rome, i
Literary History of Russia., i
Literary History of Scotland 2
Literary History of the

Adelphi(The) ............ 48

Literary History of the Arabs 3
Literary History of the Eng-
. lish People (A) ...........

Literary Influence in British

History ................. i

Literary Life (My) (Mme.

Adam) .................. 38

Literary " U " Pen (The) ---- 87

Lithography and Lithograph-

ers ..................... 36

Little Entertainments ....... 22

Little Glass Man (The) ....... 83

Little Indabas ............. 70

Little Novels .............. 20

Lives WorthTiving Series(The) 42
18

PAGE

Manors of Suffolk (The) 49

Maps of the Alps of the Dau-

phiny

67

Margaret Foster 26

Margaret Grey 9

Margaret Hetherton 85

Marguerite de Roberval 21

Mariana 4

Marionettes (The) 6

2 | Marozia 16

j Marriage by Capture (A) n

Marriage de Convenance (A) . . 18

Marsena 15

Master Mariner, A : Eastwick 46

Master Missionaries 41

Master Passions 16

Masters of Medicine 42

Match-Making Mother (The

Confessions of) 14

Mating of a Dove (The) 20

Matrimonial Institutions (A

History of) 51

Living Buddha (The) ........

Living Matter (Nature and
Origin of) ................ 74

Liza of Lambeth ............ 21

Locum Tenens (The) . .

Matterhdrn (The)

Mawkin of the Flow (The) . .
Meadowsweet and Rue

Me and Myn

j Media, Babylon, and Persia
' I Melpomene Papers (The)

( J ames Choyce) 46

Lombard Communes (The) . . 48

Lombard Studies 48

London at School 80

London (The Governance of) 50

London Lovers 9

London Plane Tree (A) 5

Lonely Way (The)

Long Vigil (The) 27

Lord Maskelyne's Daughter 19

Lost Heir (The) 16, 85

Lost Land (The) 14

Love Affairs of Some Famous

Men 41

Love and the Soul Hunters ... 1 7

Love Cure (A) 28

Love is not so Light 13

Love in the Lists 21

Love Letters of Margaret Ful-
ler 40

Love Songs of Ireland 7

Love Songs of Robert Burns . . 3

Love Triumphant 21, 85

Lucas Malet Birthday Book.. 32
Lucie and I

PAGE

Motor Cracksman (The) 12

Motorists' A B C 85

Mountain Adventure (True

Tales of) 69

Mountaineers (Early) 68

Mountaineering in the Land

of the Midnight Sun 70

Mountaineering in the Sierra

Nevada 69

Municipal Government in Con-
tinental Europe 65

Municipal Government in

Great Britain 65

Municipal Lessons from S.

Germany 63

Musical Composers (Famous). 42

Mutineer (The) u

My Home in the Shires ... 19
76
32
75

My Lady's Garden (In) . . .

Myra of the Pines

Mysterious Psychic Forces .

Mystery of Laughlin Islands n

Mystery of Muncraig (The) . . 22
33
14

Mystery of Sleep (The) .
Mystery of theCampagna (A)
Mystics, Ascetics and Saints of
India (The) 79

Memoirs of Charles Boner (The) 19
Memoirs of Constantine Dix 22
Memoirs of Dr. Thomas Evans 40
Mental Traits of Sex (The) . . 76
Meredith (Novels of George) . i

Mermaid Series (The) 5 j Natfonafc^Bo'ok'

Messianic Hope (The) 79 National Credit

Mexico 50 ' KT-i: ' ^

Mexico (S. A. Series) 68

Mid Pleasures and Palaces.. 19

Mimi's Marriage 21

Millionaire (The) 28

Millionaire's Courtship (A) .. 20

Milly and Oily 85

Minister's Experience (A) . . 79

Minister's Guest (The) 26

Minor Poet (A) 5

Mirabeau the Demi-God .. 44, 58

Mireio 6

Miriam's Schooling 25

Mischief of a Glove (The) 13

Miserrima 22

Mis-rule of Three (The) 2*

Missing Friends 46

Mister Bill: A Man 20

Luncheons 82 Mistress of Langdale Hall .19, 85

Lyrics (M. F. Robinson)

6 i Model. Factories 63

87

M.A.B

Mabinogion (The) 20, 87

Mabinogion (Tales from the). . 83
Machiavelli, Niccolo (Life

of) 42

Madagascar (Robert Drury). . 46
Madagascar before the Con-
quest 72

Mademoiselle Ixe 14

Mad Sir Uchtred 13

Magic Oak Tree (The) 83

Magic of the Pine Woods 19

Maid of Maiden-lane (The) .... 9

Maitland (Sir Thomas) 42

Major Weir 21

Makar's Dream 19

Making of a Saint (The) 21

Man and Maid 22

Man-Eaters (Among the) 68

Man in the Street (The) 12

Man's Love (A) 27

Man's Mind (In a) 32

Man who was Afraid (The) ... 15

Manners for Girls 81

Manners makyth Men < . 81

Modernism 80

Nancy Noon _ . 27

Naomi's Exodus 21

Napoleon's Court (A Queen of) 47

Napoleon's Last Voyages . . 42

Natal (Tales from) 73

... 81

... 62

National Finance 59

National Finance, 1908 50

National Liberal Federation

(The) 66

Native Wife (His) 10

Naturalist (Life and Thoughts

of a) 38

Naturalist (Recreations of a) 75

Naturalist (Travels of a) 75

Nature and Origin of Living

Matter 74

Nature and Purpose in the

Universe 76

Nature Studies 76

Nature's Story of the Year ... 77
Near East (Trave.s and Politics

in the) 70

Need and Use of Irish Litera-

ture.

pnarch (A) 20 1 Neighbours

Modern Travel Series (The). 70

Moff 28

Moffat, Robert and Mary

(Lives of) 42

Molly Darling 18

Monarch Series (The) 53

Monarchs of Merry England

(The) 48

Monastery (The) 26

Monism (Concepts of) 80

Moasieur Paulot 18

Mont Blanc (The Chain of) ... 67

Moonlight 20

Mocr and Fell (By) 27, 72

Moors, Crags of the High Peak 66

Moors in Spain (The) 52

More about Wild Nature 74

Mother, Baby, and Nursery. . 82

Mother Goose (The True) 84

Motherhood 28

Mother of Pauline (The)

Motor Car (The)

Motor Cars 86

Ne'er-do- Weel (A)' .' .' .' .' .' .' .' .' .' .' 12

Negro-Nobodies 70

14

Nero, and other Plays 6

New Arcadia (The) 6

New Chronicles of Don Q... 23

New Egypt (The) 66

New England Cactus (A) 18

New Guinea (Through) 73

Newspaper Making (The Art

of) 85

New Spirit of the Nation

(The) 34, 87

New Zealand Alps (Climbs in

the) 68

Nietzsche: His Life and

Work 34

Nietzsche (The Philosophy of

Friedrich) 34

Nine Unlikely Tales 84

Noble Haul (A) 25

No Place for Repentance 22

Norfolk
(The)

and Suffolk Coast

68

Norman-Neruda (The Climbs

of) 71

Normans (The) 51

INDEX IN ORDER OF TITLES.— continued.

