i

AX INVESTIGATION

THE SECONDAIIY UNDULATIONS

OCEANIC TIDES

CAUKiED ori' j;y the oiiDEi; or

THE EARTHQUAKE INVESTIGATION COMMITTEE

DURING

1903-1906.

po^

Frontispiece I.

No. 1.

No. 2.

Frontispiece II.

No. 8.

No. 4.

PREFACE.

The Pacific coasts of Japan have from time to time been
invaded by destructive sea waves, the so-called ' tsunamis.' Our
history abounds with the records of terrible catastrophes
wrought by ' tsunamis,' which were frequently associated with
great eartliqnakes originating in the bed of the neighbouring
ocean. The damage to life was sometimes counted by many
thousands, villages were swept away in a moment, and some-
times large extents of coast lines were buried under the water.
Before inquiring into the means of mitigating the damages
associated with the horrible inflow of the waters of the ocean,
it has in the first place been necessary to discover tlic nature
of excitement of these waves, and afterwards to search after
the necessary appliances for alleviating the effects of these
catastrophes. It was with this object in view that the second-
ary oscillations of the oceanic tide had to be studied, for
solving the problem touching the mode of excitement of the
destructive sea waves.

One of the most destructive sea waves of recent years was
that of Sanriku, by which the coasts of Eikuzen, Rikuchu, and
Mutsu bordering on the Pacific Ocean suffered serious damage.

By examining the mareograms during the disturbances,
Prof. Omori was led to the conclusion that the bays or inlets
oscillate like fluid pendulums with periods peculiar to their own.
What is the mode of excitement and how the period could be
calculated remained still unknown.

il PREFACE.

One recognises at once a close resemblance of these oscil-
lations to the seiches observed in lakes. An interview with
Mr. E. Sarasin dnring the Physical Congress at Paris in 1900,
and subsequent visit to Genève where the limnimeter is con-
stantly recording the motion of tlie lake, led me to suggest to
the Earthquake Investigation Committee the desirability of in-
vestigating the same subject in Japanese lakes, and search
after any effect which may be associated with earthquakes.
The proposal was at once taken up and limnological work was
begun in 1901, in Lakes Biwa and Hakone with Sarasin's
limnimeter. Although slight earthquakes liave been encountered
during the excursions, no special signs in the oscillation either
before or after the shock were experienced.

The Bay of Osaka being of elliptic form, and connected with
the sea at both extremities by narrow necks, partakes the charac-
ter of a large lake ; the question whether motion of the nature
of the seiches is to be traced as secondary oscillations of tides
was studied in 1902, by Drs. Nakamura, Honda, and Yoshida
with the assistance of two other students. In the records of
tide gauges at several stations were found superposed on the
principal tidal curve small undulations of constant periods, which
were approximately given by the wellknown Merian's formula.
In 1903, observations were made on the coasts of Tosa, Kii
Tôtômi, Shimôsa and PJkuchu which are open to the Pacific
Ocean. From these diagrams, it was found that on open coasts
the secondary oscillations are inconspicuous, but in bays and
inlets wliich open into the Pacific, they are significantly indicated
by the remarkable see- saw motions.

In the mean time, it appeared to me that Green's investiga-
tion concerning the motion of waves in a variable canal of

PEEFACE. iii

rectangular section of small depth can be extended to that of
non- rectangular section, and made to meet the cases of seiches.
With a shght modification, the investigation can be extended to
a wave motion in a canal, whose line of symmetry is not
necessarily straight. When the mean Tine is curved, the wave
will also participate in its course in nearly the same curvature.
The amplitude of oscillation is always affected by a factor
(breadth)"- x (depth)"^", showing how the height of the wave is
changed by the contour of the boundary and the deptJi of
water. The presence of the said factor shows that the effect
of a narrow basin is more conspicuous than its shallowness,
inasmuch as the elevation varies as the inverse square root of
the breadth, while the depth affects it inversely as the fourth
root. As a good illustration of tlie presence of this factor, we
may cite the extraordinary elevation of the destructive waves,
when the inlet gradually tapers like a wedge. The profile of
the wave is however difficult of calculation. On the coasts
bordering on the ocean, the term affecting the height is only
the deptli, so that the effect is not so ominous as in bays
and inlets ; consequently on calm days, the secondary oscil-
lations are not so pronounced. In fact, cases have often been
observed in which the boats far out at sea did not in the least
encounter the swell of the waves, although these caused great
disaster on the shore. These considerations led me to the con-
clusion that the mode of vibration of destructive sea waves is
of the nature of oscillations in a canal of variable depth and
breadth. If the vibration is stationary, and the length between
the node and loop /, then the period is 4/ — -7=^-, where /^ is the

depth, g the acceleration due to gravity and s the length
measured along the median line. Further it appeared to me

iv TEEFACE.

that stationary waves may be produced between the Kuroshiwo
and the shore, but when the water here is once disturbed, we
may expect most promiscuous groups of waves to be propagated
from the disturbance ; tliese waves will be swallowed by the
bays and estuaries lying in their way, especially when the
periods of oscillation are in close agreement.

Sir G. H. Darwin,'^' in his w^ellknown lectures on " Tides "
delivered in 1897 speaks of the tides in Venice : —

" Every visitor to Venice must, however, have seen, or may
we say smelt, the tides, which at springs have a range of some
four feet. The considerable range of tide at Venice appears to
indicate that the Adriatic acts as a resonator for the tidal
oscillation, in the same way that a hollow vessel tuned to a
particular note, picks out and resonates loudly when that note
is sounded."

Later investigation in 1904, 1905 and 1906, which were
mostly undertaken by Drs. Honda and Terada, assisted by
several graduates of the university, in nearly all the bays
bordering on the Pacific Ocean and the Japan sea, revealed the
truth of the acoustical analogy first propounded by the great
authority on the tides.

Led by this consideration, Dr. Terada treated the problem
of the secondary oscillations by bringing in the theory of re-
sonators in close contact with the vibration of bays and
estuaries. As an outcome of the discussion, a mouth correction
must be added to the period calculated according to Merian's
formula, as is wellknown in the theory of organ pipes. Still
more interesting is the mutual influence of the dumb-bell shaped
bays, bearing close resemblance to the acoustical resonators

* Tides, p. 168-1G9, First Edition.

PREFACE. V

communicating through a narrow channel. This is beautifully
illustrated in the oscillations of some bays, fulfilling the stated
condition.

When the volume of water in the bay and consequently
the depth and the breadth change, it is necessary to add a small
correction. This question was discussed by Dr. Isitani.

In limnological work, Sarasin's limnimeter is universally
recognised as a trustworthy and convenient instrument, and was
used in some of our lake surveys. In observations of secondary
oscillations, the large range of the tidal fluctuation prevented
the use of the instrument. The tide gauge in its usual form is
too cumbrous as a portable instrument, and the great damping
tlu'ough communicating tubes annihilates waves of secondary
oscillations of short periods, so that they are mostly lost on the
record. This defect was first modified by Dr. Nakamura by
balancing the pressure by means of a mercury column, and
greatly reducing the range of the tidal fluctuation without in the
least interfering with damping, which it was necessary to keep
suitably small in order that the secondary oscillations may not
be lost to view. This w^as further improved by Dr. Honda,
who greatly simplified the apparatus, and changed it to a neat
portable form. In most of the present investigations, Dr. Honda's
instrument was used.

The records obtained either by the tide gauge or with Dr.
Honda's instrument all present semidiurnal fluctuations, and on
it the undulations to be investigated appear in serrated form.
For the exact study of the phenomena, it is sometimes
necessary to eliminate the tidal undulation. This was effected
by means of Dr. Terada's tidal rectifier, by which only the
secondary oscillations were brought to view. When the bay

vi PREFACE.

responds to waves of different periods, so that they are mingled
together, this procedure was the easiest step for analysing the
different components.

Dr. Endrös, in his elegant research on the seiches in one
of the Bavarian lakes, made nse of a model for studying the
periods of oscillation. The same method was follow^ed by Drs.
Honda, Terada, and Isitani in a slightly different manner. The
models of bays having the contour lines and the magnified
depths of those already studied wei-e placed in a water tank,
so that tlie water in the model came to the level mark, and
waves were then excited in the tank. When the period of the
wave was in harmony with that of the model bay, the water in
the model responded to the exciting wave with extreme ease, and
continued vibrating for some time even after the subsidence of
the exciting wave. Not only was Dr. Endrös's experiment ex-
tended in this direction, but the courses of the stream Hues in
the model were closely studied by Dr. Honda. By an ingenious
device of sprinkling the surface of water with fine aluminium
powder, and photographing the surface by a camera with the
optical axis vertical, the trace of dust particles was observed ;
these photographs proved distinctly that the surface of the
water was oscillating and showed at a glance the mode of
response to the external source of excitement. This graphical
representation is more practical than that deduced from mathe-
matical calculation, which is next to impossible on account of
the variable deptli and tlie irregular contour. Thus in delineating
the oscillations proper to bays^ the study with models, when a
hydrographical chart can be obtained, is generally sufficient to
determine the nature of oscillations and their periods. It seldom
happened that the periods which can not be detected with the

PREFACE vii

model were ever observed. We are now in a position to infer
from the study of models how the bay oscillates without
entering into tlie actual registration of the secondary oscillations.

The contour lines of equal depths in different bays were
drawn by Dr. Isitani, who also undertook the laborious task of
integrating and determining the volume of the liay ; after suit-
ably choosing the median line, he also calculated tlie periods.
They generally agree quite closely with the observed values.

Tlie problem which still remains unsolved is how the waves
of different periods are generated in the surrounding ocean and
especiall}^ on the Pacific side. They may be due to local varia-
tions of atmospheric pressure, earthquakes, and such allied
causes. The following hint may also not be out of place as to
the cause of these waves on the Pacific coast. By far the
greater part of the destructive sea waves, which from time to
time have devastated our coast, seem to have had their origin
on the waves originating off the eastern coasts of Japan. The
existence of a sort of standing waves with the land on one
side and on the other the ocean current running nearly parallel
to the shore is quite imaginable. Along the east coast of
Rikuchii and the southern part of Hokkaido, the gulf of Tosa
and the adjacent districts, the course of the current is nearly
parallel to the line of equal depth. In such cases, the presence
of standing waves with the land and the current as the
boundaries is a matter beyond dispute. The current will not
behave exacth^ like a solid shore, but on account of its high
speed, it will partake the nature of a quasi-elastic solid, making
the waves rebound , It resembles a liquid jet in the ocean ; it
will oscillate with periods peculiar to itself ; it will thereby be
capable of transmitting vibration to the bounding waters ; it

Viii PREFACE.

will be set in forced vibrations by earthquakes and other causes.
In fact, the behaviour of the current resembles a piece of india-
rubber band, several hundred miles wide, stretched nearly
parallel to the coast on the Pacific side. It therefore appears
to me that the existence of Kuroshiwo is extremely favour-
able to the generation of exciting waves, which spread devasta-
tion along the sea coast.

Thus a portion of my proposals to the Earthquake In-
vestigation Committee has been happily brought to a close by
the indefatigable zeal of several investigators, who not only
prosecuted the observations, but improved the apparatus, deduced
corrections to observations, compared the observed with the
calculated periods, and solved the important question as to the
mode of excitement of oscillations proper to bays and estuaries.
It fell to my lot only to guide the method and fix the places
of observation, and it is on account of this responsibility that
I have allowed myself to add these words as a preface.

Finally I must not omit to state that my best thanks are
due to Dr. B. Mano, the President of the Earthquake Investiga-
tion Committee, for allotting during several years a part of the
fund granted to the committee for continuing the present research,
and the kindly interest with which he has watched the results.

H. NAGAOKA.

Physical Institute, Member of the Earthquake

May 1st, 1907. Investigation Committee.

CONTENTS.

Frontispieces

Preface page.

§ 1. Introduction 1-4

§ 2. Tide-gauges 4-11

§ 3. General results 11-17

§ 4. Special result

1. Coasts of Hokkaido 17-20

11. Japan Sea coasts of lionshin 20-23

III. Pacific coasts of Ilonsliiu 23-37

IV. Pacific coasts of Sliikoku 37-43

V. Coasts of Kiushiu 43-48

VI. Benin Islands and Formosa 48-49

§ 5. Experiments with models 4U-57

§ 6. Formula for calculating the periods of the

undulation in bays 57-67

§ 7. The method and the result of calculation for

the period of oscillation 07-70

§ 8. Sea waves hm\ secondary undulations 70-104

§ 9. Oscillation of large bays and anonudy of tides ..104-110
Name list of stations 11 1-113

PLATES.

Mareograms I-LXIV

Maps LXV-LXXXVI

Photographs of models LXXXVII-XCII

Weather charts XCIII-XCV

ERRATA.

Pfige 19, line 4, Insert ' 1905 ' after the date.
51, „ 12, for ' 2.28S ' read ' 2.20^.'
73, „ 14, „ '39.0' „ '3ß.O.'
„ 10.3, ,. 14, „ '28' „ '4.'

PI. Xn, for the vertical scale of Inuboye. replace that

similar to PI. XI.
„ XXV, in the vertical scale, for • 50,' ' 100 ' and ' 150.'
read ' 5,' ' 10 ' and ' 15.'

JOURNAL OF THE COLLEGE OF SCIENCE, IMPERIAL UNIVERSITY,
TOKYO, JAPAN,

VOL. XXIV.

Secondary Undulations of Oceanic Tides.

By

K. Honda, Binolniliahtslti, T. Terada, Iii(jahhsJii,
Y. Yoshida, lîiç/aJcmhi, and D. Isitani, TiigohisM.

With 2 frontispiecei=i and Do pJafcs.

§1. INTRODUCTION.

The tidal curves obtained by self-recording tide-gauges are
often accompanied by peculiar zigzags or secondary undulations
of considerable amplitude. The zigzags are generally conspicu-
ous at a station situated in a bay or an estuary. Tliis fact
seems to have been noticed by many earlier observers.

Without entering into these early matters of literature, let
us mention later valuable investigations on this subject. David
Milne'=' discussed tlie remarkable undulations of July, 1843, on
the coasts of Great Britain, and ascribed their origin to the
storm tlien prevailing at the district. Admiral Smythf referred
to a similar pheiiomenon at Mazzara, Sicily, where it had long
been termed Mirahia or Marroh]>lo. Sir George AiryJ studied
the phenomenon at Malta and believed that it was due to

*) D. Älilne, On a remarkable oscillation of the sea observed at varions coasts of Great
Trilain, Trans. Roy. Soc. Edin., 1844.

t) Admiral Smytb, Memoir descriptive of the resonrces, inhabitants and hydrography
of Sicily (London, 1824).

I) G. Airy, On tides in Malta, Phil. Trans. Roy. Soc. London, 169, 1878.

^ K. HONDA, T. TEPtADA, Y. YOSHTDA, AND D. ISITANI.

seiches between Sicily and the African coasts. The phenomenon
was also observed on another coast of Italy and at the northern
coasts of Enrope/''

In 1895, W. Bell Dawsonf commnnicated a paper to the
Royal Society of Canada, which showed the existence of the
secondary undulations of considerable amplitude. Professor
Duif J concluded from the observations at many stations along
the coasts of the Bay of Tandy and tlie Gulf of St. Lawrence,
that the secondary undulation had a period peculiar to each
station, and that it is of the nature of seiches excited by the
low atmospheric pressure. H. C. Russell*'-' states that at Sydney,
the undulations are in most cases dne to atmospheric disturb-
ances. Napier Denisonff of Toronto Observatory made a
systematic study of the subject in connection with the barometric
change. He attributed the phenomenon to long waves generated
by air waves of considerable wave length, accompanying the
low barometric pressure. Since several years ago Professor
Giovanni Platania'-'f has investigated the secondary undulations
in the Gulf of Catania. He attributed the phenomenon to the

*) G. Groblovitz, Eicerche snlle Maree cl'Iscliia, Eend. Ace. Lincei, 6, p. 26-32, 1890.
Sulle osservazioni mareografiche in Italia e specialmente su quelle fatte ad Iscbia, Atti del
I Congr. Ital., Geneva, 1893.

E. Sieger, Niveauveränderungen an Skandinavischen Seen und Küsten, Verb. 9te
Deutsch. Geogr., Wien, p. 224.

E. Brückner, Uebar Schwankungen der Seen und Meere ; Verb. 9tb Deutsch Geogr.,
Wien, p. 209, 1892.

t) Dawson, Notes on secondary undulations, Proc. Eoy. Soc. Canada, May. 1895.

X) Duff, Seiches on the bay of Fnndy, Amer. -Tourn. Sei., 3, p. 406-412, 1897. Perialic
tides. Nature, 59, 1899.

**) Eussell, The source of periodic waves, Nature 57, 1898.

tt) Denison, Secondary undulations of tide-gaiiges, Proc. Can. Inst., 1, p. 28, 1898.
The origin of tidal secondary undulations. Ibid, 1, p. 134.

*t) Platania, Le librazioni del mare con particolare riguardo al Golfo di Catania, Atti
del V Congresso Geogr. Ital., Najîoli, 1904. Nnove ricerche sulle librazioni del mare, An-
nuario der E. Istituto Nautico, I, 1907.

SECONDAEY UNDULATIONS OF OCEANIC TIDES. 6

plurinodal sfoitionary oscillation of the ba}^ and observed that
oscillations of conspicuons amplitude occur in connection with
barometric disturbances.

In tlie bays on the Pacific coasts of Japan, the phenomenon
is sometimes so conspicuous that it is commonly known as
yota. In the liarbour of Nagasaki, it is called the abiki ; its
amplitude of oscillation frequently exceeds 50 or 60 cms. The
yota or abiki is frequently accompanied with calm weather pre-
ceeding low barometric pressure, which is approaching our
coasts.

Professor F. Omori'^' investigated the secondary undulations
of Ayukawa, Misaki and Hososhima mareograms in connection
with the discussion of the several destructive sea waves, and
found that the periods of the waves are the same as those
observed in ordinary cases. The records of the tide-gauges
on Indian coastsf , of the waves which accompanied the great
eruption of Krakatoa, 1883, were also found to show the same
periods as frequently occur in ordinary cases. He explained
this interesting fact by the consideration that a bay or a certain
portion of the sea oscillates like a fluid pendulum with its own
period. Professor H. Nagaoka,^ in his paper on the hydrody-
namical investigation of the destructive sea waves, expressed
the desirability of a special inquiry concerning the phenomenon.
The suggestion was taken up by the Earthquake Investigation
Committee, and the task of carrying out a systematic observa-
tion was imposed upon us.

The observations were carried out during the period of 1903

*) Omori, Publications o£ Earthquake Investigation Committee 34, p. 5, 1900.
t) Omori, Proc. Tokyo. Math.-Phys. Soc. 2, p. 45.5, 1905. Publications of EartL. Inves.
Comm. 56, p. 29, 1906.

Î) Nagaoka, Proc. Tokyo Math.-Phys. Soc. 1, p. 126, 1903.

K. HONDA. T. TERADA, Y. YOSHIDA, AND D. ISITANI.

to 1 901) ; the number of bays and coasts observed amounts to
fifty one in all.

The observation consisted firstly in finding the periods of
the undulations peculiar to each bay or coast, and secondly in
comparing the phases of the undulation in the different portions
of a bay by simultaneous observations.

In' all cases, portable self-recording tide gauges were used.

The research on tlie plia se relation was carried out only
for several typical bays.

Fig. 1.

§ 2. TIDE-GAUGES.

The tide- l'auge used in our first
excursion of the summer vacation
of 1903 was that designed by
Assistant Professor S. Nakamura.'^'

The tide-gauge is very simple
and portable ; Fig. 1 shows dia-
gramatically the principle of the
apparatus. A and B are cylin-
drical vessels of glass ; A is con-
nected to sea -water by a lead tube
K through the cock li,. A suit-
able quantity of mercury is put
in A and B, which communicate
wdth each other by a thick
caoutchouc tube 6^. By sucking
a caoutchouc tube //, water is
brought into the vessel A ; when
the vessel and the lead tube are

S. Niikiinmra, Troc. Tokyo Matli.-Phys. See, 1, p. 123, 1902.

SECONDARY UNDULATIONS OF OCEANIC TIDES.

Fil

completely filled with water, the cock ^ R^ is closed. As the
level of the sea changes, the iiiercury in the vessel B moves up
or down ; if it is so arranged tliat the np and down motions
of the mercury are recorded on a vertical cylinder rotating with
a definite rate about its vertical axis, then the tide is traced on
the cylinder on a reduced scale. The cyhnder (20 cm. high and
9.4 cm. in diameter) usually rotates once per day ; it can also
be made to rotate once in two hours. Tlie cock 11^ serves for
damping the rapid up and down motions of mercury due to the
surface waves.

The recording arrangement of the tide-gauge was, in our
case, modified in, tlic following way (Fig. 2). The fioat made

of a hollow ebonite box loosely fitted
the vessel B, and on the box, a thin
aluminium rod was vertically erected.
A pen-holder p, which carried two arms
perpendicular to the ]jeii, was horizon-
tally fixed to the rod. At each end of
these arms, a friction wheel was fixed,
which rolled between the A^- shaped
grooves of two vertical guides gg.

In this way, the pen was constrain-
ed to move in a vertical line ; though
the pen was slightly pressed against
the recording cylinder E by a weak
spring, its friction was (piite insensible.
The photographs of the whole apparatus and the recording })en
are given in the frontispiece. Photo. Xo. 1 and 2.

If //j, ]}., and //., be the heights of tlie levels of sea water
and of mercury in A and B measured from the bottom of the

9 g

b K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANl.

sea, *S^^ and S_^ be the cross sections of A and B respectively,
then tlie pressure P of the water on the surface of mercury in
A is given by

when 7t is the atmospheric pressure and p the density of mercury.
We have also the equation of continuity,

S-, dh_ = — S:i dh-^ ;

taking the differential of the first equation, we have

dli, — dJt^ — p [dli-i — dh-^^ ;
eliminating dli, , we get

dih 1

This reduction-factor was nearly tV in our tide-gauge. The pre-
sent apparatus Avorked very satisfactorily, when it was possible
to set the instrument near the shore and the height of the
mercury in ^1 or B above sea level did not exceed 1 or 2 meters.
The practical difficulty, however, met with in our excursion
was that it was often necessar}^ to set up the apparatus at
high stations, where the sucking was difficult and the air dis-
solved in Waaler frequently gathered in the vessel A, and caused
an unusual rise of the pen. To avoid these inconveniences,
another arrangement has l)een used since the winter excursion
of lOOo. It is in fact a modification of LUchard's tide-gauge ;
in our case, his recording arrangement was replaced by ours,
and the caoutchouc -bag in his diving jar was dispensed with.
Our diving jar is shown in Fig. 3. A is a closed cylindrical
vessel made of brass, 12 cm. high and 12 cm. in diameter; it

SECONDARY UNDULATIONS OF OCEANIC TIDES.

Fis.

is screwed into a lieavy lead disk D. By the tulie a, water
enters tlie vessel and compresses the enclosed air. The vessel

A commnnicates with the recording-
apparatus by means of a brass tube
h and a long copper tubing / (in-
ternal diameter =2 mm.) ; the brass
tube is bent round as shown in
the above figure for convenience of
transportation. The recording ar-
rangement is almost the same as the
preceeding. In Fig. 4, B and C are

two glass vessels communicating
with each other by a thick caout-
chouc tube, and partially filled
with mercury. The copper tub-
ing / from the diving jar is con-
nected to the glass vessel B. p
is the pen, gg the guiding pillars
for vertical motion of the pen,
and E the recording cylinder. If
the jar is placed on sea bottom,
the pressure of the enclosed air
is balanced by the pressure due
to the difference of tlie heights
of two mercury columns. The
change of pressure caused by the
change of sea level al)ove the
diving jar, forces the motion of
the mercury column in the vessel
C ; this motion is recorded by the

Fig. 4.

K. HONDA. T. TERADA, Y. YORHIDA, AND D. ISITANI.

Fig.

pen on tlie vortical cylinder revolving uniformly. Tlie whole
apparatus, which is constructed in a form specially adapted for
transporting and setting, is given in tlie photograph No. 3 and
4 of the frontispiece.

The relation between the cliange of water level above the
jar and the mercury meniscus in the tube can be found in the
following way : —

Let /^ h, (Fig. 5.)
be the levels of sea
water above and inside
the jar respectively ;
//., //g be the levels of
mercury in the tubes
B and C. Let /; be
the common height of
the mercury in the two
tubes, when the jar is
not immersed in water. If tt and P be the pressure of atmosphere
and the pressure within the jar respectively, we have

where p is the the density of mercury.

If Sj, a be tlie cross section and the height of tlie jar, and
s,„ s,^ the cross section of the tubes B and C respectively, we
have, by assuming Boyle's law,

r \ .<?i(« — Aj) + 1; -f s.,{b - lu) \ = const.,

where r is the volume of the copper tube plus tliat of tlie
part of the tube B lying above the level h.

The differentials of the above two equations are

SECONDARY UNDULATIONS OF OCEANIC TIDES.

dP = d/i-M, = p{d/t-,-d/i.^
dP \ s,(a -h,) + v + s,{b - Ji,) \ - P{^,dh, + s.^m = 0 ;

we liave also the equation of continuity

,9.,dh. = —sßh^
Eliminating dh^, clh.,, clP from these equations, we get
dlh s,P

dh

p(l^^^^s,{a-h,) + v-{-s,{h-k^-\-s^P^+Ps,

Since the first three terms in the denominator of the above
expression are very small compared with the fourth, we have,
neglecting these small terms,

dh 1

dh /, s., \ S3

<i-^î)

Hence the motion of the mercury meniscus in the tube C is
practically proportional to the change of sea level. We may
also infer from the exact expression of dli^fdh that tlie volume
of the copper tu]:)ing need not be small compared with that of
the jar. Even, if the volume of the tubing is equal to that of
the jar and the change of sea level exceeds 3 m., tlio actual
value of dhjclh in the present apparatus does not difler from
the value given in the last equation by more than 0.2%'.

The effect of temperature may be calculated in a similar
way. For tliis purpose, the product of the volume and the
pressure in Boyle's law is put equal to RT, where T is the
absolute temperature, and E a constant. Here // is considered
to be constant ; we have then the equations

dP= -dh = pdk(i + ±y

10 K. HONDA, T. TEE.\DA, Y. YOSHIDA, AND D. ISITANl.

pdh/lj^Il^ L{a-h,) + v + s,{h-h;)\-P{s,dh,i-s,dJi;) = RdT,

S.J dh, = — sßh^ .

EliminatiDg dh^, dJi.., dP, we have approximately

dh B ^ B

dT ~ rA f. s.

P[o(l + A). + .,| '.^^^(1+1)

If we neglect v in comparison with the volume of the jar, R
is equal to Ps^a/T; hence

dh^

It

■"<i+x)

In our case, « = 12 cm., r —13. G and 1 + — = 1.26 ; hence at lO'C,

So

^ = 0.0025 cm.
di

When the temperature changes, the vapour tension also
changes ; but the change of vapour tension per degree rise of
temperature in the range of ordinary temperature is about 1/3
the change of pressure due to the thermal expansion of air.
Hence as the combined effect of these two, we may take

^ = 0.0033 cm.
dl

We have also experimentally determined this ratio by
heating the water in which the jar was immersed, and found 0.004
cm., wliich agrees fairly well with the above value. The greater
part of the enclosed air, which is in tlie diving jar, is subject
to the daily change of temperature by a few degrees of the sea
bottom. It is also an easy matter to protect the remaining
part of tlie air, from a considerable change of temperature.

SECONDARY UNDULATIONS UF OCEANIC TIDES. 11

Hence the error arising from the change of temperature is
usually to be neglected.

To estimate the effect of the barometric change, both h
and T are to be considered as constant ; we have then

dP = drc — dh^ = dn + pdh. (\^-l\,

dP\ s la - \) + y + s,{h - //,) \ - P{s,dh, -\- s.ßk) =^ 0

s.ßh.j. = — Sodli^ .

Eliminating dh^, diu, dP and neglecting small quantities, we get

dh.i a — /i,

dît 7-, /, 6'>,

^H^+x)

wliich is, in our case, nearly equal to —0.04 mm. for the change
of pressure by 1 cm. of mercury. Hence the barometric change
of 10 cm. in mercury only causes the displacement of the pen
not amounting to J mm. Thus in actual case, the error due
to the barometric change is quite insensible.

Thus the present tide-gauge may safely be used without
incurring any sensible error due to the changes of temperature
and pressure.

§ 3. GENERAL RESULTS.

In the excursion of the summer vacation of 1903, we were
assisted by Messrs Y. Inouye, N. Watanabe and T. Hirata,
then students of physics and now graduates. Stations were
Niiyama and Ayukawa in Rikuzen ; Inuboye in Shimôsa ; 0-
maezaki and Maisaka in Tûtômi ; Shionomisaki in Kii ; Tei,
Susaki and Yotsu in Tosa. Of these stations, Ayukawa and
Susaki are bays, and others are open coasts.

12 K. HONDA. Ï. lEllADA, Y. YOSHIDA, AND D. ISITANI.

Ill the excursion of the summer vacation of 1904, Mr. S.
Iwamoto, a graduate of physics, was our cooperator ; stations
were the bays of Ryôishi and Kamaishi in Kikuchiu, the bays
of Kojirohama, Yoshihama, Okirai, Eyùri and Ofunato in Eikuzen,
coasts of Niigata, Kashiwazaki, Naoetsu, Fushiki and Tsuruga
on the Japan Sea coasts. Besides, Shizuura in Suruga, Kame-
zaki and Kamagôri in Mikawa were chosen as our stations.
Susaki in Tosa was again observed in this summer.

In the winter vacation of the year, the excursion was un-
dertaken on the coast of Kiushiu. Observed bays were Hoso-
shima and Aburatsu in Hiuga, Kagoshima, Nagasaki and Shi-
monoseki. The bay of Hiroshima in the inland sea of Seto
was also observed.

In the spring of 1905, observations were made at Atami
on the western side of the Bay of Sagami. The summer vaca-
tion of the year was spent in the excursion to Hokkaido ; the
observed bays were Otaru, Nemuro, Hanasaki, Hamanaka,
Mororan and Hakodate. At Hakodate, Mr. Watanabe again
assisted our observations. In the winter vacation, the bay of
Shimoda in Izu was observed.

In the spring vacation of 1906, the bay of Moroiso in
Misaki was observed. The summer vacation of the year was
spent in the observation of the Strait of Naruto, which is
famous for its rapid current ; Mr. T. Fukuda was our co-
operator. Since July, 1906 the tides of the Bay of Tokyo have
been recorded by a tide-gauge of our system, set up by the
Office of the city.

Ill discussing our results, the valuable observations by As-
sistant Professor A. Imamura at Miyako and Odsuchi in Eikuchiu,
and Hiragata in Hitachi were utihzed. These observations wore

SECONDARY UNDULATIONS OF OCEANIC TIDES. 1 3

made by his portable tide-gange ; the duration of observation
was generally a day and night.

In addition, the records obtained by Lord Kelvin's tide-
gauges set up at the following ten stations were made use of :
Hanasaki in Nemuro, Ayukawa in Eikuzen, Kushimoto in Kii,
Hososhima in Hiuga, Fukahori in Hizen, Tonoura in Iwami,
Wajima in Noto, Iwasaki in Mutsu, Kelung and Takow in
Formosa.

The topographs of these stations and the records are given
in the plates annexed to the present paper.

From the thorough study of the numerous records obtained,
we may infer the following general conclusions : —

1. On the Pacific coasts free from any inlet in the coast
line, the secondary undulation is very inconspicuous, and of a
quite irregular nature.

2. On the Japan Sea side, the secondary undulation on
open coast is conspicuous, though not regular.

3. In a bay of considerable area, or a shallow bay com-
municating with the ocean by a narrow opening, the secondary
undulation is in ordinary cases inconspicuous.

4. In a deep bay or estuary, the breadth of which is not
large in comparison with its length, the secondary undulations
are most pronounced.

5. In bays or on open coasts, which are not far from each
other, common undulation is often observed.

6. The secondary undulations in many bays often change
their periods continuously, through certain ranges.

7. In some bays, the periods of the undulation are fairly
constant.

8. In many cases, the same trains of secondary undula-

14 K. HONDA, T. ÏEEADA, Y. YOSHIDA, AND D. ISITANI.

tions appear in the same phase with respect to the tidal wave
on consecutive clays of ordinary weather.

9. The phases of the prominent fundamental undulation at
different parts of a bay are equal.

10. The periods T of the most pronounced undulations is
fairly given by the relation

^/g^l

where / is the length of the bay measured along its depth, h the
mean depth of the bay, and g the acceleration due to gravity.

11. Just outside a bay, the undulation, which appears
inside the bay with considerable amplitude, may also be traced,
but its amplitude is very small.

12. In a bay, the periods of the conspicuous undulations
in the case of a storm, or a sea wave of distant origin, are the
same as those ordinarily observable in the ba}'.

It has long been believed that the secondary undulation in
a bay is the seiches between two opposite sides of the bay, but
according to our observations, the phase of the conspicuous
undulation is usually the same throughout the bay, so that this
view can not be generally true.

Napier Denison considers the undulation to be long waves
propagating from the ocean toward the bay. All results above
enumerated, except the 7th, 9th, 10th and 12th, can be ex-
plained by his view. But the fact, that there is a prominent
undulation peculiar to each bay, can not be explained by merely
considering progressive waves.

The undulation in a bay can, however, be explained in the
following way. For the sake of simplicity, take a rectangular
bay of a constant depth. Suppose a regular series of long waves

SECONDARY UNDULATIONS OF OCEANIC TIDES. 15

propagated in the direction of the length of the liay and re-
flected at its end. By the interference of the incident and
reflected waves, a stationary wave is formed, liaving its loop at
the end of the bay. If the wave length be s ach as to form
the node at tlie mouth of tlie bay, the period is the same as
that of the fundamental oscillation of a tank having double the
length of the bay, and therefore the amplitude of oscillation
must necessarily be magnified by the successive incidence of the
long wave. The case is just analogous to the acoustical re-
sonance of the air column to the vibration of a tuning fork
placed over its mouth. Tlie period of the oscillation is then,
neglecting the mouth correction, expressed by the relation

l/gh
where i^gh~ is velocity of the long wave.

If the waves of different periods proceed from the ocean
toward the shore, the one whose period coincides with that of
the oscillation liaving its node at the mouth of the bay, will
excite the most energetic oscillation of the bay water. Thus
bays on the coast line may be compared with a series of re-
sonators, each of which takes up selectively and resonates to
the note of its proper period from the chaos of very complicated
sounds or noises from the exterior. The plausibility of such
an idea seems to be established in a rather unexpected degree
by the present investigation. Moreover, the fact that the motion
of the level of a liay in the principal undulation is in the same
phase for several stations, stands in favour of the above view.
G. H. Darwin and Otto Krümmer'' seem to have entertained an
analogous idea.

*) Darwin, The Tides, CL. X, p. 1C9. O. Krümme!, Ueber Gezeitenwellen, Rede bei
Antritt d. Rektorates d. Königl. Christ.-Albr.-Uhiv. z. Kiel, 5 Marz, 1897.

16 • K. HONDA, T. TERÂDA, Y. YOSHmA, AND D. ISITANI.

In a bay, beside the uninoclal oscillation above referred to,
the oscillations with two nodes, three nodes etc., are equally
possible ; the periods of these oscillations are respectively h i
etc. of the period of the fundamental oscillation. In some
cases, the lateral oscillation of tlie bay excited by incident
waves is also possible, the period of which is principally deter-
mined by the oscillating water in the bay. These modes of
oscillations were actually found to exist in some bays such as
Hososhima, Ofunato, and Hakodate.

In the oscillation of the bay water just referred to, the
period of the forcing wave which corresponds to the maximum
resonance is not sharply defined ; l^ut within a certain range of
the period, the oscillation remains fairly conspicuous, as we
have often observed.

In bays of regular shape, such as Ofunato and Hososhima,
the position of the nodal line is determinate ; but in bays of
complicated shape, such as Shimoda and Susaki, several nodal
lines are conceivable. By the choice of the nodal lines, the
length and mean depth of the bay vary within a considerable
range, so that the period of the proper oscillation changes within
a certain range. Hence such a bay may resonate to any one
of the incident waves with the period lying within the same
range. In the two bays above mentioned, the period of the
conspicuous undulation was actually found to vary within a
moderately wide range.

As to the cause of the long waves, which manifest them-
selves as secondary undulations, we may mention the wind, the
cyclone, the earthquake, etc. It is a matter of fact that the
seiches in many lakes, which are the result of interference of
a direct and a reflected wave of long wave-length, are often

SECONDARY UNDULATIONS OF OCEANIC TIDES. 17

excited by wind. In the same way, the wind blowing on the
surface of the ocean, may cause waves several kilometers long.
Long waves of a considerable amplitude are often caused by a
deep cyclonic centre. Near a cyclonic center, the fluctuation of
pressure or of wind velocity are incessantly going on, and this
acting in an impulsive way, may cause waves of long periods.
An upheaval or depression of sea bottom due to an earthquake
or to a submarine eruption, may also be a cause of sea waves
of considerable periods.

§ 4. SPECIAL RESULTS.

In the present section, the results regarding each special
bay will be described. Here it w^ill be remarked that the num-
ber of observed periods are naturally rich at stations in wdiich
the observation was continued for a long interval, while they are
poor at stations temporarily observed during one or two days.
The general results, wdiicli we have summarized in the foregoing
section, were deduced from the following results of observations.

I. COASTS OF HOKKAIDO.

(1) Otaru (Aug. 12-15, 1005). Top. 1. PI. 1, Fig. 1.

Otaru is a city situated on the northern coast of Hokkaido.
The observation was made on the middle shore of the harbour.
Here, as in other coasts of Japan Sea, the tidal range is very
small, not exceeding 30 or 40 cm. ; the secondary undulation is
conspicuous, but not very regular. On the western side of the
harbour, Kelvin's tide-gauge is constantly working ; comparing
the record of the instrument with that of ours, we may con-
clude that the principal motion of the water in the harbour is
in the same phase.

18 K. HONDA. T. TEKADA, Y. YOSHmA, AND D. ISITANI.

The observed periods are 13.8'"-16.5'", 24.3"\ 3G.1™, 45.0"^;
in the above and in what follows, the lieavily printed figures
denote the conspicuous undulation. The calculated period
17.3"' fairy coincides with the observed period of the conspicuous
undulation.

It should be remarked that in our observation, short waves
of periods not exceeding a few minutes were always eliminated
by properly adjusting the tide-gauge.

(2) Nemuro (July 28-31, 1905). Top. 2. PI. I, Fig. 2.

Nemuro is a small bay on the eastern extremity of Hok-
kaido ; here the tidal range is tolerably large. Tlie periods
observed are 10.9", 33.7™, and 38.6"; while the calculated
period is 9.0"".

(3) Hanasaki (July 31-x\ug. 1, 1905). Top. 3. PI. I, Fig. 3.
Hanasaki is a shallow inlet on the Pacific coast not far

from Nemuro ; here also Kelvin's tide-gauge is constantly work-
ing. The undulation is generally inconspicuous, but regular
undulation of long period may often be traced : The periods
observed are, 6.9'", 14.2'"-17.7"\ 19.2'"-23.2'", 38.8", 44.5" and
61.2"'-65.6"; the calculated period is 10.9".

(4) Hamanaka (Aug. 4-5, 1905). Top. 5. PI. H, Fig. 1.
Hamanaka is a bay situated on the south-eastern coast of

Hokkaido. The observation was made at Kiritapp on the west-
ern side of the bay. During the observation, a low atmospheric
pressure was approaching from the Pacific side of Honshiu to
Hokkaido, and a conspicuous, but not regular undulation of
long period appeared on the record. Periods observed are 20.9'",
24.2", 49.5", 62.3"' and 84.3"', while the calculated is 48.2"'.