PAGE

Norway ... 48

PACK

Personal Matters (Certain) ... 32
Personal Story of the Upper
House, (The) 15

PAGE

Queen of a Day (The) .... 15
Qiieen of Napoleon's Court (A) 47
Quentin Durward 26
Quests of Paul Beck (The)., n
Quiet Hours with Nature 74
Quincy Adams Sawyer 22

Nun-Ensign (The) 37
Nutcracker and Mouse King 83
Nyria 23

Peru 68

Of Una 6

Peter Halket (Trooper) 26

Philippine Islands (The) 68
Phoenix and the Carpet (The) 84

Old Bailey 50

! Old Hall (The) 19

' Raiders (The)

1 Old Man's Darling (An) 12
' Old Mortality 26

Physiology(Studies in General) 75
Pillage (Before the Great) 51
Pinto, Ferd. Mendez, the Portu-
guese Adventurer 46

' Rainy June (A) ... 22

! Raleigh (Sir Walter)' 4 4.^

Old Tales from Greece 83
Old Tales from Rome 85

j Ranch Life and the Hunting
Trail 72

Old Time and New 44

Pirate (The) 26
Place of Animals in Human
Thought 34

Random Roaming 51

Olive in Italy 14

Recipes for the Million 82

Omnibus, De 22, 87
Once Upon a Time 83
O'Neill, Owen Roe 43, 87
Only a Kitten 84

Plant Histology (Methods in) 75
Plato's Dream of Wheels 34
Play-Actress (The) 13

Recreations of a Naturalist . . 75
Red Cloth Library (The) 30

Redgauntlet 26

! Opportunity of Liberalism .. 65
i Oriental Campaigns and Euro-
pean Furloughs 42

Plays of Beaumont, &c., see
Index of Authors
Please M'm, the Butcher ! 81
Poems of Mathilde Blind (A

Red Laugh 8
Red-litten Windows (Through
the) 16
Red Rubber 63

: Orientations 21
] Original Poem of Job (The) . . 78
Ottilie 19

Selection from) 3
Poems of Mathilde Blind -(The

Red Sphinx (The) 32
Red Star (The) 20

Outcast of the Islands (An) ... 13
Outcasts (The) . 15

Poems of Giosn6 Carducci.. 4
Poems of William Cowper
(The Unpublished) 4
Poems of John Dyer (The) ... 4
Poems of M. F. Robinson (The
Collected) 6
Poems (W. B. Yeats) 7

Popt anrl Ppnp1rm*» fTtip^ oS

Reef and Palm (By) 10
Reformer's Bookshelf (The) . . 64

Outlaws of the Marches 16

Religion and the Higher Life 78
Religion and Historic Faiths 79
Religion of the Plain Man.. 77
Religious Songs of Connacht?, 78
Religious Equality (The Last
Step to) 77

Overseas Library (The) 74

Pacific Tales 10
Pagan's Love (A) 13

Pages from a Journal 25 poHnd"' ""*" **""' «'

Renaissance Types 52
Renunciation 27
Retaliatory Duties 61

Retrospect 6

»SS' ™ay (Thc)- h K1S&;:;::::;::: It

Revelation and the Bible 78
Revolution in Tanner's Lane 25
Rhodesia (Pre- Historic) 68
Rhvmer (The) 20

Panal Monarchy (The) 47
Paradise Court 15

Political Situation (The) 65
Pope of Holland House (The) 43

Pans (Forty Years of) 52
Parish Providence (A) 20, 87
Paris-Parisien 71

Popular Copyright Novels . . 23

Ricroftof Withens 27
Ridan the Devil 10

Port Arthur (Siege of) 51

Riding, Driving, and kindred

Parker, Dr., and his Friends.. 43
Parnell Movement (The) 54

Porter, Endymion (Life and
Letters of) 43

Sports 86
Rights of Man in America . . 79
Riviera (Rambles on the) .... 72

Particular Book of Trinity

Portraits of the Sixties 42

Portugal 55

Party Organisation 63
Passion of Mahael (The) 1 1
Passports .... 8

Portugal (A Philosopher in) . . 72
Power of Character (The) . . 78
Prayers, Poems and Parables 79
Prince's Marriage (The).... 32
Prisoners of Conscience 9, 85
Prison Escapes of the Civil
War . . .46

Robinson Crusoe 82 83

Rob Roy . 26

Rock and Pool (By) 10

Pathless West (In the) ... 69

Rock Garden of Ours (That) 75
Rodin (Life and Work of
Auguste) 36
Rodman the Boatsteerer .... 10
Romance of theFountain(The) 19
Romance of a Hill Station. . . 19
Romance of a King's Life. . . 52
Romance of a Lonely Woman 22
Romance of a Midshipman . . 25

Patriot Parliament of 1680
(The) ... . 49 87

Patriotism under three Flags. 63
Patsy 27

Problem of Existence (The) . . 34
Problem of Prejudice (The) . . 12
Process of Government (The) 59
Professions for Girls 85

Patten Experiment (The) . .-. 20
Pax and Carolina 82 83

Peculiar History of Mary Ann
Susan (The) . ir

Programme of Modernism
(The) 80

Peking Garden (Round About
My) 70

Progress of Hellenism (The) . 53
Progress of Priscilla (The) .... 12

Roman Life under the Caesars. 58
Rome (Children's Study) .... 83
Rome (Story of the'Nations) . 50
Rome and Pompeii 66

Penelope Brandling .... 19

" Prosperous " British India. 68
Protection and Employment . 61
Protection (Side-Lights on) . . 65
Provence( Romantic Cities of) 67
Proverbs, Maxims, &c., of all
Ages 33

Pennine Alps (Central) 67
Pennine Alps (Eastern) 67
Pen Portraits of the British

Rome (Literary History of) i
Rome (Mediaeval) ">3

Rome (Old Tales from) 59, 85

1 People of Clop ton 10

Psalms and Litanies 80

Peoples and Politics in the
Far East 7r

Pseudonym Library (The) 23, 24

Rose, Shamrock and Thistle 19

Psychology and Training of
the Horse 75

Perceval (Spencer)... oo

Rossetti (Dante Gabriel)
(Letters of) ... ... 43

Peril of Change (In).

Psychology of Child Develop-
ment (The) 78

Peril in Natal (The) 61

Rousing of Mrs. Potter (The). 22
Royal Quartette (A) 47
Royal Rascal (A.) 16

Perils of Josephine (The) 16
Perils of Sympathy (The) 27
Persia 17

Public Purse and the War
Office ^9

Public Speaking and De-
bate 62 66 '

Persia (Literary History of ) . . i

Russia . . . . HA

'

XIV

INDEX IN ORDER OF TITLES.— continued.