(5) Mororan (Aug. 17-22, 1905) Top. 7. PI. II, Fig. 2-3.
Mororan is a small bav on the southern side of the Volcano

SECONDARY UNDULATIONS OP OCEANIC TIDES. 19

Bay, situated near its mouth. The secondary undulation is
conspicuous and fairly regular ; observed periods are 46.7",
51.1-54.0"', and 58.3"-60.0™ ; while the calculated is 48.9".

(6) Hakodate (July 21-Aug. 10). Top. 8. PI. II, Fig. 4-5 ;
PI. III.

Hakodate is the best anchorage in Hokkaido, situated on
the middle coast of the Strait of Tsugaru, which separates
Hokkaido from Honshiu. The bay is approximately of a semi-
circular shape ; here Kelvin's tide-gauge has been continuously
working during the last 20 years, and has recorded several
important waves accompanying the sea waves originated along
the coasts of Pacific. Our observations Avere chiefly made at
the innermost parts of the bay ; i.e. near the wharf of Hakodate.
The simultaneous observations between Hakodate and Kamiiso on
the opposite sides of the bay, or Hakodate and Tachimachizaki,
just inside and outside the bay respectively, were also carried out.

At Hakodate, the secondary undulation is very conspicuous,
sometimes exceeding 30 cm. and fairly regular. The periods of
the most conspicuous undulation range from 45.5" to 57.5".
Sometimes its octave 21.9"- 24.5" is found superposed on the un-
dulation of the above period. In the undulation accompanying
the sea waves, the octave always appears in a very marked
degree. The longer period was found to correspond to the fun-
damental oscillation of the bay, wMle its octave corresponds to
its lateral oscillation.

The calculated periods for these oscillations give 45.3" and
23.6" respectively. As we shall see hereafter, the periods of
oscillations corresponding to these modes, as given by our model
of the bay, are 47.0" and 23.6" respectively.

When the simultaneous observations between Hakodate and

20 K. HONDA, T. lERADA, Y. YOSlJlDA, AND D. ISITANI.

Kamiiso were carried out, the fundamental oscillation only ap-
peared on our record«. The comparison of our records shows
that the phase of the oscillation is the same for these two stations.

The simultaneous observations between Hakodate and Ta-
chimachizaki showed that notwithstanding the conspicuous un-
dulation appearing in the bay, the undulation just outside the
bay was almost insignificant. This is a good example for
illustrating our view regarding the secondary undulation, which
we have propounded in the foregoing section. Beside the
periods above described, a longer period of about 120" is some-
times traceable.

The amplitude of secondary undulation is usually increased
by a low barometric pressure approaching the bay. As a good
example, we may cite a cyclone on Sept. 21-22, 1904, wliich
was approaching from the Pacific side of Honshiu toward Hako-
date. The undulation in the bay (PI. HI, Fig. 1) continued
over a whole day with a considerable amplitude, its maximum
exceeding 40 cm. ; the periods of conspicuous undulation were
47.1™-56.9" and its octave.

The bay is especially sensitive to incident sea waves ;
waves originating on the American coasts were often beautifully
recorded by the tide-gauge in tlie bay. The periods of the
Eeuador wave in the bay were 21.9'" and 40.9™- 49.2'" ; while
those of the Valparaiso wave were 22.1'" and 48.0"- 53.0'".

The periods of the great sea waves of Sanriku (PI. HI,
Fig. 2) in 1896 were 18.8", 39.5"", and 57.5'"; those of the
small sea waves (PI. Ill, Fig. 3) in 1897 were 22.1'" and 45.5'".

II. JAPAN SEA COASTS OF HONSHIU.

(1) Aomori (July 18-21, 1905). Top. 9. PL IV, Fig. 1-2.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 21

The large Bay of Miitsii has the form of a dumb-bell, con-
nected to the Strait of Tsugaru by a wide neck. The observa-
tion was made at Aomori, when the centre of a deep low
pressure was approaching the bay from Japan Sea side (PI.
XCIII). On this occasion, a regular undulation of 103™ appeared
on the record and continued for a day and a lialf. Upon this,
an undulation of the period ranging from 23.4"' to 26.3" was
superposed. Besides, a period of about 300™ may also be traced.

The undulation of 103™ is probably the lateral oscillation of
the bay ; the period 108'" calculated on this view is in fair agree-
ment with the observed period. The undulation of the shortest
period may be its higher harmonics. The longest period is
perhaps that of the fundamental oscillation of tlie bay having
its node at the mouth ; tlie calcalation gives 284™ as the period
of this mode of oscillation.

(2) Iwasaki. PI. IV, Fig. 3-4.

Iwasaki is situated on a northern coast of Mutsu ; here
Kelvins' tide-gauge is constantly working. The undulation in
ordinary w^eather is generally conspicuous ; in stormy weather
(PI. IV, Fig. 3-4), undulations of considerable amplitude are
sometimes observed. The periods observed are 8.3™, 11.0™-
13.5™, 15.8™- 17.3™.

(3) Niigata, Kashiwazaki, and Naoetsu (Aug. 9-17, 1904).
PI. V, Fig. 1-2.

These stations are situated along the nortliern coast of
Echigo. The secondary undulation in these coasts are con-
spicuous, but much comphcated by the superposition of several
minor components. The periods observed are : 22.6™ at Niigata ;
11.6™-12.4™, 14.5™-17.2™, 22.0™-25.5™, 30.0™-35.8™ and 43.3™ at
Kashiwazaki ; and 37.6™ at Naoetsu.

22 K. HONDA, T. TERADA, Y. YOSEIDA, AND D. ISITANI.

(4) FiLsliild (Aug. 14-24, 1904). Top. 12. PI. V, Fig. 3-4.
Fashiki is situated at the end of the Bay of Toyama ;

since 1905, a tide-gauge of our system has been set up and
the record continuously taken, under the care of the meteorolo-
gical station of the city. Here the secondary undulation is not
conspicuous ; but the regular undulation of 11.3" -14.9"" is some-
times observed. In addition to this, the periods 30.0™, 54.1"",
58,0™ and 119™ are to be traced. The period calculated is 52.7™.
Here we had several remarkable examples of the instances,
in wliich a strong wind blowing toward the land often heaps
up the water on the shore to a considerable height.

(5) Wajima. PI. V, Fig. 5.

Wajima is situated on the northern coast of Noto ; there
is a Kelvin's tide-gauge at work. In ordinary weather, undula-
tion of considerable amplitude often appeared on the record.

The periods observed are 12.5™-16.4™, 21.9™, 28.0™-33.0™,
81.5™.

(6) Kanaiwa (Aug. 25-26, 1904). PI. VI, Fig. 1.
Kanaiwa is situated on the open coast near Kanazawa ;

the secondary undulation is not only inconspicuous, but also
irregular. The periods 21.2™ and 59.0™ may however be traced.

(7) Tsuruga (Aug. 28-30, 1904). Top. 13. PI. VI, Fig. 2-3.
Tsuruga is a city at the end of a long V-shaped bay, which

forms a part of the Bay of Wakasa. Usually the undula-
tion is conspicuous, but not regular ; undulations of the periods
56.7'" and 62.7'"~67.7"' often appear with considerable ampli-
tudes. We can also trace shorter and regular undulations of
the periods 10.5™ and 22.6™.

The calculated period 59.0™ fairly agrees with the observed.
It is however to be noticed that at the mouth of the bay.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 23

several nodal lines are conceivable, which may change continu-
ously from one to the other. The above value corresponds to
the mean position of the nodal lines, and tlierefore the calculated
values corresponding to the other nodal lines, may be greater or
less by several minutes than the above value. In the actual case,
we also found the periods varying continously from 5G.7"' to
62.9" or from 62.9"^ to 07. 7".

(8) Tonoura. Top. 15. PI. VI, Fig. 4-5.

Tonoura is a small inlet situated north of Hamada in
Iwami ; here a Kelvin's tide-gauge is at work. The secondary
undulation is conspicuous, especially in stormy weathers (PI. YI,
Fig. 4-5). The characteristic period in the bay is 11.9"-12.9"
while the calculated value is ll.F", in good accordance with
the actual. Besides, tlie periods 15.3'" and 21.5'"-2S.8" are
sometimes observed.

In concluding the description regardmg Japan Sea coast,
it may be observed that in many of these stations, undulations
of the periods 120'"-! 30'" and 150'"-! 80'" may sometimes be traced.

III. PACIFIC COASTS OF HONSHIU.

(1) Same (Aug. 24-25, 1905). PI. YII, Fig. 1.

Same is an open coast on the Pacific side of j\Iutsu ; here
the secondary undulation is conspicuous, but not regular.
The periods observed are 1G.4"\ 35.0'" and 41.5"\

(2) Miyako. Top. 16. PL VII, Fig. 2-3.

Miyako is a bay on the coast of Rikucliiu, where a mete-
orological station is placed. Dr. A. Imamura has set up a tide-
gauge of the Richards' type at Kajigasaki, for the purpose of in-
vestigating sea waves in connection with the earthquake, and many
valuable records were obtained, some of which are reproduced in

24 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

PI. Vir. Fig. 2-3. Tlie periods usually observable are 12.0",
21.3"- 22.0'", 23.0"- 27. G'" and 55.2". The periods observed in
the bay in the case of a storm or a sea wave of distant origin
are those usually found in the bay. The calculated period 24.0",
which corresponds to the seiches between Miyako and the end
of the bay, fairly accords with the conspicuous observed periods
21.3"-22.0".

(3) Odsuchi (Aug. 11-12, 1902). Top. 17.

Odsuchi is a bay not far from Miyako. Here the undulation
is conspicuous ; the period observed by Dr. Imamura is 27.0",
while the calculated period is 30.7."

(4) Ryôishi and Kamaishi (July 21-28, 1004). Top. 18-19.
PI. Vll, Fig. 4 ; PI. Ylll, Fig. 1-2.

The bays of Ryôishi and Kamaishi in Pikuchiu have
their mouth in common and in reality form a W- shaped bay.

The principal station was chosen at Kamaislii at the end
of the latter bay ; other stations were Heida, Kamagasaki, Washi-
nosu and Aodashi. The simultaneous observations in these
stations taken three at a time showed that the phase of the
principal secondary undulation is the same for these stations.
The amplitude of the undulation did not much diminish at
Kamagasaki and Washinosu as compared with the amplitude at
Kamaishi. At Aodashi near the mouth of the bay, the second-
ar}^ undulation was very inconspicuous. The undulations at
Ryôishi were much complicated by the superposition of shorter
waves. We could sometimes find the undulations of the same
period and phase as those at Kamaishi. The periods observed
are 12.0"-13.2", 20.3" and 22.8" at Ryôishi, and 8.6"-9.4",
20.3" and 24.8"-26.0" at Kamaishi ; the calculated periods for
these bays are 21.3" or 20.0" and 24.8" or 22.3" respectively.

SECONDARY UNDULA.ÏIONS OF OCEANIC TIDES. 25

Dr. Imamura also obtained the undulation of the same periods
in 1902.

The bay of Ryôishi is of a Y-shape, and consequently all
waves proceeding toward the bay are found at Eyôishi situated
at the end of the bay. On the other hand, the bay of Kamaishi
is somewhat crooked so that at Kamaishi near its end, the sea
is extremely calm giving rise to few short waves such as are
always observable in free coasts. A wave, whose wave length
is very large compared witli an obstacle, goes round the ob-
stacle ; but a wave whose wave length is very small, is screened
by it and the sea behind it is quite free from its influence.

At Kamaishi and Ryôishi, we met with a storm on July
27-28 ; the character of the secondary undulations was not
altered, except tliat they were much superposed by zigzags of
shorter periods, and that their amplitude was somewhat in-
creased.

(4) Kojirohama (July 26-31, 1904). Top. 20. PL YIII,
Fig. 3.

Kojirohama is a small bay, south of the bay of Kamaishi ;
stations w^ere Kojirohama and Oishi, which are facing to each
other. The simultaneous observation showed that tlie phase of
the most prominent undulation is the same for these two stations.
The observed periods are lS.S'"-20.4'" and 24.6'", while the
calculated period is 26.0"\

It is remarkable to observe that the prominent period in
the bay is nearly the same as that of Kamaishi or Ryôishi.
Dr. Imamura also observed undulation of the same period in
the bay.

(5) Yoshihama (July 28-Aug. 6, 1904). Top. 21. PL IX,
Fig. 1-3.

26 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

This bay lies in the south of the bay of Kojiroliama and
not far from it. Stations were Yoshihama, Konpaku, Senzai
and Kokabe. The secondary undulation was generally irregular
and inconspicuous ; but on Aug. 2-3, there appeared an unusual
undulation of regular type of the period 18.5"-19.6'". Probably
this undulation was connected with the low pressure then pre-
vailing over the Pacific to the south of Tosa. It was also found
that the undulation was very faint at Senzai and Kokabe near
the mouth, and conspicuous at Yoshihama and Konpaku at and
near the end of the bay respectively, and that the phases of the
principal undulation were the same for these stations. The
periods observed are 15.4"\ 16.5'"-17.9"\ 18.5™-20.r, 22.2™-
23.r\ and 32.0'"-37.2'". The calculated period is 21.1'" in good
coincidence with the period of the conspicuous undulation.

(6) Okirai (Aug. 4-7, 1904). Top. 22.

Stations were chosen at Okirai and Koisliihama. The bay
of Okirai had a rather narrow mouth. Tlie observed periods are
10.0™, 27.5'"-29.9™, and 54.5'", while the calculated period is 26.4™.

(7) Ryôri (Aug. 8-9, 1904). Top. 23.

The bay of Ryori lias a form similar to tlie bay of Yosliiliama,
but its dimension is much smaller ; the station was chosen at
Nonomae.

The undulation was not conspicuous ; but the periods 12.9"',
18.3'", 29.0"^ and 33.3'" may be traced. The undulations ob-
served by us were not conspicuous, though one of the periods
lies fairly near the calculated period of free oscillation 18.4'".

(8) Ofunato (Aug. 8-10, 1904). Top. 24. PL X, Fig. 1-4.
The bay of Ofunato lias an elongated form and is some-

A

what crooked near its mouth, so that at Ofunato situated at
the end of the bay, the sea is extremely calm. It has a form

SECONDARY UNDULATIONS OP OCEANIC TIDES. 27

specially fitted for the comparison of the phases of the second-
ary undulations at diflerent stations along the bay. Stations
were Ofunato, Sunagosaki, Takonoura and Hosoura. The
simultaneous observations between Ofunato and other stations
were taken at three different dates.

Fig. 1 and 3, or 2 and 4 are the records of the simultane-
ous observations ; 1 and 1', 2 and 2', and 3 and 3' in these curves
indicate the positions of tlie corresponding time. They clearly
show that the phase of the conspicuous undulation is the same
for these three stations.

The periods observed are 5,5"\ 12.8'"-16.8"\ 36.0"-39.1"^
and 41.5"-43.5"\ while the calculated period is 36.4'" in good

A

agreement with the observed. At Ofunato and Hosoura where
undulation of periods 12.8'"-16.8'" was sometimes observed, the
phases of the undulation are opposite to each other. The
undulation was very inconspicuous at Sunagosaki situated mid-

A

way between Ofunato and Hosoura so that it may probably
be a binodal oscillation of the bay.

Waves of the short period 5.5™ appeared at Hosoura and

A

Sunagosaki but not at Takonoura and Ofunato ; the absence of
the waves at the latter stations is possibly due to the effect
of shadow.

(9) Niiyama (July 21-Aug. 3, 1903). Top. 25. PL XI,
Fig. 1-2.

Niiyama is small V-shaped bay ; the undulation is not
very conspicuous. The observed periods are 6.4" -7.6'", 11.0"-
12.8'", 20.0"'-23.7"', 27.5'"-30.7"\ 61.5"\ 71.G"' and 90.0'"; while
the calculated period is 7.5'".

(10) Ayukawa (July 18-21, 1903). Top. 26. PI. XI, Fig.
3 ; PI. Xn, Fig. 1-2.

28 K. HONDA, T. TER ADA, Y. YOSHTDA, AND D. ISITANl.

Here a continuous record by Kelvin's tide-gauge has been
taken since some ten years ago ; many valuable records con-
nected with sea waves and low pressures were obtained. Our
observation was made at the tide-gauge station ; the observed
periods are 6.8'"-8.9'", 14.2"^-15.1™ and 20.9™-22.8"; while the
calculation gave 8.9"\ The same periods were also found in
the case of several sea waves accompanied by earthquakes or
atmospiieric low pressure.

(11) Shiogama and Hiragata.

From the records obtained by Dr. Imamura at Shiogama
in Eikuzen, and Hiragata in Hitachi, we found the following
periods : —

44"' at Shiogama,

28™ and 50™ at Hiragata.

(12) Cape of Inuboye (Aug. 6-17, 1903). PI XII, Fig. 3.
The observation was made at tlie Cape of Inuboye. The

secondary undulation was not conspicuous, being superposed
by the short waves of considerable amplitude ; the observed
undulations were 8.9'", 1(3.3™-I8.r", 20.0"\ 26.0"-29.8™, 31.0"-
34.4"\ 38.7™, 49.0™ and 66.0™.

(13) Tokyo. Top. 29. PI. XIII, Fig. 1-4.

On the coast of the Bay of Tokyo, several tide-gauges of
Kelvin's type are constantly w^orking. Our tide-gauge was set
up at Etchiujima and records were continuously taken from
Nov. 24 to Dec. 5, 1904. Since August, 1906, a tide-gauge
of our system has been placed at Kanegafuchi on the bank
of the River Sumida about 2 km. distant from its mouth. In
usual w^eathers, the undulation of the bay is very faint, but
regular and characteristic undulations of 63.1"'- 67.0™ and
72.0™-82.r" are sometimes observed. In addition, the long periods

SECONDAKY UNDULATIONS OP OCEANIC TIDES. 29

110'"-130™ are often traceable. Since the bay is very large and
shallow, it can not easily be set in oscillation as a whole by any
usual cause of excitement. Judging from the calculated periods
222"' and 158'" for the fundamental and the seiches oscillation re-
spectively, the observed periods may be the higher harmonics of
these oscillations, but considering the smallness of the amplitude
of oscillation, they are perhaps rather due to progressive waves.

In the record at Kanegafuchi, the relation between the rise of
the level by a flood and the change of the tidal range deserves notice.
As the level of the river increases, the tidal range (PI. XIII,
Fig. 4) becomes gradually less and at last very small. As the
level gradually falls the tidal undulation is again restored.

(14) Moroiso. Top. 30. PI. XIV, Fig. 1-5 ; PI. XV, Fig. 1-4.

About 4 km. north of Misaki, there lies a small branched
bay ; the one branch is called Moroiso and the other Abura-
tsubo.

At Aburatsubo, a Kelvin's tide-gauge is constantly working,
to the record of which Professor F. Omori has frequently re-
ferred as Misaki mareogram. In the spring vacation of 1906,
we also made simultaneous observations at different parts of
the bay.

The undulution is very regular and conspicuous, having the
periods 13.8™-15.6"' ; the calculation gives a fairly coincident
value 13.4"\

The record shows an appearance of the beat of two waves
of nearly the same wave length. So it was suspected that the
phenomenon may be due to the interference of the two distinct
modes of oscillation of the two branches of the bay which
constitute a vibrating system with two degrees of freedom ; but
this is not the case, since the simultaneous observations at

30 K. HOKDA, T. TEßADA, Y. YOSHIDA, AND D. ISITANI.

different parts of the bay showed the identity of waves with
respect to their forms and phases. PI XIV, Fig. 2 and PL XV, Fig.
1 , or PL XIV, Fig. 4 and PI. XV, Fig. 2 are the records of the simul-
taneous observations at Moroiso and Abm-atsubo. PL XIV, Fig.
5 and PL XV, Fig. 3 are the records of the simultaneous ob-
servations inside and outside the bay; placing the one record
upon the other, we can distinctly trace undulations in the two
records, which correspond to each other. The amplitude of the
wave outside the bay is however very small, as compared with
that of the undulation inside the bay. PL XV, Fig. 4 is a
record at Aburatsubo in a stormy weather.

(15) Atami (April 2-7, 1905). Top. 31. PL XVI, Fig. 1-3.
Atami is a town situated on the western side of the Bay

of Sagami and famous for the geyser Ji The secondary undula-
tions were so inconspicuous as to make it difficult to detect
their periods. We can, however, sometimes trace on the records
the periods 12.8'", 72.4"'-7C).2" and 97.G'".

(16) Shimoda (Jan. 4-8, 1906). Top. 32. PL XVII, Fig. 1-3.
Shimoda is a small liarbour at the southern end of Izu

peninsula. The amplitude of the secondary undulation is so
conspicuous that it is generally known as ijota. The oscil-
lation becomes conspicuous, when a centre of low pressure is
approaching from the Pacific towards the place. The periods
observed are 11.9™, 13.8"-18.2™, 21.5"' and 30.9'".

In the bay, two extreme nodal lines are conceivable, the
periods corresponding to these lines are calculated to be 13.3'"
and 15.9'". Hence any wave of the period lying between the
values 13.3"' and 15.9'" may excite the osciUation of the bay;
the periods actually observed fall nearly witliin the same
limits.

SECOND AKY UNDULATIONS OF OCEANIC TIDES. 31

(17) Shizuura (Sept. 4-6, 1904). Top. 36. PI. XVIII, Fig. 1.
In Shizuura near the end of the Bay of Suruga, the

secondary undulation is not conspicuous. The periods observed
are 18.r-19.6" and 71.0'". The calculated value is 54.5™, so
that the conspicuous undulation may be a binodal oscillation of
the bay, but the amplitude of the wave being very small, the
wave is possibly a progressive one.

(18) Omaezaki (July 31-Aug. 5, 1903). PI. XVIII, Fig. 2.
The station is situated on a south-eastern corner of Tôtômi ;

the undulation is very inconspicuous. The periods observed are
IS. 6'" and 27.7"\

(19) Maisaka (July 17-28, 1903). PL XVIII, Fig. 3.
Maisaka is situated on an open coast of the same province.

The undulation is inconspicuous ; the observed periods are
10.0'", 16.0^ 20.2"'-23.4™, 30.2'" and 55.0™.

(20) Kamagôri (Sept. 1-3, 1904). Top. 38. PI. XIX, Fig. 1.
Kamagori is situated near the eastern end of the Bay of

Mikawa ; this bay has a considerable area, and is very shallow,
so that its oscillation can not be easily excited by any ordinary
cause. The undulation is not very conspicuous, observed periods
are 18.7", 36.5'^^ and 43.2^-45.1'". An undulation of long period
of 208'" may also be traced.

(21) Kamezaki (Aug. 31-Sept. 2, 1904). Top. 38. PI. XIX,
Fig. 2.

Kamezaki is situated near the northern end of the same
bay. Inconspicuous undulations of 44.5'" and 68.0'" are observed ;
a period of 390™ may also be traced.

During our observation, we met with a storm, but the am-
plitudes of the slow undulation were not much affected by it.

The Bay of Mikawa and the Sea of Ise form a large con-

32 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITAXI.

nected system. Three modes of oscillation are possible : (a) the
first and gravest mode is the oscillation of the system as a
whole, (b) the second is that of seiches between the Bay and the
Sea, and (c) the last the oscillation of the Bay only.

The calculated periods corresponding to these modes of oscil-
lation are respectively 363", 278™ and 217"\ Though long periods
obtained from observation fall near the calculated values, it is
difficult to decide, from the scanty data, whether the observed
periods actually correspond to the modes of oscillations above
referred to.

(22) Shionomisaki (July 29-Aug. 7, 1903). PI. XIX, Fig.
3 ; PI. XX, Fig. 1-3.

Shionomisaki is the foremost promontory of Kii, where a
light- house is placed. The observation was made at a beach
below the light-house ; the secondary undulation is very incon-
spicuous, but we can sometimes trace the undulation of tlie
periods 11.3"-16.3^ 25.8'" and 34.1'^

In a small bay of Kushimoto, whicli is not far from the
promontory, Kelvin's tide-gange is constantly working. It is
remarkable to observe that while tlie secondary undulation at
the promontory is inconspicuous, the undulation in the bay is
very conspicuous. The periods 11.6™-13.0-, 16.5" -18 6™, 21 5'"- 23.7"^
and 32.1™ are observed with considerable amplitudes, especially
in connection with the cyclones (PL XX, Fig. 2-3). The cal-
culated periods 12.8™ and 18.3™ fairly coincide with the observed.
The tide-gauge frequently recorded the sea waves originated on
the American coast of the Pacific.

The periods observed in the case of a cyclone or of sea
waves are the same as those observed in ordinary case.

(23) Bay of Osaka (Aug. 2-1 5, 1902). Top. 43. PI. XXI-XXV.

SECONDARY UNDIlLATIONS OF OCEANIC TIDES. 33

Before the present investigation was commenced, the oscil-
lation of the Ba}^ was observed loy the seiches -party of the
Committee, S. Nakamiira, K. Honda, Y. Yoshida, S. Iwamoto
witli Dr. Nakamnra's limni meters.

For tlie convenience of reference, tlie resnlt is included in
the present pnpor. The Bay has the form of an ellipse and
communicates by two necks xVkashiseto and Yuraseto to Harima-
nada and tlie Pacific respectively.

Stations were chosen at Imazu, Kishiwada, Yura, and Iwaya,
and observations were made simultaneous! v. As shown in the
topograph, these stations are evenly distributed aloug tlie shore
line of the elliptical bay.

The original records, in whicli waves of short periods are
l)eautifully traced (PI. XXIII, XXIV, XXV), are not convenient
for detecting the secondary undulations with long periods of
several tens of minutes, or for studying the tide itself. For this
purpose, the original records were reduced to a proper scale,
some examples of which are given in PI. XXI and XXTI. Since
the tide in Harimanada is nearly in opposite phase to that of
the Pacific, the tidal wave at the stations is not naturally
simple. Comparing tlie tidal phases at these four stations, it
may be concluded that as we go from Yura inwards along the
eastern coast of the bay, the tidal phase is gradually retarded,
and at Kishiwada, the difference amounts to about 20'" to 75'".
The phase of the tide at Imazu is not however much retarded
on the average as compared with that of Kishiwada. At
Iwaya, facing Akashiseto, on the two sides of which the tidal
phase is considerably different, the tide is naturally very
complex.

Thus, as compared with the tide at Yura, the phase of the

34 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

tide at Iwaya is sometimes accelerated and sometimes retarded
by several tens of minntes. The tidal Avave in the bay chiefly
enters throngh Yuraseto ; but the Harimanada component, which
enters through Akashiseto, is easily to be traced.

As regards the secondary undulations, the longest waves
found in the records, have periods of 2 GO" -310'"; the amplitude
exceeded ten cm. in one case, (PI. XXII, Fig. 1-3). The
phase of oscillations for the four stations, is the same, so
tliat this undulation is probably due to the oscillation of the
whole basin as a bay witli its narrow necks at Akashiseto and
Yuraseto. The result of calculation of the period for the mode
of oscillation gives 270™, which agrees well with the observed
value. Along with the long wave, one with the period of ca.
100" -140"' is often recognized ; the pliase of this undulation is
generally the same for the northern statious Iwaya, Imazu and
Kishiwada, while for Yura at the southern end of the bay, it
is apparently opposite, in so far as we may judge from the
faint traces of this component. It is possible that under favour-
able conditions, this undulation may become very prominent,
though in tlie records at hand, it is scarcely to be detected.
Tlie undulation is probably due to the uninodal seiches of the
bay along its longer axis. The calculated period of 120" for
the suspected seiches is in good agreement with the observed
period. Besides, conspicuous undulations with the period of
50"- G 5'" are often recognized. Comparing the phases of the
undulation at different stations, it is at once found that for
Kishiwada and Imazu, the motion is always opposite, and
also tliat tlie phase of Yura is the same as that of Imazu.
The undulation is probably that of the binodal seiches of
tlie bay between Imazu and Yura. The calculated period of

SECONDARY UNDULATIOMH OF OCEANIC TIDES.

35

GO"" for this mode of oscillation falls fairly within the range of
the observed values.

As to the secondarv undulations of shorter periods, it may
be generally observed that for each of the four stations, con-
spicuous waves with the periods 8'"-lS'" are found very fre-
quently. Periods of 20"-25™ and 32"'- 30'" are also met witli.
For Iniazu and Kishiwada, waves of 8" -18'" periods occur very
conspicuously ; and apparently idential trains of waves may
often be traced at the two stations. Comparing the records of
the four stations on the same days, waves common to different
stations are often recognized. For examples : —

Kishiwiidci

Imazu

Iwaya

Yura

Aug. 2 1

13.0'"
9.4

~

13.6'"
9.8

—

o
O

11.2

—

13.6

12.7'"

8

22.0

22.8'"

—

/

12.7

12.1

—

']

10.1
20.0

10.1
21.6

—

11.4

(

8.9

9.0

—

—

■•1

15.5
13.3

15.6
13.6

14.8

—

14

16.2

16.3

16.6

—

Whether these waves are due to some higher modes of stationary
oscillation of the sea, or they are merely progressive waves
generated by meteorological or other causes is a question still
to be solved.

Waves with periods shorter than about 8'" are also generally

36 K. HONDA, T. TEEADA, Y. YOSHIDA, AND D. ISITANI.

met with widely varying periods and often with considerable
amplitudes.

For Kishiwada and Imazu, the short waves are generally
very complicated, periods of 1.4'"- 1.5'", and 2.0'"- 2.5'" being very
frequent.

The records of Iwaya, when compared with those of the
other stations are characterized by tlie simplicity of the short
waves, the most prominent waves being of two groups, i.e. 1.0'"-
1.3'" and 2.r"-2.5'".

(24) Bay of Hiroshima (Jan. 17-23, 1904). Top. 44. PI.
XXVI, Fig. 1-2 ; PI. XXVIl, Fig. 1.

The observation was simultaneously made in a small bay
of Yedajima and in the harbour of Ujina.

In Yedajima, the tidal curve was often accompanied by a
regular and inconspicuous undulation of 00.0'". The period is
far greater than the value calculated from the dimensions of
the small bay of Yedajima. In Ujina, the undulation of the
same period and phase as in Yedajima was also observed ;
hence the undulation wdiich was observed at Yedajima and
Ujina, is probably due to the oscillation of the bay of Hiroshima
as a whole. The calculation according to this consideration
gives a fairly coincident value Ol.G'".

Beside this undulation, an oscillation of a shorter period
9.5'" was occasionally found both at Y^edajima and Ujina.

Tlie tidal wave in the bay undergoes a considerable change
both in its form and phase, as compared with the tide on the
Pacific coast. Here the tidal range is considerably large, and
its form in the neighbourhood of its maximum or minimum
is comparatively steep, as it is usually the case in a deep
inlet. The retardation of the tidal phase is about 3 hours as

SECONDARY UNDULATIONS OF OCEANIC TIDES. ö /

compared with the tide on the Pacific coast of Shikokn.

(25) Shimonoseki (Jan. 14-17, 1905). PI. XXVII, Fig. 2.

As it is to be expected, the tidal cnrvc at Shimonoseki
has a pecnliar character, superposed by the secondary un-
dulations of short duration of the periods 4G.5"\ 54.o"-57.0'"
and 04.8'". \ye can also trace an undulation of longer period
of about 150'".

IV. PACIFIC COASTS OF SHIKOKU.

(1) Strait of Xanito (Aug. 1-25, 1900). Top. 43. PI.
XXVIII-XXXll.

The Strait of X^aruto is famous for its rapid current and
the eddies accompanying it. The strait separates Harimanada
from tlie Pacific by a narrow neck about 1.1 km. wide. The
phase of the tide in the sea is just opposite to that of the
Pacific ; and when the Pacific is in the high water or in the
low water, the sea is in the low water or in the high water
respectively, so that at the strait, a level difference of 1 to 1.5 m.
is produced, and consequently a torrent of water rushes from
the ocean into the sea or in the reverse direction, according to
the tidal phase. When tlie current attains its maximum velo-
city, it often exceeds 10 knots per hour. The current is always
accompanied with roaring sound and eddies. Eddies are usually
formed behind the stream ; their diameter exceeds G meters,
and they have funnel-shaped surfaces. If a boat be drawn into
them, it is very difficult for it to get out.

The observations were made at 5 stations — Shioyasumi,
Hinoura, Yebisujima Ogeura and Kameura, of which dif-
ferent pairs were simultaneously observed. The records at
Shioyasumi and Kameura give the tide on the Harimanada

ob K. HONDA, T. TEE ADA, Y. YOÖHIDA, AND D. ISITANI.

siele, while those at Hinoura and Yebisujima give the tide on
the Paeific side. The tide at Ogeura is aflected by these
two.

The tidal curves of the strait are much complicated by the
influence of tlie two tides in opposite phases and by the super-
position of the secondary undulations.

The records of Shioyasumi show a characteristic feature
(PI. XXVIII, Fig. 1-3); the tides at Hinoura (PI. XXX, Fig. 1)
and Yebisujima (PI. XXIX Fig. 2, 4) are not simple.

At Ogeura, which communicates with Ilarimanada and
the Pacific, the tidal curve (PL XXX, Fig. 2, 3) has a very
peculiar form. As regards the high or low water at this station,
it agrees roughly with that on the Pacific side.

In these four stations, conspicuous, but not regular, undula-
tions are observed, the periods of which are

63^", 90'"-120'" at Shioyasumi.

43"\ 54™-59'", 75'"-86"\ lir"-12r" at Hinoura.
5r"-63"\ 08--74"\ 84™, 94™-llG™ at Yebisujima.

54'"-57'", 120,"180'"-200"' at Ogeura,

The tide of Kameura, which is about 1 km. distant from
Shioyasumi and in the inside of the strait, is comparatively
simple. The secondary undulations are very inconspicuous,
though we can sometimes trace the undulations of the periods
16'"- 20'" and 51'"-{]4-".

Comparing the phases of the tide just inside and outside
the strait, we observe that they are nearly opposite to each
other (PI. XXIX. Fig. 1,2; PI. XXVIH, Fig. 3 ; PL XXX, Fig. 1.)
a fact which at first sight appears very curious. X^ow, Hari-
manada is connected to the other seas by three necks, namely
Naruto Strait, Bisanseto and Akashiseto, of which the first.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 39

being very narrow as compared with others may be put out
of consideration. Tlie Avestern neck Bisanseto is much wider
than the eastern neck Akashiseto, the cross section of the
former being more than twice that of tlio latter. Moreover the
tidal range at Bisanseto is much greater than tliat at Akashi-
seto so that the flux of the sea water through the former neck
will proba]3ly amount to more than three times that through
the latter. Thus sea-level in Harimanada is principally deter-
mined by the tide from the western neck. The tidal wave of
the Pacific enters tlie inland sea of Seto through the channel
of Bungo, propagates eastward through the seas of lyonada
and Bingonada and arrives at Bisanseto, so that it requires
about 5 liours to travel through the distance. This wave takes
still 40 or 50 minutes to get at the strait of Naruto, so that
inside and outside the strait, the phase differs by about 6 hours,
as actually observed.

It is a matter of considerable interest to compare tlie
phases of the components constituting the tidal wave on both
sides of the strait. By means of a rectifier constructed by one
of us,* we may eliminate the semi-diurnal or diurnal component,
if it be known to exist. In this way, wo may resolve a tidal
wave into a certain number of components. Thus, the tides at
Hinoura (PL XXX, Fig. 1) and Shioyasumi (PI. XXVIII, Fig. 3)
were respectively resolved into three components as shown in
PL XXXI, Fig. 1, 2. They clearly show that the principal
semi-diurnal components have opposite phases for Hinoura and
Shioyasumi. In a similar way, the tides at Kameura (PL
XXIX, Fig. 3) and Ogeura (PL XXX, Fig. 3) were respectively

*) T. Terada, A Tide rectifier, Publications of the Earthquake Investigation Comiuittee
in Foreign Languages. No. 18, 190 1.

40 K. HONDA, T. TERADA, Y. YOSHIDA AND D. ISITANl.

resolved into three components shown in PI. XXXTI, Fig. 1, 2.
The principal semidinrnal components at Ivamcura and Ogenra
have nearly opposite pliases to each otiier. It is to be observed
that in these fignres, the dinrnal components were not separat-
ed ; they are very conspicnons at Kamcura and Ogenra, bnt
not at Hinonra and Shioyasnmi.

When the current was rnshing from tlie Pacific into Ilarima-
nada an interesting phenomenon was observed. As the current
increased its velocity, a regular undulation of about 2.5'" (PI.
XX VII I, Fig. 4) became gradually conspicuous and attained a
maximum amplitude of about 18 cm., and tlien gradually de-
creased with the diminishing velocity of the current. In the
records of Shioyasnmi (PI. XXVIII, Fig. 1-3), thickly zigzaged
portions indicate the existence of such waves. Thus it seems
very probable that the current behaves like a jet of air blown
into the mouth of an organ pipe, causing standing oscillation
of the air column in the pipe. Tlie torrent of watei' rushing
from tlie Pacific into the strait excites a standing oscillation
of the water in tlie neighbourhood of tlie Strait, A few years
ago. Professor H. Nagaoka expressed the possibility that the
KurosJiiwo, which is the current along the coast of Japan with
a velocity of a few knots per hour, may be the origin of the
long waves observable on our coasts. The present case affords
a good example for ilUistrating the above view on a small
scale.

If we bring two records of consecutive days of normal
weather into coincidence as regard the tidal phase, we observe
in each record, the same succession of the secondary undula-
tions following one after another ; this remarkable fact is also
noticeable on some other coasts.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 41

(2) Tei (July 23— Aug. 3, 1903). PI. XXXIII.

This station is situated on the Pacific coast of Tosa. The
records show undulations of tlie periods 7.5"\ 25.9", 30. ß'"-
32.9"\ 39.9"\ 49.r^-52.9'" and 73.9'"-77.5"\ small in amplitude
and short in duration.

On July 30 to 31, the sea was very rough notwitlistand-
ing calm weather, when a remarkably simple secondary undula-
tion of considerable amplitude appeared, lasting over 12 liours
with a mean period of 51'". The appearance of this remark-
able undulation is probably connected with the low atmospheric
pressure then prevailing over the vicinity of Formosa (PI. XCIII).

(3) Susaki (Aug. 9-28, 1903 and Aug. 20-Sept. 7, 1904).
Top 45. PL XXXIV-XXXVII ; PI. XXXVIII, Fig. 1-2.

Susaki is a deep bay on the middle coast of Tosa. The
observations were made at 5 stations Yamasakibana , Shiraiwa,
Otani, Heshima and Kure. The diagrams of Yamasakibana
are characterized liy simplicity of undulation, the periods ob-
served are 30.9", 35.4"- 38.5", 39.9-41.6", 43.1 "-46.8" and 50.0"^
-54.0".