PAGE

Russia and its Crisis 63

Russia (Literary History of) . . i
Russia Under the Great

Shadow f>5, 73

Russian Priest (A) . 23

Rutherford, Mark (The Auto-
biography of) 25

Rutherford's Deliverance 25

Sacrifice (The) 13

Saghalien Convict (The) 19

Saints in Society 9

St. Mark (The Legend of ) 82

St. Mark's Indebtedness to St.

Matthew 77

St. Ronan's Well 26

St. Stephen in the Fifties . . 59

Samhain 34

Sand-Buried Ruins of Khotan 72
Sanitary Evolution of London

(The) 62

Saracens (The) 5°

Sarah P. G 19

Sarsfield (Patrick) (Life of) 43, 87

Savage Club (The) 45

Savage Europe (Through) . . 73
Savonarola, Girolamo (Life

of) 4,3

Scandinavian Question (The) 6
Schiller's Dramas in England 3

Schiller's Werke

School for Saints (The) 17

School of Art (The) 27

School Out-of-Doors (Our) ... 79
Schulz Steam Turbine (The) 85
Scott's Novels (History in)., i
Scotland (Children's Study) . . 83
Scotland (Story of the Na-
tions) 53

Scotland (Literary History of) :
Scottish Literature (Short His-
tory of) ;

Scottish Seals (History of) 4:

Scrambles in the Eastern

Graians 7

Sea and the Moor (The) i'

Sea Children 8

Search of El Dorado (In) . . 7'

Searchers (The) i

Secret History of the English

Occupation of Egypt 4

Secret of Petrarch (The)

Secret Rose (The)

Secret of the Sargasso (The). 8

Segantini (Giovanni) 3

Segovia (Pablo de) 3

Seneca (Tragedies of)

Sentinel of Wessex (The)

Seven Nights in a Gondola .
Seven Splendid Sinners ....
Seventeenth Century Men of

Latitude

Sex and Society

Shacklett

Shadowy Waters (The)

Shakespeare in France

Shakespeare the Man

Shakespeare's Church

Shakespeare's Complete Son-
nets

Shakespeare Studied in Eight

Plays

Shakespeare Studied in Six

Plays

Shakespeare Studied in Thre<

Plays

Shameless Wayne

i She Loved Much n

Shelley in Italy (With) 70

Shen's Pigtail (The) 24

i

PACK

ervintons (The) 44

icrwood Forest (The Scenery

of) 71

illing Reprints of Standard

Novels 31, 87

lipp (Memoirs of the Mili-
tary Career of John) 46

iorter Plays 7

nilamite (The.) 8, 87

beria 73

berian Klondyke (In Search

of a) 73

cily 50

de-Lights on Protection . . 65
ege of Port Arthur (The) ... 51

ena (Guide to) 69

lena and her Artists 37

erra Nevada (Mountaineer-
ing in the) 69

;gn of the Peacock (At the) 26

ilas Strong 9

ilk of the Kine 20

ilver Age of the Greek World 53

ilver Christ (The) 22

imon Ryan the Peterite 18

mpson (Sir James Y.) 44

nnerVComedy (The) 17

ns and Safeguards (The).. 79

iren's Net (The) 25

ister of Marie Antoinette(A) 47

ister Teresa 22

isters of Napoleon (The) . . 58

isters of Ombersleigh 19

ituations of Lady Patricia. . 28

ix Girls 18, 85

iipenny Editions. 31

PAGE

outh American Republics

(Rise of the) 49

outh American Series (The) . 72
pain (Children's Study) .... 83
pain (Story of the Nations). 58

pain and her People 73

pain (The Bridle Roads of) 67

pain (Modern) 51

pain (The Moors in) 52

pain (Saunterings in) 72

pecimen Spinster (A) 32

pectre of Strathannan (The) 22
ipeeches on Questions of Pub-
lic Policy 60

iphere of " Man " (The) . . 65

splendid Cousin (A) 14

spoiled Priest (A) 26

>port and Travel : Abyssinia
and British East Africa .... 69
ports Library (The) 86

49

Squire Hellman
Squire to Prince (From) ,
Stansfeld (James)

lixty Years of an Agitator's

Life 41, 62

ikipsey (Joseph) 45

Slave Power (The) 79

slave to College President

(From) 4

sleeping Fires 15

Slight Indiscretion (A) 12

°mith and Modern Sociology

(Adam) 65

Smugglers and Foresters . . i
Social Classes in a Republic . 79
Social Ideas of Alfred Tenny-
son 33

Social Message of the Modern

Pulpit 6(

Social Reform (Towards) $<

Socialist Movement.inEngland 6;
Society in a Country House . . 41

Society in the New Reign 3

Society of To-morrow (The) . . 6

Sociology (General) 6

Some Emotions and a Moral.. 17

Somerset House 54

Son of Arvon (A) 23

Son of Don Juan (The) 4

Song of a Single Note (A) ... 9

Songs of a Sourdough 7

Songs of the Uplands 5

Sorrow's Gates (Through) 27

Soul of a Priest (The) 20

Soul's Departure (The) 7

Souh of Passage 9

South Africa (Story of the

Nations) 57

South Africa (Big Game Shoot-
ing) 6S

South Africa (Fifty Years of

the History of) 58

South Africa, Labour and
Other Questions 69

tarry Heavens (How to

Know the) 75

Stars of Destiny 28

Stem of the Crimson Dahlia

(The) 20

Stephen Kyrle 8

Stickit Minister (The) 13

Stokes (William) 44

Stolen Waters 12

Stops, or, How to Punctuate . . 77

Stories from Fairyland 82, 83

Story of the Amulet (The) . . 84
Story of a Crystal Heart(The) 23
Story of a Devonshire House 39, 49
Story of an Estancia (The) . . 13
Story of a Puppet (The) . . .82, 83
Story of My Struggles (Vam-

bery) 44

Story of the Nations (The) 56, 57
Stray Thoughts of R. Wil-
liams 80

Stronger than Love t

Stuarts (The) 5°

Studies by a Recluse 5r

Studies Historical and Critical 58

Studies in Biography 45

Studies in Black and White. . 86
Studies in General Physiology 75

Study in Colour (A) 27

Study of Temptations (A) 17

Suburbs (The Increase of the) 63

Suffolk (The Manors of) 49

Sullivan (Barry) 44

Summer Shade (In) 21, 87

Sunny Days of Youth (The) . . 8r

Supreme Moment (A) 27

Surgeon's Daughter (The). ... 2(

Susannah 20

Swanwick (Anna) 44

Sweden's Rights 65

Swift, Dean (Unpublished

Letters of) 44

Swift in. Ireland 44, 87

Swiss Democracy (The)

63

Switzerland

Sword and Pen (With) 18

Sydenham (Thomas) 44

Sylvia in Society n

Tale of a Town (The) 21

Tales abou t Temperamen ts .. 17

Tales from Natal 72

Tales from Plut,arch as, 84

Tales from Sptnser 84

South Africa (Little History of) 57 Tales of John Oliver Hobbes 17

South African History (The i Tales oi the Pampas 67

Beginning of) 57 i Tales of the'Trancvaai 72

INDEX IN ORDER OF TITLES.— continued.

PACK

Tales of Unrest 13

Tales told in the Zoo 84

Talisman (The) 26

Talks about the Border Regi-
ment i 85

Taxes on Knowledge 60

Teacher and the Child (The) . . 7g

Temple (The) 4, 7?

Tempting of Paul Chester

(The) 8

Ten Sermons 79

Tenants of Beldornie (The) . . 19
Terror of the Macdurghotts

(The) 22

Tessa 1 1

That Girl 28,84

Theism and Atheism 79

They Twain 25

Third Experiment (The) 19

Thomas Atkins (Mr.) 16,87

Thousand Pities (A) 28

Three Dukes 32

Three Generations of English-
women 43

Three of Them 13

Threshing Floor (The) 13

Thursday Mornings at the

City Temple 77

Thus Spake Zarathustra 34

Thyra Varrick 10

Tibet and Chinese Turkestan 68
Tibet (Through Unknown)... 73

Todi (The Range of the) 67

Tom Gerrard 1 1

Tongues of Gossip 26

Tormentor (The) 27

Tourgueneflf and his French

Circle 44

Towards the Heights 80

Towards Social Reform 59

Town and Jungle (Through). . 73

Town Child (The) 60

Toxin 22

Traitor's Wife (The) 32

Tramps Round the Mountains

of the Moon 69

Transient andPermanent(The) 79

Transplanted Daughters 16

Transvaal (First Annexation

of the) 52

Transvaal (Tales of the) 72

Travels of a Naturalist 75

Treasure Seekers (The) 84

Treasure Seekers (New) 84

Trend in Higher Education . . 78

Trinity Bells 10

Trinity College (Particular

Book of) 53

Triple Entanglement (A) 16

Trooper Peter Halket 26

Tropic Skies (Under) n

True Tales of Mountain Ad-
venture 69

Turbines (Steam) 85

Turf Smoke (Through the) ... 20

Turkey 52

Turkey and the Armenian

Atrocities 47

Tuscan Republics, with Genoa 49

Tussock Land 8

Twelve Bad Men (Lives of) ... 43

Twelve Bad Women 45

Two Countesses (The) 14

Two Standards (The) 10 I

Two Strangers (The) 22 j

PAG E

Tychiades 14

Uganda to Khartoum 70

Ultima Verba 3

Uncle Jem 32

Under the Chilterns 24

Under the Pompadour 18

U.S.A. and Spanish America

(Diplomatic Relations of) . . 52
University Problems in the

U.S.A 78

Unprofessional Tales 22

Unfilled Field (The) 22

Unwin's Green Cloth Library 28

Unwirc's Red Cloth Library . . 30

Unwin's Sixpenny Editions . . 31

Unwin's Half-Crown Standard

Library of History and

Biography 45

Unwin's Nature Books .... 76
Unwin's Popular Series for

Boys and Girls 85

Un win's Shilling Reprints of

Standard Novels 31, 87

Unwin's Theological Library 80

Up from the Slums 19

Upper Berth (The) 13

Uprising of the Many (The) . . 64
Up-to-Date Beginner's Table

Book 79

Up-to-date-Tables (Weights,

&c.) 79

Vagrant Songs 6

Valois Queens (Lives and Times

of the Early) fj

Value and Distribution 61

Vambery (Arminius) His Life 44

Vanity 25

Vanity Fair (In) n

Variety Stage 37

Vaughan (Henry) 87

Vedic India 55

Veldt and Kopje (By) 26

Venice 59

Village Politician (A) 60

Vineyard (The) 17

Vocations for Our Sons 86

Vulture's Prey v'The)

27

Wagner (The Case of) 34

Wakefield (Edward Gibbon).. 45

Wales (Story of the Nations) . . 49

Wales (A Short Story of) 49

Wales (Medieval) 52

Wales (The Statutes of) 59

Wanderer (A), and Other

Poems 5

Wander Years Round the

World 71

Warp and Woof 5

War to Date (The) 55

Washed by Four Seas 73

Washington Society (Forty

Years of) 44

Washington (The Youth of) . . 45

Was it Right to Forgive ? 10

Watcher on the Tower 16

Waterloo (Before and After) . 55

Waverley 26

Way to Keep Well (The) .... 82

Ways of Men (The) 15

Wellington's Operations 1808-

PAGE

Well-Sinkers (The) 71

Welsh Fairy Book (The) 84

Welsh Library (The) 87

Welsh Literature (Short His-
tory of) 87

Welsh People (The) 58

Wer Ist's 86

Wesley and his Preachers .... 45
West African Empire (The

Advance of Our) 73

West Indies and the Spanish

Main 55

West Indies (A Guide to) 71

Westminster Cathedral (The) 37
What I Have Seen While

Fishing 75, 85

What is Religion 1 77

When Wheat is Green 32

Where There is Nothing 7

Which is Absurd 16

White-Headed Boy (The) 10

White Umbrella (A) 26

White Woman in Central Africa 67

Who's Who in Germany 86

Why not, Sweetheart ? 16

Wide Dominion (A) 66

Wilberforce (Wm.) (Private

Papers of) 45

Wild Honey from Various

Thyme i

Wild Life in Southern Seas ... 14
Wild Nature Won by Kindness 75

Willowdene Will 27

Winning Hazard (A) 8

Winter India 72

Wisdom of Esau (The) 12

Wisdom of the Wise (The) 4

Wise Words and Loving

Deeds 40

Wistons 8

Wit of the Wild (The) 75

Within Four Walls 7

Wizard's Knot (The) , . 10

Woman (The) 15

Woman and the Sword (The) 20
Woman's Own Lawyer(Every) 82
Woman's Suffrage (The Case

for) 65

Woman's Wanderings (A) 40

Woman's Work and Wages . . 60
Woman Thou Gavest (The) . . 28
Woman Who Vowed (The) .. 16
Women Adventurers (The) . . 46

Wonderful Weans 20

Woodlanders and Field Folk . 77

Woodstock 26

Wordsworth's Grave 7

Working of the Workman's

Compensation Act 59

World at Eighteen (The) ... 13

World is Round (The) 20

World of Matter (The) 79

Would-be-goods (The) 84

Wreckers (The) 19

Yarn of Old Harbour Town . . 25

Yellow Fiend (The) 8

Yellow Library- (The) 32

Yorke the Adventurer n

Yorkshire Ramblers' Club
Journal 73

Young Ireland 49

1814 48 Young Sam and Sabina 13

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &c.— continued.

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &c.— con.inued. 12

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T. FISHER UNWIN'S PUBLICATIONS.

13 NOVELS, SHORT STORIES, &c.— continued.

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &.Q.— continued. 14

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T. FISHER CJNWIN'S PUBLICATIONS.