As an illustration of the modes of superpositions of a
series of different waves, rectified diagrams are given in PI.
XXXV, A. B. C. In curve A, a train of waves of the period
38™ is superposed on waves of the period 7G"\ the former com-
ponent being most conspicuous between he, wliile the latter is
pronounced between ah. In curve B, the waves of the period
76™ are superposed on the waves of the period 38™ between
ah, the latter component gradually passing into the waves of
36™ between he. In curve C, between ah, waves of the periods
51™ and 35'" form an apparent beat, and between he, waves of
100'" are superposed on waves of 50™,

42 K. HONDA, T. TERADA, Y. YOSHIDA AND D. ISITANI.

When different rectified curves ai'c compared with one an-
other, the remarkable fact is revealed that almost identical
forms of waves occur very frequently during the course of suc-
cessive days. The examples of such a coincidence of wave-
form are given in PI. XXXVI, cui've D-J. It appears that
some particular form of waves is often repeated at the cor-
responding part of the tidal curve, for two consecutive days ;
this is shown in curve D and D', in which identical waves
occur in the same relation to the tidal phase. It also occurs
that the same train of waves is recognized at the low water
of one record and at high water of another, as shown in curve
E and E', or F and F'. When, however, different records, which
are several days apart, are compared, the same waves are found
apparently with no definite relation to the tidal phase as shown
in curves H and H'. Curves I and I' show an example in
which a train of wave occurs on different days in apparently
inverted form. In curve J', the direction of the time is inverted.
Curve K shows an example in which secondary waves of
shorter periods are very faint, whereas a long wave of about
100" is rather conspicuous. Curves L and L' which are the
rectified records of Yotsu, are given for comparison with K.

At Shiraiwa, the sea is very calm, whereas the secondary
undulation of the period 31.0" (PI. XXXVIII, Fig. 1) is most
pronounced. The periods observed at Otani are 17.6"-18.2'\
35.4" and 53.3", and those at Heshima are 24.6"-27.6'", 39.7"
and 55.1". At Kure, secondary undulation of the periods 15 0"-
16.3" and 61.3" are noticeable.

Comparing the records of Kure and Yamasakibana on the
same days (PI. XXXVII, Fig. 3-4), it will be seen that while
the wave somewhat longer than 60" is common to both

SECONDAEY UNDULATIONS OF OCEANIC TIDES 43

stations, the shorter waves of 35'"-42™ period appear only in the
latter station, and those of 10'" only in the former. Again,
comparing the records of Yamasakibana and Otani on the same
days (PL XXXVII, Fig. 1,2), 35"M2™ waves are found common
to both stations, while 18™ waves are peculiar to the latter
station. At Heshima, which is situated at the mouth of the
minor inlet of X^omi, the IG™ wave is absent, and 35™-42"
waves are apparently traced, though not of such great ampli-
tude as at Yamasakibana.

Thus we may infer that the undulation of 3 5 '"-4 2™ has a
node near Kure, and that the period of about 16'" at Kure seems
to be due to the oscillation of the minor inlet. The undulation
of about 18" is probably due to the seiches between Awa and

A

Otani.

Calculated values of the periods corresponding to these sup-
posed modes of undulation show a fair agreement with the
actual periods.

As will be seen soon after, investigations with models also
lead to the same conclusion.

(4) Yotsu (Aug. 28-30, 1903). PI. XXXVIII, Fig. 3.

This station is situated on the western part of the Pacific
coast of Tosa ; the secondary undulations were very incon-
spicuous. Periods of 14.0"-15.4'" and 75.8'" could however be
traced.

V. COASTS OF KIUSHIU.

(1) Hososhima (Dec. 21-26, 1904). Top. 56. PI. XXXIX-
XL.

Hososhima is an elongated bay on the eastern coast of
Hiiiga ; here Kelvin's tide-gauge is constantly working. It has

44 K. HONDA, T. TEEADA, Y. YOSHIDA, AND D. ISITANI.

recorded several sea waves, which were oriofinated on the
American coasts and traversed across the Pacific. Simultaneous
observations were made at Hososhima and Isegahama situated
inside and outside the bay respectively. In the bay, extremely
regular undulations appeared superposed on the tidal waves ; the
periods varied from 17.8'" to 20.3™ according to the tidal phase.
In calm weather, the amplitude of undulation amounted even to
25 cm. The period of the undulation slightly decreases, as the
tide passes from low water to high. The calculated period is
19.0", which fairly agrees with the observed one. The change
of the period caused by the change of the depth by tidal motion
has also the range, which is to be expected from the theory.
Besides, longer periods 34.0"- 38.7'" and 43.4'"- 49.1" are some-
times observed.

Outside the bay, undulations of the periods 17.8"- 20.3'" are
very faint, and inconspicuous undulations of the longer periods
are also observable. Placing a record in the bay upon the
corresponding one of the open coast, we can distinctly trace
undulations in the two records, which correspond to each
other.

On the open coast of Hososhima, we actually met with two
small inlets some ten meters long, each of which was constantly
excited by Avaves of short periods proceeding one after another
toward the inlets, and made an approximate standing oscillation
of considerable amphtude, having the node at its mouth.

If we bring two records of any consecutive days into coin-
cidence as regards the tidal phase, we observe the same suc-
cession of undulations.

PL XL, Fig. 1-3 are tlie records in stormy weather obtained
by Kelvin's tide-gauge. In the first two curves, the period

SECONDARY UNDULATIONS OF OCEANIC TIDES. 45

corresponding to the binoclal oscillation of the bay is very con-
spicuous while in the third curve, the periods of fundamental
oscillation only are observable.

(2) Aburatsu (Dec. 27-31, 1904). Top. 58. PI. XLI.
Aburatsu is a small bay on the southern coast of Hiuga ;
simultaneous observations were made at Alniratsu and Umega-
hama, inside and outside the bay respectively. In the bay,
we observed conspicuous undulations, though they are not reg-
ular. The periods observed are 15.0'"- 19.0'", 21.ry"- 24.5'",
37.5"- 39.2™ and 43.0"; they are nearly the same as those ob-
served at Hososhima. In ordinary weather, the amplitude of
the conspicuous undulation often exceeds 13 cm. The calculated
period is 15.1"\

Outside the bay, the undulations are very inconspicuous ;
but the same periods as those inside arc also traceable. If we
bring two corresponding records in and outside the bay into
coincidence, we can distinctly trace the corresponding undula-
tions of one record in the other (PI. XLI, Fig. 1 and 3, or 2 and
4). As in the case of Hososhima, if we bring two records of
any consecutive days into coincidence as regards the tidal phase,
we notice the same succession of secondary undulations.

(3) Kagoshima (Aug. 1-7, 1905). Top. 59. PI. XLII-XLIII.
The large Bay of Kagoshima has an elongated form, 77 km.
long and 20 km. broad in its widest part. The island of Sakura-
jima, an active volcano, situated about 11km. from its end,
divides the bay into two portions communicating with each
other by two channels on both sides of the island. The ob-
servation stations were Kajiki, Kagoshima and Ibusuki ; they are
situated at the end, along one of the channels and at about
10 km. from the mouth of the bay respectively. The first and

46 K. nONDA, T. TEEADA, Y. YOSHIDA AND D. ISITANI.

second stations, as well as the second and third stations were
simultaneously observed.

At Kajiki, the tidal curve was extremely smooth, showing
no trace of secondary undulation. It appears then that Sakura-
. jima nearly screens long waves from Ijeing propagated into the
bay. The tidal curves at Kajiki and Kagoshima almost coin-
cided with each other, showing tliat the narrow channels have
neither dauiping nor retarding effect for the oceanic tide of ex-
tremely long wave length.

The record of Kagoshima was generally very simple, but
frequently regular undulations of 17.2" and 22.8'"- 23.9" are
observed.

At Ibusuki, the observed periods are 14.2" and 18.3"-
20.6". Since tlie undulations at Kagoshima were very faint
during our observation, the existence of the corresponding waves
at the station is not certain.

In the calculation of the peiiod of the oscillation in the
bay that part which extends from the mouth to Sakurajima,
is only to be taken into consideration, because the rest is not
disturbed by ordinary waves. The calculated period of the
fundamental oscillation is 107", whicli exceeds very much the
observed value. The observed undulation may possibly be
due to progressive waves, which have the same periods as
those frequently found in different coasts of Kiushiu. That
the amphtude of the undulations is considerably less in Ka-
goshima than in Ibusuki, indicates the plausibility of the above
view.

(4) Nagasaki (Jan. 9-13, 1905). Top. 60. PL XLIV-XLV.

Nagasaki is a well known liarbour on the western coast
of Kiushiu. The observation was made near the end of the

SECONDARY UNDULATIONS OF OCEANIC TIDES. 47

bay. Since March 1905, a tide-gauge of our system has been
set up in the same place by the Office, and many beautiful
records obtained.

In the bay, tlie secondary undulation is so conspicious
that it is usually known as ahiki. The observed periods are
22.5™- 25.2", 31.9"- 32.4", 34.5"-37.6"\ 40.1", 44.5"- 45.2", 53.G"
and 69.0"- 72.0"; the amplitude of the conspicuous undula-
tions often exceeds half a meter. On one occasion, about 10
years ago, the amplitude of the ahild was over 2 meters, and
a large number of boats and steamers are said to have been
damaged. The largest amplitude since the beginning of the
tide-gauge observation was 1.54 m., at midnight on May 1,
1905. PL XLIV and XL Y are records of the famous abild
together with records of less remarkable undulations.

The conspicuous ahiki is generally associated with weather
in which the isobars in the neighbourhood of the district is
much crooked by two coexisting low barometric centres (PI.
XCIII — XCIV). It is well known that a tornado is frequently
associated with such a distribution of isobars ; then it seems
very probable that a sudden local disturbance of pressure may
often be accompanied with an unstable baromomotric distribu-
tion. The ahild is often found in apparently calm weather ; a
deep barometric centre with regular concentric isobars, which
is approaching the district, excites short waves of considerable
amplitude, but does not cause the ahiki in a marked degree.

As to mode of oscillation of the bay, two are conceivable.
The one is seiches between Fukahori and the end of the bay ;
the other is the fundamental oscillation having the node at the
mouth. The periods calculated on this supposition are 22.6" and
37.5" respectively, closely agreeing witli the observed periods ;

48 K. HONDA, T. TER ADA, Y. YOSHIDA, AND D. ISITANI.

experiment with the model gave also fairly coincident values.

(5) Fukahori. Top. 60. PL XL VI.

Fukahori lies near the western mouth of the bay of Naga-
saki ; here Kelvin's tide-gauge is always working. The undula-
tion is generally inconspicuous ; the same periods as those
observable at Nagasaki are also traceable. It is interesting to
notice that though the ordinary oscillation of the bay is very
prominent at Nagasaki, it is not conspicuous at Fukahori, the
latter being situated at the node of the oscillation. Even the
great ahiki of Nagasaki on May 2, 1905 (PI. XLVI, Fig. 1-2)
was only 30 cm. in amplitude at Fukahori. On the other
hand, the seiches between Nagasaki and Fukahori are rather
conspicuous at the latter station, where the oscillation forms
its loop. Fig. 1 and 2 are two records, when large ahikis
appeared at Nagasaki ; Fig. 3 is an example of the record in
stormy weather.

VI. BONIN ISLANDS AND FORMOSA.

(1) Futami. Top. 04. PI. XLVII.

Since December, 1900, a tide-gauge of our system has
been set up in the bay of Futami in Bonin Islands (Ogasawa-
rajima) about a thousand kilometers south off the coast of
Honshiu. The undulation in tlie bay is always very regular
and conspicuous, with periods 15.3'"- 16.5", 17.2"^ and 18.0" - 21.2 \
indicating that in this portion of the far ocean, there always
exist waves of moderately long periods with greater or less
amplitude. The period calculated is 13.0'" which is somewhat
less than the observed vahie.

(2) Kelung. Top. 05. PL XL VIII, Fig. 1-2.

Kelung is a harbour at the northern end of Formosa ; here
Kelvin's tide-gauge has been set up since ten years ago. The

SECONDARY UNDULATIONS OF OCEANIC TIDES. 49

undulation is not very conspicuous ; the observed periods are
25.3"-29.6" and 57.2™. The calculated period 25.8" fairly coin-
cides with tlie observed.

(3) Takow. PI. XL VIII, Fig. 3-4.

Takow is situated on the southern coast of Formosa ; here
Kelvin's tide-gauge is also constantly working. The undulation
is very inconspicuous; the periods observed are 11.9"- 13.7'"
and 24.4"-26.5'".

§ 5. EXPERIMENTS WITH MODELS.

To confirm our theory, it appeared interesting to experiment
with models, and thereby find the actual modes of oscillation of
different bays. Models of several bays were formed with definite
proportions to the actual dimensions, and the periods of the
models were compared wath those observed in bays. In reducing
the period of the model to the actual one, it was assumed that
the period is proportional to length and inversely proportional
to the square root of depth, provided the latter is a small frac-
tion of the former.

To construct a model, contour lines of a bay were drawn
on separate zinc plates, wdiicli were afterwards cut along these
lines. The plates were then placed one upon another ; the
distance between two consecutive plates was kept by blocks
of w^ood of such thickness that it bears a definite ratio to the
actual depth. The interspaces between the plates were then
filled with cement. The models thus constructed were immersed
in a large rectangular tank (150 x 7Gxl9 cm.^) filled with water
up to the water line of the model.

The waves were excited by a pendulum bob oscillating in

50

K. nONDA, T. TEEADA, Y. YOSHIDA, AND D. ISITANI.

Fin:. G.

the water ; a lead ball. 7 cm in diameter
was suspended by two strings passing
through two lioles in a horizontal rod, as
shown in Fig. 0. The joart of the pendulum,
which oscillated with the bob, was thus
restricted to that part of the strings below
the horizontal rod ; the length of this
portion could be varied at will by moving
the rod upward or downward. With this
arrangement, it was easy to obtain a
period less than three seconds. For a
longer period, however, it would be neces-
sary to use a pendulum of considerable
length. To avoid this inconvenience, a horizontal pendulum
was utilized. As shown in Fig. 7, a bar was horizontally sup-
ported by means of a string
suspended from a knife edge,
and of a steel cup, in which
the point of the horizontal
bar rested. A heavy lead
ball was hung by a three-way
string from a frame attached
to the horizontal rod. By
properly inchning the support
of the pendulum, periods
greater than tln-ee seconds
could easily be obtained.
When the pendulum was made to oscillate in front of the model
with its bob under the surface of water, the water in the model
oscillated smoothly with no appreciable surface wave. Though

/: ■:/■■/■'/'//////■

SECONDARY UNDULATIONS OF OCEANIC TIDES. 51

the amplitude of oscillation of the pendulum gradually decreased,
if it were once started and left to itself, it could be kept fairly
constant by applying a small force by hand at suitable intervals.

To avoid the reflection of the excited wave from the walls
of the tank, a tliick layer of a damping material, such as
wood shavings, was laid in front of the reflecting walls.

By exciting waves with tlie above arrangement, the water
in the model of the bay made a standing oscillation, whose
amplitude was generally small ; but as the period of the pendulum
approached the proper period of the bay, the amplitude of oscil-
lation gradually increased, and when the period exactly coincid-
ed with that of the model the amplitude of the latter was
a maximum. In this case, the mode of oscillation proved to
be that conceived by us, that is, the end of the bay was a
loop for vertical motion and a node for horizontal motion,
while its mouth was a node for vertical motion and a loojj
for horizontal motion. The phase of the water particles in the
bay was the same for all parts of the bay, when the oscilla-
tion was the fundamental one. In an elongated bay, a binodal
or trinodal oscillation was easily produced.

For observing the mode of oscillation of the water, it was
convenient to follow the motion of line cork powders or better
fine aluminium powders scattered over the surface of the water.
To diminish the effect of surface tension of water on the motion
of the powders as much as possible, drops of oil were put
into the tank ; the powder was then finely scattered, the
surface of water being well stirred.

In this way, experiment with the model showed clearly the
paths, along which the water particles moved. We also took
photographs of the model in the tank, when the bay water was

52 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

oscillating. By placing a photgraphic camera in a vertical posi-
tion over the model and exposing the dry plate about lialf a
period of oscillation, a fine path was traced on the plate by
each moving aluminium particle, and an aggregate of such tracks
of the particles showed beautifully the actual mode of the hori-
zontal motion.

To determine the proper period of oscillation of a model, the
period of the pendulum was so adjusted as to give a nearly
maximum amplitude of resonance. The pendulum was then
stopped, and the period of the subsequent free oscillations was
determined by means of a stop-watch. Though the period of
the pendulum varied slightly from the proper value, the period
of the subsequent oscillation was quite constant.

If the period of the exciter differed considerably from the
proper period of the bay, the oscillation after the stopping of
the pendulum was rapidly damped, and this gave us a good
means of detecting, whether the period of the exciter was near
to the proper one, or not.

We experimented with models of seven bays, in which
regular and conspicuous undulations were observed ; the results
of experiments are given below : —

(a) Bay of Hakodate. PI. LXXXVII.

The scales of the model were as follows : — Length 1 : 20,200,
and depth 1 : 548, so that the factor r, which was to be multi-
plied into the observed period in order to obtain the period of
oscillation of the actual bay, was 863. The bay had two modes
of oscillation ; that is, the one was the fundamental oscillation
with its node at the mouth and the other tlie lateral oscillation
between Hakodate and Tomikawa with its node midway between

SECONDARY UNDULATIONS OF OCEANIC TIDES. 53

them. The periods of these oscillations were 3.27' and 1.64'
respectively ; multiplying by r, we get 47.0"' and 23.6™ in good
coincidence with the observed values. These tw^o modes of
oscillation are clearly seen from the photographs No. 1 and 2.
Though the photographs show beautifully the line of motion of
the water particles, they do not give the direction of motion ;
hence in Fig. 1 and 2 the direction of motion, as actually observed
by experiments, is indicated by arrow^s. It is very interesting to
trace the stream lines in the case of the lateral oscillation (Fig.
2). Certain stream lines extend from Hakodate to Tomikawa
and gradually diverge toward the middle, while other lines run
toward the mouth of the bay from the Tomikawa side.

In experimenting with models, it was observed that the
period of the forcing wave, which corresponds to the maximum
resonance, is not well defined ; wdthin a certain range of the
period, wliich did not much differ from the period of free oscil-
lation, the oscillation remained fairly conspicuous.

In the actual bay, such a phenomenon was also observed :
conspicuous undulations of 45.5"-57.5"' were frequently observed,
the period of free oscillation of the bay being 47.0"'.

(6) Bay of Aomori. PI. LXXXVIII.

The scales of the model w^ere as foUow^s : — Length 1 :
110,700, and depth 1 : 731, so that the factor v w^as 4,090.

The model had also two modes of oscillation as in the case
of Hakodate, i.e. the fundamental and the lateral oscillation. The
periods of their free oscillations were 4.45' and 1.60' respective-
ly ; multiplying by r, we get 303"" and 108"\ During our ob-
servations on the actual bay, two oscillations of the periods
300™ and 103™ were observed, which well accord with the above

54 K. HONDA, T. TEBADA, Y. YOSHIDA.. AND D. ISITANI.

values. The photographs No. 3 and 4, together with Fig. 3 and
4, show the motion of the water particles corresponding to these
modes of oscillation. The stream hnes (Fig. 3 and 4) in the
case of the lateral oscillation deserve a special notice. The
greater part of these lines extends from Aomori to Ominato side,
while the remaining lines run from Aomori toward the entrance
of the bay ; the case is just analogous to tlie corresponding
oscillation in the bay of Hakodate.

(c) Bay of Moroiso. PI. LXXX\^I1L

The scales of the model were as follows : — Length 1 : 6,066
and depth 1 : 226 ; the factor r was 404. The fundamental
oscillation was 2.28'; multiplying by /■, we get 14.8™ in a good
accordance with the observed period. The photograph No. 5
and Fig. 5 show this fundamental mode of oscillation.

{(l) Bay of Susaki. PI. LXXXIX.

The scales of the model were as follows : — Length 1 : 24,300,
and depth 1 :915, so that the factor r was 803.

The bay has a very complicated form and many small inlets
inside it. By exciting short waves, some inlets energetically
oscillated, while the others stood almost still, showing beauti-
fully the phenomenon of resonance.

Waves of different periods were excited and corresponding
modes of oscillation of the bay were studied. A period 2.80'
was that of the oscillation of the bay as a whole, period 1.36''
that of the lateral oscillation between Awa and Otani, and
period 1.25' that of the oscillation of the small inlet of Kure.
Multiplying them by r, we get 37.5™, 18.2™ and 16.7™ respectively,
which agree very well witli the observed as well as the
calculated values.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 55

The photograph No. 6 and Fig. G show a fundamental
oscillation of the principal part of the bay as a whole, in which
case the small inlet of Kure almost stands still. The photo-
graph No. 7 and Fig. 7 indicate an oscillation of the inlet of
Kure, where the water energetically oscillates between Kure and
a neighbouring inlet.