15 NOVELS, SHORT STORIES, &c.— continued.

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &o.— continued. 16

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17 NOVELS, SHORT STORIES, &c.— continued.

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NOVELS, SHORT STORIES, £c.— continued.

18

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IRVING.

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and Lord Wickenham. By
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i9 NOVELS, SHORT STORIES, &c.— continued,

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NOVELS, SHORT STORIES, &e.— continued.

20

(6)

By

The Bond of Blood.

R. E. Forrest.

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Newton Sanders.

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &c.— continued. 22

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23 NOVELS, SHORT STORIES, &c.— continued.

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Stronger than Love. GYP.

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A Winning Hazard. HOBBES (JOHN OLIVER).

BARR (AMELIA E.). The Herb-Moon.

I, Thou, & the Other One. McMANTTS /T \

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Was it Right to Forgive? ^ of the Br'%*d*'

BECKE (LOUIS). OUIP£ -

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The Strange Adventures RITA.

of James Shervington. The Ending of My Day.

Tessa and The Trader's Vanity! The Confessions

Wife. of a Court Modiste.

BUCHANAN (ROBERT). RUSSELL (W. CLARK).

s
(b. R ). shipman.

U.S 8nd SALA (GEORGE AUGUS-

The Stickit Minister. TUS).

CROMMELIN (MAY). Margaret Forster.

Half Round the World for SCHREINER (OLIVE).

a Husband. Trooper Peter Halket.

POTAPENKO (J.). Russian Priest. See Pseudonym Library. No. 7.

- - General's Daughter. See Pseudonym Library. No. 17.

- - Father of Six. See Pseudonym Library. No. 26.

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,-jr.Ll v3 -i •
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(1) Mademoiselle Ixe. By (6) The Hotel d' Angleterre.
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(2) The Story of Eleanor (7) A Russian Priest. By
Lambert. By Magdalene J. Potapenko. Translated
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(3) A Mystery of the Cam- (8) Some Emotions and a
pagna. By von Degen. Moral. By John Oliver

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T. FISHER UNWIN'S PUBLICATIONS.

NOVELS, SHORT STORIES, &c.— continued. 24

PSEUDONYM LIBRARY, THE.— continued.

(10) John Sherman. 8t Dhoya.

(30) The Passing of a Mood,

By Ganconagh (W.B.Yeats).

and Other Stories- By

(n) Through the Red-Litten

V. O. C. S.

Windows. By Theodor

(31) God's Will, and Other

Hertz- Garten.

Stories. By Use Frapan.

(12) Green Tea. A Love Story.

Translated by Helen A.

By V. Schallenberger.

Macdonell.

(13) Heavy Laden, and Old

(32) Dream Life and Real Life.

Fashioned Folk. By Use

By Ralph Iron (Olive

Frapan. Translated by Helen

Schreiner).

A. Macdonell.

(33) The Home of the

(14) Makar's Dream, and Other

Dragon. A Tonquinese

Russian Stories. By V.

Idyll. By Anna Catharina.

Korolenko, and Others.

(34) A Bundle of Life. By John

(15) A New England Cactus.
By Frank Pope Humphrey.

Oliver Hobbes.
(35) Mimi's Marriage. By
V. Mikoulitch.

(16) The Herb of Love. By

Georgios Drosines. Trans-
lated by Eliz. M. Edmonds.

(36) The Rousing of Mrs.
Potter, and Other Stories.

By Jane Nelson.

(17) The General's Daughter.

(37) A Study in Colour. By

By J. Potapenko. Translated

Alice Spinner.

by W. Gaussen.

(38) The Hon. Stanbury. By

(18) The Saghalien Convict,

Two.

and Other Russian Stor-

(39) The Shen's Pigtail, and

ies. By V. Korolenko, and

Other Stories of Anglo-

Others.

China Life. By Mr. M— .

(19) Gentleman Upcott's Daugh-
ter. By Tom Cobbleigh.
(20) A Splendid Cousin. By
Mrs. Andrew Dean.
(21) Colette. By Philippe St.

(40) Young Sam and Sabina.
By Tom Cobbleigh.
(41) The Silver Christ, and a
Lemon Tree. By Ouida.
(42) A Husband of No Import-
ance. By Rita.

Hilaire.
(22) Ottilie. By Vernon Lee.

(43) Lessor's Daughter. By
Mrs. Andrew Dean.

(23) A Study in Temptations.

(44) Helen. By Oswald Valen-

By John Oliver Hobbes.

tine.

(24) The Cruise of the "Wild

(45) Cliff Days. By Brian

Duck." By Holger Drach-

Rosegarth.

mann.
(25) Squire Hellman, and

(46) Old Brown's Cottages. By

John Smith.

Other Finnish Stories.

(47) Under the Chilterns. By

By Juhani Aho. Translated

Rosemary.

by R. Nisbert Bain.

(48) Every Day's News. By

(26) A Father of Six, and An

R. E. Francis.

Occasional Holiday. By

(49) Cause and Effect. By

J. Potapenko. Translated

Eilinor Meirion.

by W. Gaussen.

(50) A White Umbrella, and

(27) The Two Countesses.

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By Marie von Ebner-

(51) When Wheat is Green.

Eschenbach. Translated by

By Jos. Wilton.

Mrs. Waugh.

(52) Anthony Uasper. By Ben

(28) The Sinner's Comedy. By

Bolt.

John Oliver Hobbes.

(53) As a Tree Falls. By L.

(29) Cavalleria Rusticana, and

Parry Truscott.

Other Tales of Sicilian

(54) A 'Ne'er-Do-Weel. By

Peasant Life. By Gio-

Valentine Caryl.

vanni Verga. Translated

(55) Penelope Brandling. By

by Alma Strettell.

Vernon Lee.

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25 NOVELS, SHORT STORIES, &c.— continued.

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__1

NOVELS, SHORT STORIES, &o.-confinucd.

26

II

RYVES. At the Sign of ths Peacock. By K. C. Ryves. (First Novel
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ST. HILAIRE (Philippe). Colette. See Pseudonym Library. No. 21.

SALA. Margaret Forster: A Novel. By George Augustus Sala. (Popular
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SAN DERS. A Comedy of Three. See under " Little Novels." No. 8.
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SCHREINER. Dream Life and Real Life. By Olive Schreiner.
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Ivanhoe.
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Quentin Durward.

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Redgauntlet.

The Betrothed and Highland

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Castle Dangerous.
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SCULLY (W. C.). Kafir Stories. See Autonym Library. Vol. 10.
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SHEEHAN. A Spoiled Priest, and Other Stories. By the very Rev.
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27 NOVELS, SHORT STORIES, &c.— continued.

SMITH (John). Old Brown's Cottages. See Pseudonym Library, 46.
SNOW (Isabel). School of Art. See Pseudonym Library. No. 4.
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T. FISHER US WIN'S PUBLICATIONS.

ART AND MUSIC— continued. 36

FURNISS. Harry Furniss at Home. By Himself. With over 120

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T. FiSHEK UNWIN'S PUBLICATIONS.

37 ART AND MUSIO-continued.

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T. FISHER UNWIN'S PUBLICATIONS.

BIOGRAPHY, MEMOIRS, CORRESPONDENCE, &o. 38

BIOGRAPHY, MEMOIRS,
CORRESPONDENCE, &c.

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- Robert Adam, Artist and Architect. By Percy Fitzgerald.
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ADVENTURE SERIES, The. See at the end of this Section.

AUSTIN (Mrs. Sarah). See Ross, " Three Generations."

BAM FORD'S Passages in the Life of a Radical. See under
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BEARNE (Mrs.) Works. See under " History."

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BERNARD. Claude Bernard. By Sir Michael Foster. With Photo-
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BRODIE. Sir Benjamin Brodie. By Timothy Holmes. With Photo-
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BROWN. Captain John Brown of Harper's Ferry. By John
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BUILDERS OF GREATER BRITAIN. Edited by H. F. Wilson.
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[For full titles see under:']

(1) Sir Walter Ralegh. (5) Lord Clive.

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(4) Edward Gibbon Wakefield. (8) Sir Stamford Raffles.

8/6

2/6

10/6
3/6

a-

2/6

3/6

3/6
10/6

T. FISHER UN WIN'S PUBLICATIONS.

39 BIOGRAPHY, MEMOIRS, CORRESPONDENCE, &c.— continued.

BURTON. The Real Sir Richard Burton. By Walter Pbelps Dodge.

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CESARESCO. Italian Characters in the Epoch of Unification.
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CHEVALIER. Before I Forget. Being the Autobiography oi a
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CLIVE. Lord Clive: The Foundation of British Rule in India. By Sir
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" Politics."

COILLARD. CoHlard of the Zambesi. The Lives of Francois and
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COLERIDGE. TheStory of a Devonshire House. By Lord Coleridge,

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T. FISHER UNWIN'S PUBLICATIONS.

BIOGRAPHY, IIEMOIRS, CORRESPONDENCE, &Q.—continucf*. 40

DAVITT. Michael Davitt : Revolutionary, Agitator, rnd Labour
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DE LA REY. A Woman's Wanderings and Trials During the
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DOYLE. Bishop Doyle. By Michael MacDonagh. (New Irish Library.

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DU MAURIER. By Felix Moscheles. See under "Art"

ELIZABETH. The Correspondence of Princess Elizabeth of Eng-
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EVANS. The Memoirs of Dr. Thomas W. Evans. Recollections of
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FITCH. Ralph Fitch: England's Pioneer to India and Burma. His
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FITZMAURICE-KELLY. The Nun-EnsJgn. Translated from tbe
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Montalban. With Illustrations by Daniel Vierge, Illustrator of
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FULLER. The Love-Letters of Margaret Fuller (1845-1846). With
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FURNISS (Harry). Confessions of a Caricaturist. See under
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At Home. See under "Art."

GAMBIER. Links in My Life on Land and Sea. By Commander

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Demy Svo, cloth. net 1 5/ -

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GLADSTONE. My Memory of Gladstone. By Goldwin Smith. With

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GORDON. The Life of General Gordon. By Demetrius C. Boulger.

Illustrated. New and Cheaper Edition. Demy Svo, cloth. 6/-

(Lady Duff). See Ross, " Three Generations."

GOETHE. Life of Goethe. By Heinrich Diintzer. Translated by
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GOULD. Concerning Lafcadio Hearn. By G. M. Gould, M.D. With

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GRAY. Wise Words and Loving Deeds. See under "Lives Worth
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T. FISHER UNWIN'S PUBLICATIONS.

4i BI03KRAPHY, MEMOIRS-, CORRESPONDENCE, &c.— continued.

HAECKEL. Haeckel : His Life and Work. By Wilhelm Bolsche.
Translated and with an Introduction and Supplementary Chapter by
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Illustrations. Demy 8vo, cloth. net 15/-

HARDY. The Love Affairs of Some Famous Men. By the Rev. E.

J. Hardy, M.A. Imp. i6mo, cloth. 6/-

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HARVEY. William Harvey. By D'Arcy Power. With Photogravure

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HELMHOLTZ. Hermann von Helmholtz. By Prof. John G. McKen-
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HILL. Sir Rowland Hill. The Story of a Great Reform. Told by his
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HOLYOAKE. Bygones Worth Remembering. A Sequel to "Sixty
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HORRIDGE. Lives of Great Italians. By Frank Horridge. Illus-
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Prize Edition. 3/6

HUNTER. John Hunter. By Stephen Paget. With Photogravure

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IRVING. Sir Henr/ Irving. A Biography. By Percy Fitzgerald.
With a Photogravure Frontispiece and 35 other Illustrations. Demy
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JAPP. Master Missionaries. See under "Lives Worth Living."

Labour and Victory. See under " Lives Worth Living."

Good Men and True. See under " Lives Worth Living."

JULIAN The Apostate. A Historical Study. By Gaetano Negri.
Translated by the Duchess Lita-Visconti-Arese. With an Intro-
duction by Professor Pasquale Villari. Illustrated. 2 vols.
Demy 8vo, cloth. net 21 /-

KEENE (Charles). By Joseph Pennell and W. H. Chesson. See
under "Art."

KERR. Commissioner Kerr— An Individuality, By G. Pitt-Lewis,
K.C. With Photogravure and half-tone Portraits. Demy 8vo,
cloth. net 10/6

KRUGER. The Memoirs of Paul Kruger. Four Times President of
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Also a Fine Edition on Japan paper. Price on application.

LAURENSON. Memoirs of Arthur Laurenson. Edited by Catherine

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LEAR. The Letters of Edward Lear (Author of "The Book of
Nonsense ") to Chichester Fortescue, Lord Carlingford, and
Fiances, Countess Waldegrave (1848 to 1864). Edited by Lady
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net 15/-

T. FISHER UNWIN'S PUBLICATIONS.

BIOGRAPHY, MEMOIRS, CORRESPONDENCE, &,o.~conlinned. 42

By John G. Nicolay and
IQ Illustrations, Portraits

LINCOLN. Abraham Lincoln. A History.
Colonel John Hay. With many full-pa!
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11 LIVES WORTH LIVING," THE, Series of Popular Biographies.

Illustrated. Cr. 8vo, cloth extra, gilt edges. per vol.

3/6

(i)

Leaders of Men. By H.
A. Page.

(2) Wise Words and Loving
Deeds. By E. Conder
Gray.
Master Missionaries.

(3)

(4)

Studies
Work.

in Heroic Pioneer
By A. H. Japp.

By

Labour and Victory.
A. H. Japp, LL.D.

(5) Heroic Adventure. Chap-
ters in Recent Explorations
and Discovery. Illustrated.

(6) Great Minds in Art. By
William Tirebuck.