(e) Bay of Hososhima. PI. XC.

The scales of the model were as follows : — Length 1 :
10,140, and depth 1:366, so that the factor r was 531. The
fundamental and the binodal oscillations were found to have the
periods 2.2r and 0.90' ; multiplying In^ r, we get 19.6™ and 8.0'".
The phase of the fundamental oscillation is the same for all
parts of the bay, while that of the binodal is opposite for the
mouth and near the end of the bay ; the photographs No. 8 and

9 show also these two modes of oscillation. In the actual bay,
the periods corresponding to these two modes of oscillation were
also observed.

(/) Bay of Nagasaki. PI. XCI.

The scales of the model were as follows : — Length 1 : 12,130,
and depth 1 : 548, so that the factor r was 518.

The bay had two modes of oscillation, that is, the funda-
mental and the seiches -like oscillation. The former had its node
at tlie wide mouth opened to the north-western direction, while
the latter had its loops of opposite phases on the Nagasaki
and Fukahori sides. The photographs No. 10 and 11 and Fig.

10 and 11, show the two modes of oscillation. It is interesting
to observe that in the seiches oscillation (Fig. 11), when the
water flows from tlie wide mouth toward Fukahori, there is

56 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. LSITANI.

also a stream in the direction from Nagasaki to Fukahori, and
when the water flows in the opposite direction, there is also a
stream directed towards Nagasaki, thus forming an oscillation
similar to the seiches between the two places.

The proper periods corresponding to these two modes of
oscillation are 2.68' and 4.45' ; multiplying by r, we get 23.3™
and 38.4™ in good agreement with the observed periods.

(r/) Bay of San Francisco. PI. XCII.

During the last fifty years, the tide-gauge at San Francisco
has recorded several sea waves which originated at different
coasts of the Pacific ; the periods of the waves recorded are
17.3'"- 19.2™, 24.3™- 27.8™, 34.3™- 41.2™, 47.4™ and 116™, of which
the first is an octave of the third.

Now the Bay of San Francisco is of a very complicated
form, so that it is very difficult to find out by calculation what
modes of oscillation correspond to the actual periods. Hence a
model of the bay was constructed after the chart published by
Washington Coast and Geodetic Survey and presented to Pro-
fessor F. Omori by Dr. 0. H. Tittmann, superintendent of the
Office. The scales of the model were as follows : — Length
1 : 40,000, and depth 1 : 366, so that the factor r was 2,076.
The model was too large to be put in the tank and so it w^as
placed in a small pond of the University. Since the greater
part of the model was very shallow, the oscillation rapidly sub-
sided, when the exciting wave was stopped, so that the period
was always determined by observing tlie maximum resonance
of the bay. For tlie exciting wave incident on Golden Gate,
the principal modes of oscillation of the water were the oscil-
lations between the West Berkeley and Sausahto sides. The

SECONDARY UNDULATIONS OF OCEANIC TIDES. 57

remaining portion of the bay extending to both sides seems to
have httle influence on these modes of oscillation.

By exciting waves of periods ranging from 3.P to 3.5', the
water in tlie bay energetically oscillated with tlie fundamental
mode of oscillation, having its node at Golden Gate and its loop
at the West Berkeley side. The most easily excitable mode of
oscillation was a binodal seiches between the narrowest mouth
line and West Berkeley side ; the positions of the loops are
clearly seen from the photograph No. 12 and Fig. 12 (a chief
part of the model). The period of the exciting wave, which gave
a marked resonance to the binodal seiches of the bay, ranged
from 1.1' to 1.4". By slightly changing the period of tlie wave,
the corresponding displacement of nodal line was observed. We
could also produce a trinodal seiches of the bay, whose period
of oscillation was 0.8\ Multiplying these periods by f, we get
107^-122'", 38'"-48'", and 28.'" The period 116"\ which probably
corresponds to tlie fundamental oscillation of the bay, was act-
ually found in the sea wave from South Anierica, 1808, observed
in the bay. Periods corresponding to the bi nodal and trinodal
oscillations were often observed in the bay in the case of
several sea waves.

§ 6. FORMULA FOR CALCULATING THE PERIODS
OF THE UNDULATION IN BAYS,

{a) Picctangular bay of constant depth.

The oscillation of the water in a bay is the same as the
seiches in a lake of double length, the mouth correction being
taken into account. Hence if / and Ji denote respectively the
length and the depth of a rectangular bay of a constant depth,

58 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

the period T of the free oscillation of the bay, having the node
at its mouth and the loop at its end, will be given by the
formula

provided the correction due to the mouth be neglected. This
correction may easily be found in the following way.

Take the origin of the rectangnlar co-ordinates at the
middle point on the month of the bay, .I'-axis in the direction
of length, positive inwards, and y/-axis upwards. Assume the
vertical displacement -q inside the bay to be given by

. nx Int

T, = a sm— r^ cos

21 T •

If we neglect the vertical acceleration, we have

where ç is the horizontal displacement of the lipuid element ;
thus

21 nx 27rt

q=a—r COS -7^7- COS

Tth 21 T '

4Z 7tx . 2nt

and ç-=-rt^^ cos -—sm— - ,

If h be the breadth of the bay, the kinetic and the potential
energy inside the bay are respectively given by

-^ pliblqrdx =

WlH)p . .,27tt
sm-

T'h T

_ aHhgp „ 2nt

and TT ü^^P \ 'ffd^ - — -A — cos-

— ghpjr/dx =

4 2^ •

Assume the kinetic energy outside the bay to be

SECONDARY UNDULATIONS OF OCEANIC TIDES. 59

„,,, ..2 IGPa'bJp . , 27Tt

r/ib-pç^ -^ ^j^. sm-

TVi T '

where Iq is the vakie of ^ at x=o, and P is of the dimension
of a number. Neglecting the potential energy outside the bay,
which is very small, we have

4:aH''bp . „ ^Ttt cclhgp .^IttI 16 Pa'lrl'p . „^rrt
rp2j^ sm- -^ + —^ cos- -^ + ^^ sm-— = const. ;

the relation is to be satisfied for all values of t.

T
4

Putting ^=0 and also t=^-f, we get

a-hlc/p ,
ii- = const.,

4

-, àa-Php , 16 Pa-Pb'p , crblc/p
and — TT, — — + ~ = const. = ^^^

Hence t^^^(i + 4:F±^

gh
l/gW

or ^=Ä(' + ^^t)' (2)

Lord Rayleigh found the reaction of air upon a vibrating
rectangular piston, whose length y is very great compared with
its breadth h, to be equal to the addition of a mass

V f?j , Jib \

9_

where r is Mascheroni's constant and = 0.5772, and ^^ = ^, -^ bein^-
the wave length. If the reaction be uniform over the piston,
we have for y=^h,

111?

W ( 3 , nb \

-(,-2-/--log-2-J-

Now, in a problem of long waves, we usually neglect ver-
tical acceleration and consider the horizontal acceleration nearly

60

K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITAN].

constant for different depths. Vertical planes, which are parallel
to wave ridges and fixed relative to water, make a to and
fro motion similar to the case of aerial vibration. The nodes of
aerial stationary waves correspond to the loop of the water
wave and vice versa.'^' If we nse the analogy for the expression
of the kinetic energy, wo have

1/8 7rb\. 1 f'S 7th

7ih\

This relation seems to be sufficient for the estimation of the
order of magnitude of the mouth correction. It is to be remarked
that if we assume

] «t sin __— cos

%

T

the result is not altered.

In the following table, the mouth corrections are given in

terms of the ratio of the breadth to the length of the bay : —

Here it is to be remarked that the
applicability of the above formula
becomes less, when the ratio of the
breadth to the length becomes
greater than unity, since in such
a bay, the nonuniformity of hori-
zontal displacement for each
transverse section becomes too
great.

{h) Irregularly shaped bay.

The problem of finding the period of oscillation in an irreg-

Breadth

Corrected Period

Length

Uncorrected Period

1

1.340

^

1.262

1

"5

1.218

1

1.187

i

1.163

1

1.107

i.

1.064

*) See Lamb, Hydrodynamics. 3rd Ed. § 188.

SECOND AKY UNDULATIONS OF OCEANIC TIDES. 61

iilarly shaped bay is also reducible to that of seiches in an
irregularly shaped lake. Professor Chrystar=' in his hydrody-
namical theory of seiches, worked out this problem in a most
elegant manner ; he compared the oscillation of an irregularly
shaped lake with vibration of a string with variable linear
density, and gave a minute discussion on a number of special
cases.

When the shape of a lake does not much differ from a
rectangular tank, the following method of calculating the period
may be of some practical importance. In accordance with the
above supposition, we may assume that the normal velocity at
any section S is constant over it, and that the elevation of the
free surface is the same along the entire breadth corresponding
to the section S. The vertical acceleration is neglected in com-
parison with the horizontal.

Take the origin of rectangular co-ordinates at one end of
the lake, .r-axis being in the direction of the length, c, /;, h
have the same meaning as before. Then the kinetic and the
potential energy are respectively given by

K E. — — jpSç'dx iiiid P.E. = — I cjhfr/j'dx

where S is the sectional area.

Again, from the equation of continuity, we have, putting

hence l^.^.^\p^^dx and ^•^' --\ ^JP Wi^)'^"^'

*) Prof. Chrystal, Trans. Roy. Soc. Edin. Vol. XLT, p. 599, 1905. Prof. Chrystal and E.
Maclngen-Wedderburn, do, p. 823, 1905.

62 K. HONDA, T. TEKADA, Y. YOSHIDA, AND D. LSITANI.

If we assume for X an expression of the same form as
would be obtained, if *S were constant, the length being straight
or curved, that is

or

then l'^^'«^"^^-

and 3^-2^-— •^.;

hence K.E. = l-p f—l^] »iu — .(j>Xdx

V^ >r^ f 1 r 1 . IcTtx . mnx 7 1 r ,*
and P.E. ---. 1 i/p|l {2-^ cos i:^ ^\lx

-^1 2 p J b I r'

yr\ -^l 1 kmn'-qo C 1 hnx imtx 7)1,

k III ^ -J t J U i i

where the summation imder the sign ^ 2j must be taken such
that k:^m.

Since <^'s are approximately normal co-ordinates, the quan-
tities under the sign ^^ are small, so that for simplicity's
sake, we may write

K.E. = 2^(J, + oX)^r + Z E''^'^"^^'^'" '
P.E. = 2(6; + oa) <^,^ + 2?2'^^^^-4'.4>"< ,

SECONDARY ÜNDÜLUTIONS OF OCEANIC TIDES. 63

where A^-i-dA,, = — p f-~ sin- _i^ dx ,

C, + Ja - i llÙ^LÇL co.^ ^ dx .
^ 2 Ir J b I

Hence, we get'-'

-2 C. + oC, y{oC,,,-p^jA„„y
^' A, + dA "^ A,A,,{pJ-p:r)

■ A + oA,'
or denoting the period of the k th harmonic l)y T^ ,

/I . n JCTTX 7
Sin" dx
^ S I

^P'^^ ^^^ rlcos-^^cZo.'
J b I

Pntting S=Sf, + AS and b = b,, + ^b, and neglecting the sqnares and
the prodncts of AS and âb, we get

fsin^ i!^ dx { r^' sin^ I^dx f ^ cos'- i^!^ fZ^]

^ ^ I COS" dx I sm- cte / cos- dx

J I y J I J I

where //,= — • If the integration Ix^ effected between the hmits 0

and /, we get

21

n =

kv^ghj"^^ 2 A, 2 27,, 2 j V v„ ^ ?>„/ / J ' '

where ^u = Z?^ , v^ = IS^^ ,

JA = fAbdx, Av=fjSdx.

The above expression can also be transformed into a simpler
form :

*) Eayleigh, Theory of Soiind, 2ik1. Edition, Vol. I. p. 115.

64 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

^.=(n)„ll4/(f + |)eo.ÄV.] (4)

by taking r„ and A„ sncli that Jv and JA vanish, and putting

By mechanical integration, we can easily evaluate the values
— I àb cos — — dx and — / à S cos — dx ,

and thus arrive at an expression representing tlie change of
period due to a slight variation in the area and volume of
the oscillating liquid. The expression shows that any con-
traction or expansion at the middle part of tlie lake prolongs
or shortens its natural period respectively, and that a con-
traction or expansion at the end portion shortens or prolongs
it respectively.

To apply the above expression to the case of a bay, we
need only to consider a lake whose shape is symmetrical witli
respect to the vertical plane through the mouth line, and to
find the period of tlie seiches in the lake. This period, if it
be corrected for the mouth, is the required period of the
oscillation of the bay water.

(c) Dumb-bell- shaped bay.

The above assumption does not hold for the case, when a
portion of the lake is very much contracted. In such case,
however, we may treat the problem in quite a different wav.
When two basins communicate with each other by a narrow
canal, the gravest mode of oscillation takes place such that
the levels of the two basins rise and fall respecti /ely. If the
breadth of the canal is very narrow compared witli the two

SECONDARY UXDULATIOXS OF OCEANIC TIDES. 65

dimensions of the basins, we may assnme that the rise and fall
of the level is uniform for eacli basin, and that in the canal
the level is invariable, the motion of tlie water being chieflj^
horizontal. Then, denoting the areas of the basins by S and
S', the breadth, the depth and tlie length of the canal by
b, h and / respectively, the displacemeiit of water in the canal
along its length by ç, and the vertical displacement of the
surface of S and S' by -^ and 7^ respectively, the kinetic and
potential energies are given by

K.E. = £^r, P.E. = ^(Sf + Sr).

Again, the correction to tlie kinetic energy on each end of the
canal is nearly

phi)-/ 3 , nb

7t\2, ' ^ IP'

in which ; is the wave length, if the basins are infinitely
wide, and may be considered nearly equal to four times the
leno-th of tlio basin in the direction of oscillation.

Since S-rj=-S'fj' a nd S-fj = bh ?,

we obtain, in the usual manner, for the period of oscillation

/SI (, '26/ 3 , 7tb w

(5:

In order to test the validity of the result, several tanks
were made of zinc plates, two circular basins communicating
with each other by a canal of uniform rectangular section.
These were filled with water to a suitable depth and set into
oscillation ; the results of experiment were found to agree well
with the above theory.

GQ K. HONDA, T. TEE ADA, Y. YOSHIDA, AND D. ISITANI.

Special interest is attaclied to the case, when one of the
basins becomes infinitely large ; the problem is then reduced to
the case of a bay communicating witli open sea by a narrow
neck. Taking ;.=A'=:4L, where L is the length of the bay
measured along tlie probable direction of propagation of waves,
we obtain from the above equation,

Another simple case frequently met with is that of a

dumb-bell sliaped bay communicating with an external wide

sea by a narrow mouth or neck at the end of one basin.
Using tlie same notations as before, we get

and 2P.E-fj{S-ri'-vS'-f-\

where ).^^, X and /' may be put equal to mean lengths of tlie two
basins for the first approximation. Since Sy^ = bhç — h'h'ç' and
S'r/ = yii'^', we get

c c

and 2P.E.=gi^ Ä^"^";^}'

where hhç = X, .h'h'ç' = X\

^ + 4(0.923 + logqi') = i,

t nil \ no J c

V 2 / V'-^N 1

_,+._(0.9^3 + log^) = -;

SECONDARY UNDULATIONS OF OCEANIC TIDES. 67

whence the equation of motion are at once written down ;

X X-X'

.V /X'-X X'

Eliminating X', and putting X-—e'^'^, we have

If we put S'-mS, c' = nc, then

2.T l~(fc~

where ^ = l^n-\ — . (i^n)- + — + — ^ ^ ;

my 111- m

whence the vahie of T can be obtained. It m=n=l, (p=?j±i/5.

The case, in which both ends of the dumb-bell shaped

bay open to the sea, can also be treated in a similar manner.

§ 7. THE METHOD AND THE RESULT OF
CALCULATION FOR THE PERIOD OF OSCILLATION.

In the calculation of the period of oscillation in a bay by
the simplest formula, it is necessary to evaluate the length
and the mean depth of the bay from the charts ; the charts
used were those published by the Hydrographical Section of the
Naval Department. As the mean depth, we took the ratio of

68 K. HONDA, Ï. TERADA, Y. YOSHIDA, AND D. ISITANI.

the total volume of the water in a bay to the area of the sur-
face. The length of the bay was measured along a median
line drawn parallel to what was considered to bo the main
stream line.

To find the mean depth of a bay, we began wibh drawing
contours on the chart in which the depths at a number of
points in the bay referred to low water springs are given. After
drawing as many contours as the case requires, we measure by
a planimeter areas bounded by successive pairs of contours.
These areas multiplied by the corresponding depths, increased
if necessary, by the half range, give the partial volumes of
water. Dividing the sum of these partial volumes by the area
of the free surface, we get the mean depth.

We calculated by formula (1) the period for all observed
bays, and also for those not yet observed, whicJi seem to
have the forms specially favourable for oscillation. For several
typical bays, w^e also calculated the correction due to the change
of the section as well as that due to the mouth, and compared
the corrected values with the observed. The calculation was
carried out in the following way.

(a) Bay of Aomori.

According to our investigation, the Bay of Aomori oscillates
in two different modes, that is, the lateral and the longitudinal
oscillation with the periods 103'" and 295'" respectively. Con-
sidering the bay as a rectangular tank, wdiose length is 55.3
km. and whose mean depth is 36.5 ra., w^e get 9 7. 5"' as the period
of the oscillation.

In order to obtain the correction due to the variation of the
section, we draw on tlie chart several lines at suitable positions

SECONDARY UNDULATIONS OF OCEANIC TIDES. 69

normal to the line of the length, and then taking the length as
abscissa and plotting corresponding breadth as ordinates, we
o-et a breadth- diagram. Draw mean breadth line, at a distance
eqnal to tlie whole snrface of the bay divided by the length.
Taking now this line as the new axis of co-ordinates, we can
easily draw the diagram for ^ b cos — — ; whence by mechanical

integration, we get 0,113 as the value of— M 6 cos -1— dr. Pro-

ceeding in a similar way for the sectional area, the value of

— j J S co-i ^-- (Ix is found to be 0.002. Applying these values

of corrections to 97.5'", we finally get 100'" as the period of the
lateral oscillation of the bay, in good accordance with the ob-
served value 10o"\ In this case, the correction due to the mouth
is of course unnecessary.

As for the longer period, the calculation of the period as a
rectangular bay gives 213'"; the correction due to the variation
of the section, as calculated in the manner above described, is
24.8'". The correction due to the mouth is 46.5"\ so that the
corrected value for the period of longitudinal oscillation is 284™,
which fairly accords with the observed value.

(b) Bay of Ofunato.

The simple calculation of the period of fundamental oscil-
lation on the assumption that the bay is a rectangular tank,
whose depth is 19.0 m. and whose length is 8.1 km., gives 39.5™.
The corrections due to the variation of the section and due to
mouth are respectively -10.7'" and +8.6'"; tlie corrected value is
therefore 36.4'". In this case, the correction of the section and
that of the mouth have opposite signs, tiie former a little over-
weighing the latter.

70 K. HONDA, T. TEKADA, Y. YOSHIDA, AND D. ISITANI.

(c) Bay of Tsuruga.

If the bay is considered as a rectangular bay, whose depth
is 28.5 m. and whose length is 15.1km,, the period of oscil-
lation is calculated to be GO.O" ; tlie corrections due to the
section and to the mouth are respectively -Iß.S''' and +15.8"\
The corrected value is therefore 59.0™ in a fair accordance
with the observed period.

The last two are good examples showing that the correction
due to the section and that due to the mouth, nearly cancel
wdtli each other. Similar remarks apply for many other bays.