(7) Good Men and True.
By Alex. H. Japp, LL.D.

(8) Famous Musical Com-
posers. By Lydia Morris*

(9) Oliver Cromwell and His
Times. ByG. Holden Pike.

(10) Captain John Brown. By
John Newton.

(u) Story of Thomas Carlyle.
By A. S. -Arnold.

(12) Wesley and His Preachers.
By G. Holden Pike.

(13) Dr.Parker& His Friends.
By G. Holden Pike.

MCCARTHY. British Political Leaders. By Justin McCarthy. Illus-
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Portraits of the Sixties. By Justin McCarthy, M.P., Author of "A

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MACHIAVELLI. Life and Times of Niccolo Machiavelli. By Pro-
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MADD1SON. The Life of W. Randal Cremer, M.P. By Fred

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MAITLAND. Sir Thomas Maitland : The Mastery of the Mediter-
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MASTERSOF MEDICINE. EditedbyC. Louis Taylor. Cr. 8vo, cloth.

each 3/6
For full Titles see under :

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(2) William Harvey. (6) Hermann von Helmholtz.

(3) Sir James Y. Simpson. (7) Claude Bernard.

(4) William Stokes. (8) Thomas Sydenham.
MAUDE. Oriental Campaigns and European Furloughs. The

Autobiography of an Indian Mutiny Veteran. By Colonel Edwin
Maude, late H.M. 2nd (Leinster) Regiment. With a Photo-
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MOFFAT. The Lives of Robert and Mary Moffat. By their Son,

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MORRIS. Famous Musical Composers. See under " Lives Worth
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NAPOLEON. Napoleon's Last Voyages. Being the Diaries of
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NORTHCOTE (James). By Stephen Gwynn. See under "Art."

T. FISHER UNWIN'S PUBLICATIONS.

43 BIOG-RAPHY, &EMOIRS, CORRESPONDENCE, &c,— continued.

O'NEILL. Owen Roe O'Neill. By J. F. Taylor, K.C. (New Irish

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PAGE. Leaders of Men. See under " Lives Worth Living."

PARKER. Dr. Parker and his Friends. By G. Holden Pike. With

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PHILLIP. Admiral Phillip ; the Founding of New South Wales. By
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PLOWDEN. Grain or Chaff ? The Autobiography of a Police Magis-
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PORTER. Life and Letters of Mr. Endymion Porter. By Dorothea

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PRAED. My Australian Girlhood. By Mrs. Campbell Praed. With

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RAFFLES. Sir Stamford Raffles ; England in the Far East. By Hugh
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RALEGH. Sir Walter Ralegh ; the British Dominion of the West By
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RODIN. The Life of Auguste Rodin. By Frederick Lawton. With

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HISTORY AND HISTORICAL LITERATURE— continued. 52

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53 HISTORY AND HISTORICAL LITERATURE— continued.

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HISTORY AND HISTORICAL LITERATURE— continued. 54

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55 HISTORY AND HISTORICAL LITERATURE— co«/«mcd.

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THE SOUTH AMERICAN SERIES. See under " Geography."
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T. FISHER UNWIN'S PUBLICATIONS.

HISTORY AND HISTORICAL LITERATURE— continued. 56

10/6

STORY OF THE NATIONS, THE. The volumes occupy about
400 pages each, and contain respectively, besides an Index
and Coloured Map, a great many Illustrations. The size is large cr.
8vo. There are published now (Autumn, 1908) 65 volumes, which
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payment of £17 73. Delivered free in the London Postal district.

LIST OF VOLUMES.
[For full Titles see under Authors' names.']

(1) Rome: From the Earliest
Times to the End of the
Republic. By Arthur Oil-
man, M.A.

(2) The Jews. By Prof. James
K. Hosmer.

(3) Germany. By S. Baring-
Gould, M.A.

(4) Carthage. By Professor
Alfred J. Church, M.A.

(5) Alexander's Empire. By
John Pentland Mahaffy,
D.D.

(6) The Moors in Spain. By
Stanley Lane-Poole.

(7) Ancient Egypt. By Prof.
George Rawlinson, M.A.

(8) Hungary. By Professor
Arminius Vambery.

(9) The Saracens : From the
Earliest Times to the Fall
of Bagdad. By Arthur
Gilman, M.A.

(10) Ireland. By the Hon.
Emily Lawless.

(11) Chaldea: From the Earliest
Times to the Rise of Assyria.
By Zenaide A. Ragozin.

(12) The Goths. By Henry
Bradley.

(13) Assyria : From the Rise of
the Empire to the Fall of
Nineveh. (Continued from
"Chaldea.") By Zenaide
A. Ragozin.

(14) Turkey. By Stanley Lane-
Poole.

(15) Holland. By Prof. J. E.
Thorold Rogers.

(16) Mediaeval France. By
Gustave Masson, B.A.

(17) Persia. By S. G. W. Ben-
jamin.

(18) Phoenicia. By Prof . George
Rawlinson, M.A.

(19) Media, Babylon and
Persia : From the Fall of
Nineveh to the Persian
War. By Zenaide A.
Ragozin.

(20) The Hansa Towns. By
Helen Zimmern.

(21) Early Britain. By Prof.
Alfred J. Church, M.A.

(22) The Barbary Corsairs.
By Stanley Lane-Poole.

(23) Russia. By W. R. Morfill,
M.A.

(24) The Jews under Roman
Rule. By W. D. Morrison.

(25) Scotland. By John Mack-
intosh, LL.D.

(26) Switzerland. By Lina
Hug and R. Stead.

(27) Mexico. By Susan Hale.

(28) Portugal. By H. Morse
Stephens, M.A.

(29). The Normans, By Sarah
Orne Jewett.

(30) The Byzantine Empire,
By C. W. C. Oman, M.A.

(31) Sicily: Phoenician, Greek,
and Roman. By Prof. E.
A. Freeman.

T. FISHER UNWIN'S PUBLICATIONS.

57 HISTORY AND HISTORICAL LITERATURE- continued.

STORY OF THE NATIONS, THE.— continued.

(32) The Tuscan Republics, (48) The Franks,
with Genoa. By

Bella
Duffy.

(33) Poland. By W. R. Morfill.

(34) Parthia. By Prof. Geo.
Rawlinson.

(35) The Australian Common-
wealth. (New South Wales,
Tasmania, Western Austra-
lia, South Australia, Vic
toria, Queensland, New
Zealand.) By Greville Tre-
garthen.

(36) Spain : Being a Summary
of Spanish History from the
Moorish Conquest to the
Fall of Granada (711-1492
A.D.). By Henry Edward
Watts.

(37) Japan. By David Murray,
Ph.D., LL.D.

(38) South Africa. By George
McCall Theal.

(39) Venice. By Alethea Wiel.

(40) The Crusades : The Story
of the Latin Kingdom of
Jerusalem. By T. A. Archer
and C. L. Kingsford.

(41) Vedic India. By Zena'ide
A. Ragozin.

(42) The West Indies and the
Spanish Main. By James
Rodway, F.L.S.

(43) Bohemia: From the
Earliest Times to the Fall
of National Independence
in 1620 ; with a Short Sum-
mary of later Events. By
C. Edmund Maurice.

(44) The Balkans. By W.
Miller, M.A.

(45) Canada. By Sir John
Bourinot, C.M.G.

(46) British India. By R. W.
Frazer, LL.D.

By Lewis

By Sidney Whit-

Sergeant.

(49) Austria,
man.

(50) Modern England before
the Reform Bill. By

Justin McCarthy.

(51) China. By Prof. R. K.
Douglas.

(52) Modern England under
Queen Victoria. By Justin
McCarthy.

(53) Modern Spain, 1878-
1898. By Martin A. S.
Hume.

(54) Modern Italy, 1748-1898.
By Prof. Pietro Orsi.

(55) Norway. By Professor
Hjalmar H. Boyesen.

(56) Wales. By Owen Ed wards.

(57) Mediaeval Rome, 1073-
1535. By William Miller.

(58) The Papal Monarchy :
From Gregory the Great
to Boniface VIII. By
William Barry, D.D.

(59) Mediaeval India under
Mohammedan Rule. By
Stanley Lane-Poole.

(60) Parliamentary England :
From 1660-1832. By Edward
Jenks.

(61) Buddhist India. By T. W.
Rhy Davids.

(62) Mediaeval England. By
Mary Bateson.

(63) The Coming of Parlia-
ment. (England 1350-1660.)
By L. Cecil Jane.

(64) The Story of Greece
(from the Earliest Times
to A.D. 14.) By E. S. Shuck-
burgh.

(65) The Story of the Roman
Empire (B.C. 29 to A.D. 476).
By H. Stuart Jones.

(47) Modern France. By Andre

Lebon.

THEAL. The Beginning of South African History. By Dr. George
McCall Theal. With Maps and Illustrations. Demy 8vo, cloth.

A Little History of South Africa. By Dr. George McCall Theal.

Third Edition. Cr. 8vo.

South Africa. (The Cape Colony, Natal, Orange Free State, South

African Republic, Rhodesia, and all other Territories south of the
Zambesi.) By Dr. George McCall Theal, D.Lit., LL.D. Ninth Im-
pression (Sixth Edition). With 39 Illustrations and Maps. (Story
of the Nations. Vol. 38.) Large cr. 8vo, cloth.

16/-
1/6

T. FISHER UNWIN'S PUBLICATIONS.

HISTORY AND HISTORICAL LITERATURE— continued. 58

THOMAS. Roman Life under the Cassars. By Emile Thomas.

Numerous Illustrations. Small demy 8vo, cloth. 7/8

The Australian Commonwealth. (New South
Wales, Tasmania, Western Australia, South Australia, Victoria,
Queensland, Jew Zealand.) By Greville Tregarthen. Fourth
Impression. / \Tith 36 Illustrations and Maps. (Story of the
Nations. Vcl 35.) Large cr. 8vo, cloth. 5/-

TROWBRIDGE. Court Beauties of Old Whitehall. By W. R. H.
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Illustrations. Demy 8vo, cloth. net 15/-

• Mirabeau, the Demi-God. Being the True and Romantic Story

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cloth. net 15/-

Seven Splendid Sinners. By W. R. H. Trowbridge. With a

Photogravure Frontispiece and other Illustrations. Demy 8vo,
cloth. net 15/-

TURQUAN. The Sisters of Napoleon. Edited from the French of
Joseph Turquan by W. R. H. Trowbridge. Illustrated. Demy 8vo,
cloth. net 15/-

VAMBERY. Hungary : In Ancient, Mediaeval, and Modern Times. By
Prof. Arminius Vambery. With Collaboration of Louis Heilprin.
Seventh Edition. With 47 Illustrations and Maps. (Story of the
Nations. Vol. 8.) Large cr. 8vo, cloth. 6/-

VILLARI. The Barbarian Invasions of Italy. By Prof. Pasquale
Villari. Translated by Linda Villari. With Frontispiece and Maps.
2 vols. Demy 8vo. ' 32/-

The History of Florence. (The First Two Centuries of Florentine

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• Studies HistoricaF and Critical. By Professor Pasquale Villari,

Author of " Girolamo Savonarola," &c. With 7 Photogravure
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VOIGT. Fifty Years of the History of the Republic in South Africa
(1795-1845). By J. C. Voigt, M.D. With Coloured Maps, Sketches,
and Diagrams. Maps and Plans. 2 vols. Demy 8vo. net 25/-

WATTS. Spain : Being a Summary of Spanish History from the Moorish
Conquest to the Fall of Granada (711-1492, A.D.). By Henry Edward
Watts. Third Edition. With 36 Illustrations and Maps. (Story
of the Nations. Vol. 36.) Large cr. 8vo, cloth. 5/-

WEBSTER (Alexander). See " Needham."

WELSH PEOPLE, THE: Their Origin, Language, and History. Being
Extracts from the Reports of the Royal Commission on Land in
Wales and Monmouthshire. Edited, with Additions, Notes and
Appendices, by John Rhys, Principal of Jesus College, and Professor
of Celtic in the University of Oxford, and David Brynmor Jones,
K.C., M.P. Second Edition, Revised. Demy 8vo, cloth. 16/-

Also a cheap Edition. Large cr. 8vo, cloth. net 5/-

WHITMAN. Austria. By Sidney Whitman. With the Collaboration
of J. R. Mcllraith. Third Edition. With 35 Illustrations and a
Map. (Story of the Nations. Vol. 49.) Large cr. 8vo, cloth. 5/-

T. FISHER UNWIN'S PUBLICATIONS.

59 HISTORY AlfD HISTORICAL LITERATURE-co»tf»//<jd.

WHITTY. St. Stephen's in the Firties. By E. M. Whiity. With an
Introduction by Justin McCarthy. And Notes by H. M. Williams.
With Frontispiece, Demy 8vo, cloth. net 10/6

Also in Reformer's Bookshelf. Large cr. 8vo, cloth. 3/6

WIEL. Venice. By Alethea Wiel. Fourth Edition. With 61 Illustra-
tions and Maps. (Story of the Nations. Vol. 39.) Large cr. 8vo.
cloth. 5/_

Also Tourist Edition in Baedeker Binding. 5/-

WILKINSON. The Personal Story of the Upper House. See under
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7i GEOGRAPHY, TRAVEL, MOUNTAINEERING, &c.— continued.

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GEOGRAPHY, TRAVEL, MOUNTAINEERING, &c.— continued. 72

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GEOGRAPHY, TRAVEL, MOUNTAINEERING, &o.-««//,«/«/. 74

OVERSEAS LIBRARY, THE.

Cr. Svo.

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75 NATURAL HISTORY, &Q. -continued.

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79 RELIG-ION AND EDUCATION— continued.

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82

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