When the mouth of a bay is decidedly contracted, the
simplest formula completely fails to give the period of oscilla-
tion, in wiiich case formula (G) is to be used. We give here
two examples of calcidation by formula ((3) or (7) and show how
the results of calculation accord with the observed values.

(a) Bay of Aomori.

This bay may also be taken as an example of double-bays
discussed in p. GO. lîeferring to the annexed figure which
show^s the general outline of the bay, tlie shaded portions were
considered as necks connecting external sea and two basins S
and S'. Necessary data for the calculation of periods, estimated
from tlie chart are as follows : —

6==13.5km. b' = U.7km.

/ =11). 0 km. r= 5.3 km. ;.= 120km.

/^=54.8m. h' = il.5m.

.S=4.75xlOMan.' .S' = 9.4xl0Mvm.'^
whence for two values of (^ we obtained 5.25 and 0.49, and for
the two periods 100™ and 325™ in fair accordance with the ob-
served values.

SECOND AEY UNDULATIONS OF OCEANIC TIDES. 71

It is interesting to observe that the formula, which is
derived from a quite different consideration as compared with
tlie usual view, will give fairly concordant values.

(b) Bay of Osaka.

The Bay of Osaka which is almost surrounded by land,
communicating with external sea by two narrow necks, Akashi-
seto and Yuraseto, may be taken as an example of those bays
discussed in p. 64. For the resultant conductivity of necks, tlie
sum of separate conductivities was duly taken. Data for the
calculation of the period estimated from the chart are as
follows :

Akashiseto : b^= o.d km.

l,= 6.2 km.
/?i = 41. m.
Yuraseto : b.,= 5.0 km.

l,== 1.2 km.
7^,-27. m.
>S'=1.47 X 10'' km'., / =^150 km.,
whence from (6) 2'=270"\ which fairly accords with the largest
period observed.

In the following tables, the mean depth, the length and the
period calculated by formula (1) are given in the 4th, the 5th
and the 6th columns respectively ; in some bays, the periods
corrected for the variation of the section and for the mouth are
given with the figures underlined. The observed periods, which
would possibly correspond to the calculated values, are given
in the last column. The letter S placed after some calculated
periods indicates that the periods followed by S are those for
the lateral or seiches oscillation in the bavs.

72

K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

Coast of Hokkaido.

Top.
No.

Bay

Province

Deptli

Length

Calc. Period

Obs. Period

1

Otaru

Shiribeshi

9.1m

2.4 km

17.3-"

13.8"'-16.5™

2

Nemnro

Nemuro

4.2

0.86

9.0

10.9

3

flanasaki

j>

7.5

l.H

10.9

—

4

Bokkiriso

j>

5.5

1.7

15.2

—

5

Hamanaka

Kiisliiro

8.5

6.G

48.2

49.5

6

Akkeslii

>>

10.6

13.0

67.2

—

7

Mororan

Iburi

8.1

6.G

48.9

51.1-54.0

8

Hakodate

Osliima ■

10.7
>>

9.2
9.1

45.3

23.6 S.

45.5-57.5
21.9-24.5

Japan Sea Coast of Honsliiii.

Top.

No.

Bay

Province

Daptli

Length

Calc. Period

Obs. Period

(

38.8 m

62.4 km

213;" 284"^

295."^

9

Aomori

Mntsu ]

'

36.5

55.3

97.5,106 s

103.

10

Yebisu

Sado

135.

10.9

20.1

—

11

Futami

J5

16.6

8.4

44.0

—

12

Fusliiki

Etcliiu

662.

63.4

52.7

541

13

Tsuruga

Echizen

28.5

15.1

60.0, 59.0

56.7-62.9-07.7

14

Mij'azu

Tango

15.5

9.9

53.4

—

15

Tonoura

Iwami

ii.n

1.8

11.1

11.9-12.9

SECONDARY UNDULATIONS OF OCEANIC TIDES.

73

Pacific Coast of Honsliiu.

Top
No.

Bay

Province

Deptli

Length Calc. Perioc

Obs. Period

16

Miyako

Rikncliiu \

22.0m
9.7

' 10.0km
7.0

45.4™
24.0 S

21.3^-22.0™

17

Odsuclii

>)

29.9

7.9

30.7

27.0

18

Rj'oishi

j

51.9
33.1

7.2
5.4

21.3

20.0

22.8
20.3

19

Karaaishi

/■ 1

40.8
19.3

7.4
4.6

24.8
22.3

24.8 - 26.0
20.3

20

Kojiroliama

Rikuzen

25.8

6.2

26.0

24.6

21

Yo3hiliama

>>

51.8

7.2

21.1

18.5-20.1

22

Okirai

>>

31.8

7.0

26.4

27.5 - 29.9

23

Ryori

>>

25.9

4.4

18.4

18.3

24

Ofuaato

»>

19.0

8.1

39.5, 36.4

39.0 - 39.1

25

Niiyama

j>

11.8

1.2

7.5

6.4- 7.6

26

Ayukawa

>j

12.7

1.5

8.9

6.8- 8.9

27

Katsiinra

Kazasa

7.9

1.8

13.4

—

28

Tateyama

Awa

49.4

6.8

20.5

— .

29

Tokyo

Musaslii

52.7

75.5

222.

—

30

Moroiso

Sagami

2.95

1.1

13.4

13.8 - 15.6

31

Sagami

j>

461.

19.9

19.8

—

32

Sliimoda

Izn 1

22.2

3.5

15.9

13.8 - 18.2

I

15.0

2.4

13.3

— ■

33

Merakoura

)j

12.7

1.4

8.6

—

34

Tago

»»

18.8

1.0

4.7

—

35

Heda

>•

24.3

1.4

6.1

—

36

Suruga

Suruga

55.7

60.4

54.5

—

37

Sliimizu

v

15.6

3.9

21.2

—

38

Ise and Mi-

Ise and

18.4 '

73.0 (f/)

363.

390.

kawa Sea

J
Mikawa

18.4

111. (by 278. S

—

,

9.5

31.4(c) 217.

208.

74

K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

Pacific Coast of Honshin (Continued).

Top:

No.

Bay

Province

Depth

Length

Calc. Period

Obs. Period

39

Toba

Shima

18.2m

6.5km

11.4"^

—

40

Kiikiura

Kii

20.9

3.0

14.1

—

41

Kushimoto

■■ 1

15.4
5.0

3.4
1.3

18.3
12.8

16.5"^ - 18.6-"
11.6 -13.0

42

Adashika

5>

16.4

2.7

14.0
270*

260. - 310.

43

Osaka

Settsn, Izumi
and Awaji

27.0

3>

61.0
1x61.0

126 S

63 S

106. - 150.
61.- 66.

44

Hiroshima

Aki

15.0

11.2

61.6

60.0

* The period was calculated by formula (6) as described in p. 71.

Shikoku.

Top.
No.

Bay

Province

Depth

Length Cak. Period Obs. Period

45

Susaki

Tosa

17.9m

7.8km

39.1'"

39.9™-41.6™

No mi

>j

17.2

6.2

16.0 St

17.6 - 18.2

Kure

>>

13.2

2.8

17.0

15.0 - 16.3

46

Shimizn

5»

7.2

5>

2.9

4- X 2.9

22.8
7.6

—

47

Okuchi

lyo

29.6

4.5

17.8

—

48

Uwajima

j>

204.

16.7

49.8

—

49

Shitama

5>

35.0

3.1

11.0

—

50

Yawatahama

J>

30.9

4.6

17.6

—

51

Amai

J>

24.6

o o
O.O

14.2

—

52

Ikeda

Siodoshima

9.8

5.5

37.3

—

53

Uchinoumi

>)

11.2

7.0

42.9

—

54

Shido

Sanuki

8.4

6.2

45.7

—

t The seiches between Otani and Awa.

ÖECONDAKY UNDULATIONS OF OCEANIC TIDES.

/O

Kiushiu.

Top.
No.

Bay

Province

Depth

Length

Calc. Period

Obs. Period

55

Ariake

Hiûga

42.8ni

21.8km

71.1™

—

56

Hososliima

}i

11.7

55

3.0
ix3.0

19.0
6.3

17.8'°-20.3'"
6.6- 8.7

57

Yonozu

5>

23.3

4.1

18.2

—

58

Aburatsu

J>

8.0

2.0

15.1

15.0-19.0

59

Kagosliiraa

Satsnma

103.

51.0

107.

—

60

Nagasaki

Hizen

18.7
15.3

7.7
8.3

37.5
22.6 S

34.5 - 37.6
22.5 - 25.2

61

Karatsu

" ,

16.4

55

13.5
19.7

71.0

51.8 S

—

62

Shisliimi

Tsushima

13.7

1.5

8.8

—

63

Sasiiua

j>

11.1

1.9

12.1

—

Bonin Island and Formosa.

Top.
No.

Bay

Lsland

Depth

Length

Calc. Period

Obs. Period

64
65

Futami
Kehmg

Ogasawara
Taiwan

23.9m
10.4

3.1km
3.9

13.6™

25.8

16.0™-20.0™
25.3 - 29.6

China and Korea.

Top.
No.

Bay

Country

Depth

Length

Calc. Period

Obs. Period

66

Pusan

Korea

10.7m

5.9km

38.4™

—

67

Onshantin

55

9.9

3.6

30.7

—

68

Weihaiwei

China

8.7

55

7.4
9.9

53.3
33.8 S

—

76 K. HONDA, T. ^lERADA, Y. YOSHIDA, AND D. ISITANI.

It will be seen from the above table that in most cases,
the period calculated by the simplest formula (1), that is,

agrees fairly well with those actually observed. Thus for many
cases, the corrections due to the mouth and the variation of the
section seem to be superfluous. This probably arises from the
fact that in many bays, the correction due to the section nearly
cancels the mouth correction. For many bays have the form
gradually contracting and the depth decreasing, as we approach
towards the end, so that the correction due to the variation of
the section is negative. The mouth correction being always
positive, the two corrections usually tend to annul each other.
As exemplified in the cases of Ofunato and Tsuruga, the total
correction nearly vanishes for many bays, and then results an
apparent validity of the simplest formula. If the mouth of a
bay be contracted and the depth be shallower than in the in-
side, the correction due to the section is positive, so that the
calculated value by the simplest foi'mula decidedly falls short of
the observed value, and can only be brought into coincidence
by taking the tw^o corrections into consideration ; a good example
of this is furnished in the case of the Bay of Aomori. That
the calculated periods for the bays of Mororan and Okirai which
have rather narrow mouths, are a little less than the observed
values, is also explained on the same view.

§ 8. SEA WAVES AND SECONDARY UNDULATIONS.

As we have already remarked. Professor F. Omori found
that the periods of sea waves observed in a bay are the same

SEœNDARY UNDULATIONS OF OCEANIC TIDES. 77

as those of the usual secondary undulation. He explained the
phenomenon by supposing that a bay or a certain portion of
sea oscillates like a fluid pendulum with its own proper period,
when it is excited by an earthquake or any other disturbing causes.
We have also investigated the periods of the sea waves for
different bays and found that the above relation is generally
well satisfied, especialh' in the sea waves of distant origin. As
we shall see soon below, the period of a sea wave in a bay is,
in most cases, given by the formula

T=-4L
l/gh '

It is then very probable that in such cases, the sea waves are
of a similar nature to the secondary undulations. Now the sea
waves are probably of such a complex nature as to be repre-
sented by the sum of a series of long waves of different periods
and amplitudes. If a group of these waves proceeds towards a
bay, the bay takes up and resonates to the undulation, whose
period approximately coincides with that given by the above
relation.

This consideration chiefly applies to the sea waves of dis-
tant origin. If however its origin is not very far from a bay
or an open coast, progressive waves of long wave length, irre-
spectively of their period, are sufficient to cause a disastrous
effect on the coast ; for by Green's law of amplitudes long waves
considerably increase their amplitudes as they approach a
shallow shore. Thus in actual destructive sea waves, we almost
always have reports of high wave fronts approaching towards
the shore, indicating that the waves are of the progressive
nature, but not of the stationary character. For the sea waves
of 1896, on the coasts of Sanriku, there are instances which

78 K. HONDA, T. TEßADA, Y. YOSHIDA, AND D. ISITANI.

seem to indicate that the periods of the sea waves did not
coincide with those observed in ordinary cases.

In the investigation of the nature of sea waves, the tide-
gauge is the only instrument available at present ; but for this
purpose, it is necessary to set up the instrument on an open
coast, or better on a small isolated island, and not in a bay,
where the waves are much modified by the oscillation proper
thereto.

In the following pages, discussions regarding to several sea
waves in the light of our present investigation will be given.

(a) Sea waves of Ansei, 1854.

The destructive sea waves of 1854, which accompanied the
great earthquake of Ansei, devastated the great part of our
Pacific coast, and were felt by the tide-gauges at San Francisco
and San Diego.

On December 23, at 9'' 15" a.m., a strong shock was felt at
Shimoda in Izu ; at 10", it was followed by a large wave 9 m. in
height. The rising and falling of the water continued several
hours ; in all, there were six large waves, the period of which
seems to have been 15"-20"\ if we judge from the descriptions
by a suflferer. The period is the same as that usually observed
in the bay. A Russian man-of-war then at anchor, was de-
stroyed by the waves.

At Tanabe in Ivii, seven or eight waves were observed from
the morning to the evening ; at Nagashima in the same province,
the first wave was the highest, after which two weak waves
were counted. At Toba in Shima, the first and fourth waves
are said to have been tlie highest. An irregularity of tides was
also observed in Tosa ; at Kôchi, three ebb-and-flows were counted
from 9'' a.m. to 2" p.m.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 79

On the 24th, similar waves visited the Pacific coast from
Tosa to Izu.

On the 23rd-24th, a regular train of sea waves was recorded
on the tide-gauges at San Francisco and San Diego (PI. XLTX,
Fig. 1). The average period of oscillation at San Francisco was
34.9'", whilst that at San Diego was 34.7"\ The wave took 12"
12™ and 12" 37'" to arrive at San Francisco and San Diego
respectively.

Now, the Bay of San Francisco, as we have shown by the
model, can be put in the oscillation between Sausalito and
West Berkeley sides by waves incident on Golden Gate. The
period 34.9" falls a little short of the period of the binodal
oscillation of the bay.

The Bay of San Diego is too long to be put in its uninodal
longitudinal oscillation ; the contraction of the bay near San
Diego also prevents the fandamental oscillation. The oscillation
between Quarantine wharf and San Diego, which also forms a
part of a trinodal oscillation of the whole basin, gives the period
of 34. ,5'". In this calculation, the depth was estimated from the
available charts to be 3.5 m., while its length was taken as
0.07 km.

If the path, by which sea waves travelled from Japan to
America across the Pacific, be known, the velocity of propaga-
tion can be estimated. Now the sea wave, which has usually
a large wave length compared with the depth of the ocean, must
be refracted according to the condition of the bottom, so that it
is very difficult to know tlic path by which the sea wave
actually travelled through the ocean. We therefore conceived
several paths between the origin of the wave to the observed
station in question, of wliich we measured lengths, and also

80

K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

mean deptli by mechanical integration.* Tlie velocities of pro-
pagation of the long waves along these paths were then cal-
culated from the depths. The time of transmission of the wave
along these paths was compared, and the path of the minimum
time was taken to correspond to the actual path. From the
path thus found and the actual time of transmission, we found
the mean velocity of propagation of the sea wave, as given in
the following table. As tlie time of occurrence of the sea wave
in its origin, we took the time of the earthquake.

Station

Distance

Mean Depth

\/gh

Time Interval

Velocity

San Francisco
San Diego

8,190 km.
9,000

5.50 km.

12.20^
12.62

186 ^.
198

Hitherto it has been customary to measure the path along
the great circle of the earth ; but the actual distribution of the
depth being complicated, this is not a proper method.

The value Vgk of the fourth column in the above table
represents the theoretical velocity of a long wave. Strictly
speaking, the mean velocity should be deduced from the dis-
tance s along the path and the time interval /f given by

J\/gh

*) The chart pnbHshed by " Deutschen Seewarte," 1896, -was used. One of the authors
CYaUiated the mean depths by Berghaus' Physikalischen Allas and obtained considerably
large values (Proc. Tokyo Matb.-Phys. Soc. 3, p. 1G5.).

t) C. Davison, Phil. Mag. 50, p. 579, 1900 ; H. Nagaoka, Proc. Tokyo Math.-Pbys. Soc,
p. 12G, 1902.

In deducing the above formula, no account is taken of the curvature of the earth;
if this is taken into account, the general tendency is to reduce the velocity from that given
^^y \/y/r. Of course there is some dependence on the wave length and the configuration
of the sea. H. N.

SECONDARY UNDULATIONS OF OCEANIC TIDES.

81

where ds is the elementary distance, and It the depth at the
point under consideration. It was therefore recalculated by the
above relation; but we did not find the increase of its value
more than 1 per cent. In the other sea waves, the difference
did not exceed the same limit. At any rate, tlie calculated
velocity is considerably greater than the actual value ; this point
has been noticed by several earlier writers, such as Milne, W.
J. H. Wharton, E. Geinitz, C. Davison, etc.

(b) Sea waves of South America, 1868 and 1877.

At about 5^' p.m. on August 13, 1808, a destructive sea
wave, which followed a severe shock, swept away many cities
on the coast of South America. It originated between Iquique
and Arica, and was felt at different coasts of the Pacific.

In Northern America, it markedly disturbed the tide-gauges
at Astoria, San Francisco and San Diego (PI. L).'=' The time of
arrival in local time (8"W.) and the periods observed are given
in the followin": table : —

Station

Beginniuo;

Period

Astoria

8au Francisco

San Diego

&' 32'" a.m.
2'' 2-4'" a.m.
1" 17"" a.m.

24.0"\ 27.6'", 36.3'"
19.2'", ?)C)A"\ 41.2'"
31.0'", 35.1"\ 4G.8'"

Here it is to be noticed that the observed periods did not
remain constant, but varied within a certain range, the periods

*) Dr. Tittmann presented to Professor F. Omori at his request several valuable records
concerning sea waves. The curves in PI. L are those reduced by a pantograph from the
records. Periods given in the above table were obtained from the same records. The same
remarks also apply to sea waves of Iqnique.

82 K. nONDA, T. TER ADA, Y. YOSHIDA, AND D. ISITANI.

in the above table being the mean vakies of several oscillations
in comparatively regular trains and therefore the period of
single undulation may differ from the mean In^ a few minutes.
At San Francisco, the waves of about 41"' appeared most fre-
quently, though the period SS"' of Shimoda wave also manifested
itself. By referring to the result of experiment with models,
it may be noted tliat these periods probably correspond to the
higher modes of oscillation of the bay. At San Diego, the
period 31™- 3 5"" appeared most conspicuously, which probably
corresponds to trinodal seiches of the bay. It is a characteristic
feature of this sea wave that at these stations, the initial waves
are not conspicuous and their amplitudes gradually increase.

The mean velocity of propagation of the Avave from South
America to Astoria, San Francisco or San Diego can be cal-
culated, if the path through which the wave actually travelled
be known ; but this is not an easy matter, the condition of the
bottom along the coast line of America being complex.

In Japan, the wave was observed at Hakodate by Captain
T. Blakiston, who wrote the following passage to Professor
Milne : —

"On August 15, at 10'' 30"" a.m., a series of bores or tidal
waves commenced, and lasted until 3'' p.m. In ten minutes,
there was a difference in the sea level of 10 feet, the water
rising above high water and falling below low water mark with
greater rapidity."

Now the periods of the ordinary conspicuous undulation in
the Bay of Hakodate are éS'-oT" and 22'"-24". In the case of
sea waves, the latter period always appears superposed on the
former. According to the report of tlie captain, half the period
of the present sea wave is 1 0™ ; allowing errors of 1 or 2 minutes

SECONDARY UNDULATIONS OF OCEANIC TIDES.

83

of observation, it is probable that the wave corresponds to the
oscillation proper to the bay with the shorter period, probably
superposed on the longer period. The wave took 24" 57'" to
arrive at Hakodate across the Pacific.

As in the former case, we calculated the mean velocity of
the sea wave with the result given in the following table : —

Station

Distance

Mean Depth

V'fjh Time Interval

Velocity

Hakodate

1G,600 km.

4.78 km.

1
2.14 ^. 1 24.95"

185 ^,

Thus the mean velocity of the sea wave fairly coincides
with that between Shimoda and San Francisco ; it is decidedly
less than the value of x/gh

The terrible earthquake of Iquique on May 9, 1877, also
caused destructive sea waves, which were felt across the basin
of the whole Pacific, from New Zealand in the south to
Japan and Kamschatka in the north. In Japan, the waves
were observed at Hakodate, Kamaishi and the coast of
Kazusa.

The earthquake originated at 8"2()'" p.m. on the 9th, and
the consequent sea waves broke on the shore of Iquique 30'"
afterwards with disastrous eflect. At 6" 21'" a.m. on the 10th,
a group of sea waves suddenly invaded the bay of San Fran-
cisco (PI. XLIX, Fig. 2) and put the bay water into oscillation ;
the oscillation seems to have been renewed at 2" 50'" p.m. by
another group of incident waves. The oscillations continued
over 2 whole days ; their periods of oscillation in comparatively
regular trains were 17.3'", 27.8'", 34.3"^ and 47.4'". Tlie most
conspicuous periods were 34.3'" and its octave 17.3'", tlie former

84 K. HONDA, T. ÏEllADA, Y. YOSHIDA, AND D. ISITANI.

falling near the period of the binodal oscillation between Sau-
salito and West Berkeley sides.

In Japan, at 11" 30'" a.m. on the 11th (in our time), the sea
at Hakodate was observed to rapidly retire, and then to rise in
level to about 2 m.; tlie rising and falling of the level lasted the
whole afternoon with a period of about 20"'. Betw^een 2" 30™
and 2'' 35'" p.m., the oscillation was renewed with the largest
amplitude of 2.4 m. Admitting errors of observation of a few
minutes, the oscillation possibly corresponds to the oscillations
proper to the bay.

The tide in the bay of Kamaishi began to oscillate between
9'' and 10'' a.m. of the same day, and the amplitude of oscil-
lation gradually diminished. At 0'' and 2" p.m., tlie phenomenon
was renewed ; and until TV or 6" p.m., the bay was observed to
oscillate with an amplitude of 3 m. and with period of 5"\ At
midnight, the sea was completely calm. Comparing the waves
with those in the Bay of Hakodate, we notice that the first
wave was not observed in the latter bay.

At noon of the same day, large waves invaded the open
coast of Kazusa, but the sea soon became calm. At 4'' p.m.,
still larger waves devastated the same coast, causing the loss
of many lives. These two waves possibly correspond to the
waves which visited the bays of Hakodate and Kamaishi a
little earlier.

The calculation of the velocity of propagation of these
waves gave the following results : — •

SECONDARY UNDULATIONS OF OCEANIC ÏIDKS.

85

Station

1
Distance | Mean Depth

1/ ijh

Time
Interval

Velocit}-

Hakodate
Kamaisiii
Kazusa

16,600 km.

5)

4.78 km.
4.80

5>

214 ^.
216

J5

25.00"
22.92
25.25

185 ^.

201

183

Thus, the velocities in the first and third rows in the
above table are decidedly less than the velocity in the second
row ; this discrepancy is probably due to the fact that, the
first wave was not observed at Hakodate and Kazusa probably
on account of its small amplitude. Here also the value
of i/ cjk is a little greater than the actual velocity.

(c) Sea waves of the Krakatoa eruption, 1883.

Great sea waves caused by the eruption of Krakatoa,
August 27, 1883, swx^pt over the entire area of the Indian
ocean and forced their way as far as to the northern parts
of the Atlantic and the Pacific, leaving their traces on the
tide-gauges situated along their way, the records of which are
reproduced in the Report of the Royal Society of 1888, and
described by Captain W. J. H. Wharton. Tiiese records as
well as numerous matters of information from difTerent quarters
of the world, in wdiich the Report abounds, if reviewed under
the light of the results of our present investigations, may be of
some interest, inasmuch as the former reporter seems to have
put a little wx^ight on the secondary undulation peculiar to bays
and estuaries.

As to the cause of the periods of the great Krakatoa waves,
few theories have been proposed. Captain Wharton" attempted

*) Wharton, The leport of the Krakatoa eruption, p. 97.

86 K. UONDA, T. TEßADA, Y. YOSHIDA, AND D. ISITANI.

to explain the period of two hours by assuming that the sea
bottom was upheaved for about an hour. According to Pro-
fessor H. Nagaoka,* the earth is continuously vibrating with a
period 07™ of fundamental oscillation, and it is this vibration that
actually determined the periods of the Krakatoa waves. Our
theory differs from the above by not assuming the slow up and
down motion of sea bottom. Now, according to the results of
our observations, any portion of sea partly bound by land, is
capable of its own mode of stationary oscillation, which if pro-
perly excited, may last for some time, after the cause of the
excitement has receded. In this respect, the Sunda Strait (Top.
09) presents a highly suggestive form by its boundary. The
south-west end of the channel opens widely into the Indian
ocean, while the north east end is narrow and shallow com-
municating to the Java Sea. The strait, as a whole, may be
compared in its acoustical analogy with a conical open pipe,
provided that in the case of the hydrodynamical problem, both
ends are to be considered as the nodes of the wave profile. The
loop of the gravest mode of oscillation possible in such a
channel must lie nearly midw^ay but somewliat nearer the nar-
rower end. Hence the eruption of Krakatoa lying nearly at the
loop of this oscillation would be very favourable to excite the
natural stationary oscillation of the strait as a whole. The
initial disturbance, would soon settle into a regular oscillation
natural to the system ; this again would be propagated into the
external ocean as a train of regular waves, whose period of
oscillation is determined by that of the source.

Taking the length of tlie strait as IGOkm., and its mean
depth as 183 m. (i=100 fathoms), we obtain from our formula

*J Prof. H. Nagaoka, Proc. Tokyo Math. Phys. Soc. 4. p. 35, 1907 ; Nature, May 24, 1907.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 8 /

2^=126"\ which was actually recorded in the tide-gauge of
Batavia (PL XLIX, Fig. ?,f. Though the position of the node
at the southwest end is not very determinate, tlie ambiguity
does not affect tlie value of the calculated period in any serious
manner, because the bed to this end slopes down very steeply
toward the deep sea, so that if the virtual length of the strait
be assumed to be a little longer or shorter, tlie mean depth of
the oscillating basin becomes greater or less in a considerable
proportion, so that the value of //i/X remains fairly constant.
The fact that at Anjer at the northwest mouth of the strait,
the reported height of the waves was small, seems to stand in
liarmony with our supposition that the node lies near that place.

Besides the mode of oscillation above described, a binodal
oscillation between the two sides of the strait, Java and Sumatra
sides, might possibly be generated by the eruption of Krakatoa,
wliicli lies at the loop of this mode of oscillation. The period
of the oscillation is calculated to be about one hour, wliicli
nearly coincides with the periods recorded at many stations
along the Indian coast. In addition, the higher modes of oscil-
lation than the above two with comparatively small amplitudes
might possibly have been in co- existence.

Beyond tlie northeast end of the strait, the sea is shallow
and abounds in irregularities of bed, which may scatter the
weaves propagated from the end of the strait by complicated
reflection and refraction. Besides, the sectional area of the
northeast end of the strait is estimated to be about ^V that of
the southwest end, so that the energy j^ropagated from the
former mouth must liave been a small fraction of that from the

*) All tide-gauge records regarding the Krakatoa eruption are the reproduction from the
Report of the Royal Society of London.

88 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

latter. These considerations probably account for the smallncss
of waves propagated in the northeastern direction.

The tide -gauge nearest Krakatoa at tlie time of the eruption
was that of Batavia. It beautifully recorded two hour waves,
but did not trace one hour waves. The absence of this latter
period in Batavia raises no serious objection against our sup-
position, because the narrow opening to the northeast of the
strait, is very unfavourable for the propagation of the energy of
the lateral oscillation, as compared with that of the longitudinal.

Thus the energy of the oscillations was, in its greater part,
propagated into the Indian Ocean (PI. LI) and strikingly affected
the tide-gauges so far as the ports of Soutliern Africa (PI. LII,
Fig. 1-2). Examining the records given in the above cited
reports, we may generally distinguish two types of waves, —
one includes those types of waves propagated directly from Kra-
katoa and the other the stationary oscillation of bays or
estuaries excited by the incident waves. Prominent undulations
recorded along the coast of India belong to the former type.
Comparing the records at Madras and Vizagapatum or Nega-
patum and Port Blair, the identity of waves may easily be
recognized. We see also the trace of Vizagapatum waves in
the Negapatum record and vice versa. Most of these stations
are not situated in either bay or estuary possible of oscillation
with such a long period.

For remoter stations, we see generally that the disturbances
are chiefly due to the second type, i.e., to the proper oscillation
excited by the synchronizing components of the incident waves.
Hence for such bays, the periods of oscillation for Krakatoa
waves may be calculated from their dimensions, provided a good
chart is at hand. Since, at present, we are in want of reliable

SECONDARY UNDULATIONS OF OCEANIC TIDES. 89

chart on sufficient scales, we satisfy ourselves by deducing the
mean depths of different bays, quoted in the Krakatoa Report,
from their period of oscillations and their lengths estimated
from the charts* available. The results of calculation are as
follows : —

(1) Port Ehzabeth, Cape Colony. PI. LIT, Fig. 1.

The node of the Algoa Bay was taken from Cape Receife
to the coast of Alexandria opposite to the Bird Island ; taking
the length / = 25km. and the period 7^=74™, we found the mean
depth h to be 52 m.

(2) Table Bay, do. PI. LII, Fig. 2.

The node was taken from Green Promontory to the coast
opposite to Rabben Island; taking ^= 11.3 km. and 7'= 60"", we
get li = lQ m.

It will be noticed that the shape of the above two bays is
very similar to that of Hakodate, and also that the records of
secondary undulations in these bays are, in their character, quite
similar to each other.

(3) Port Adelaide, Australia. PI. LII, Fig. 3.

The period of 150'" traceable in the record of Port Adelaide
may be explained, if we suppose it due to the oscillation
between Port Adelaide and York Peninsula. In this case we
obtain // = 21.5ra. which very nearly coincides with the result of
our estimation from the chart. Besides, a period of about 200"
is traced, which is probably due to the oscillation of the In-
vestigator Strait, with nodal lines at its two ends. The period
calculated for the latter modes is 228"".

(4) Port Phillip. PI. LII, Fig. 4.

*) Berghftiis' Physikalische Atlas, Stieler's Hand Atlas, Encyclopedia Britanica etc.

90 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

The period of 86"" may be accounted for, if it be attributed
to the binodal seiches of the enclosed basin.

(5) Lyttelton, New Zealand. PI. LTII, Fig, 1.

Very conspicuous oscillation of this port with tlie unusually
long period of 165™ is probably due to the Pegasus Bay.
Taking the node between Table Island and the end of Bank
Peninsula, the calculated mean depth is about 30m. which seems
allowable. On the other liand, if we suppose the period due
to tlie oscillation in the narrow inlet of L^^ttelton, the calculated
mean depth would only be 8 m.

(G) Honolulu, Hawai. PI. LIII, Fig. 2.

Taking /= 2.25 km. for the narrow inlet and T—27.7"\ we
obtain h=o.7m, which seems reasonable. Another conspicuous
period is probably due to the binodal oscillation of the inlet.

(7) San Francisco. PI. LIII, Fig. 3.

The conspicuous periods of the Krakatoa waves observed
in the bay were 24.0", 36.2" and 48.6'". These periods were
frequently found in the same bay for other sea waves, and as
we have already remarked, probably correspond to the multi-
nodal seiches between the West Berkeley and Sausahto sides.

{d) Sea wave of Sanriku, 1896.

On June 15, 1896, a destructive sea wave originated in a
distance of about 150 km. off the coast of Sanriku in Japan.
The wave was the most disastrous one in modern time ; its
lieight in Yoshihama even amounted to 24 m. It swept away
many towns and villages along the coast line of Sanriku, ex-
tending to about 320 km. ; 22,000 lives were lost.

At Miyako in Rikuchiu, the earthquake was felt at 7'' 32"
p.m. and the tide began to retire at about 7'\50'" ; it then in-
creased and attained a maximum at about 8^ Then it decreased

SECONDARY UNDULATIONS OF OCEANIC TIDES. 9 1

and again increased ; at S*" 7"\ the largest wave invaded Miyako.
The subsequent large waves rolled on the shore at the following
epoch : —

8" 15'", 8".32"\ 8" .48", 8\59"\ 9M6™, 9\50'";
the intervals between two consecutive waves are 8™, 17"\ 16™,
11™, 17™ and 34.™ The period of the conspicuous undulation of the
bay of Miyako commonly observable in ordinary weather is 21™,
which is somewhat different from the period of the present sea
wave. From the above intervals, it may be concluded that the
sea wave w^as probably composed of the period of about IG™
and its octave. /Without the aid of a tide-gauge, it would often
be difficult to observe every incident wave of 8™ out of waves
so composed.

The record of the nearest tide-gauge was that of Ayukawa
(PI. LIV, Fig. 1) ; it shows a series of gigantic waves of the period
8™, which continued over two days ; during the first twelve hours,
the rising and falling of the level followed each other most ener-
getically. Comparing the period of the wave with that observed
at Miyako, it may be concluded that the period of the waves
incident on the bay nearly coincided with the period of its free
oscillation. Examining the record of the tide-gauge, we observe,
in the latter part of it, a beautiful series of beats which pro-
bably shows that the period of the incident wave is slightly
different from that of the free oscillation of the bay.

The sea wave also shghtly affected the tidctgauge of Abura-
tsubo in Misaki (PI. LIV, Fig. 2), which is about 600 km. distant
from its origin. Its period of undulation was 15™ in a good
coincidence with that usually observable. The same w^ave also
affected the tide-gauge at Hakodate ; unfortunately, this instru-
ment stopped at the very beginning of the sea wave, and began

92 K. HONDA, T. aEllADA, Y. YOSHLDA, AND D. IÖITANI.

to work again after several hours. The oscillation of the bay
continued over two days with its proper periods of 23.6"" and
45.5"'-57.5'" (PI, III, Fig. 2).

In the above four cases, the wave was more or less affected
by the proper oscillations of the hays. The tide-gauge at Chôshi
in Shimôsa has however been set up in a mouth of the river
Tone, so that its record in the case of the sea wave is the
most suitable for the investigation of the wave, inasmuch as
the sea is not much affected by any proper oscillation of
enclosed water. The record of the tide-gauge at Hanasaki,
which is situated on a small inlet in the Pacific coast of
Nemuro, possesses the same advantage as that of Chôshi. Thus,
in the records of Hanasaki and Chôshi (PI. LV, Fig. 1-2), w^e
observe, for the first one hour,'^' a similar series of waves of the
period of about 7". This period was found superposed on the
larger waves of some ten minutes.

The sea wave also crossed the Pacific and reached the
western coast of America. It disturbed the tide-gauges of
Honolulu and San Francisco (PI. LV, Fig. 3-4). The period of
the w^ave in Honolulu w^as 23.4,"- 26.0'" which is nearly the
same as that of Krakatoa waves ; in the first part of the record,
we may however observe a wave of double period. The record
of San Francisco was marked by irregular zigzags ; we can
however trace waves of periods 24.3'" and G.2.™

In the following table, the result of the calculation for the
velocity of sea waves through the Pacific are given : —

^) After the first hour, the tide-gauge at Hanasaki stopped.

SECONDARY UNDULATIONS OF OCEANIC TIDES.

93

Station

Distance

Mean Depth

l/gJi jTime Interval

Velocity

Honolulu
San Francisco

6,000km.
7,970

4.92 km.
5.51

220,^.
234

7" 44"'
10" 34™

216^^

-'^^ sec.

209

Thus the mean velocity of propagation of the sea wave is
somewhat greater than the velocities of other waves. The
mean value of i^~gh between Sanriku and Honolulu fairly agrees
with the observed, while the value between Sanriku and San
Francisco is decidedly greater.

(e) Sea waves of South America, 190G.

The earthquake of Ecuador originated, in our time, at
Qh^.2™ a.m.,1 February 1, 1906, and was accompanied by a
sea wave, which traversed across the Pacific from America to
Japan. The wave was recorded by the tide-gauges of Hakodate,
Ayukawa, Kushimoto, Hososhima and Fukahori (PI. LVI, Fig.
1-4 ; PL LVII, Fig. 1). The earthquake of Valparaiso, which
was also followed by a sea wave, originated at 9'' 45"' a.m.,
July 17 in the same year. The wave arrived at Hakodate,
Ayukawa, Aburatsubo and Kushimoto (PI. LVII, Fig. 2-3 ; PI.
LVIII, Fig. 1-2). In the two waves, the periods observed in
these bays were as foUow^s :—

Stations

Ecuador Wave

Valparaiso Wave

Ordinary Case

Hakodate

49.2™-40.9'"

53.0"»-48.0"'

57.5™-45.5"'

21.9"^

22.1»

24.5"-21.9"'

Ayukawa

7.3"'-8.3'",20"'

7.3™, 23'"

6.8™-8.9'",20.9'°-22.8™

Aburatsubo

—

96.0™

13.8™-15.6™

Kushimoto

21.0'", 13.2'"

21.4'", 12.3'"

21.5"'-23.7'",11.6"^-13.0"^

Hososhima

20.4"'

—

17.8'"-20.3'^

Fukahori

10.4"\ 13.6"'

—

12™

94

K. HONDA, T. TEK ADA, Y. YOSHIDA, AND D. ISITANI.

Thus in these bays the periods of the sea waves are the
same as those observed in other sea waves and also in ordinary
cases. Only one exception is found in the bay of Aburatsubo
for Valparaiso wave the period of which is several times greater
than the period of free oscillation of the bay.

The following tables contain the results of calculation for
the velocity of the sea waves through the Pacific.

Ecuador Wave.

Station

Distance

Mean Dei)tli

1/i/A

Time Interval

Velocity

Hakodate

14,330km.

4.92 km.

220^.

20'> 16"^

i-Jo {^_

Ayukawa

3>

jj

)j

20" 12'"

200

Kusliimoto

15,280

4.81

217

20" 44™

208

Hososliima

15,610

5J

5>

20" 38™

211

Fukahori

16,080

3>

3J

21" 5™

233

Valparaiso Wave.

Station

Distance

Mean Depth

l/(/Ä

Time Interval

Velocity

Hakodate

17,080km.

4.66 km.

214£:

23" 48"

200>:

Ayukawa

3)

33

3 3

23" 17™

204

Aburatsubo

17,280

33

33

()L)h Qui

217

Kusliimoto

17,600

4.58

212

23" 31™

208

From the above tables, it is easily seen that notwithstand-
ing the considerable distance travelled by these sea waves, the
velocities in the two cases fairly coincide with each other. In
comparing velocities of the same wave at different stations, it
wiU be observed that the velocity slightly increase with dis-
tance, though the mean depth of the ocean remains nearly
constant or rather decreases slightly. The exceptionally large

SECONDARY UNDULATIONS OF OCEANIC TIDES.

95

velocity in the case of Aburatsnbo, when sea wave had a con-
siderable long period, is probably due to the effect of the wave
length, on the velocity. The increase of velocity with distance
is also noticed in the case of the sea waves accompanied by the
Krakatoa eruption. This seems to indicate that the earthquake
may excite short waves almost simultaneously with shocks, but
it takes some time to excite long waves of a permanent type
of a considerable period.

In the sea waves above referred to, the observed velocities
nearly coincide witli the values of i^'gh , except for Hakodate
and Ayukawa, in which the difference is considerable.

The sea waves also slightly affected the tide-gauge* at San
Francisco, San Diego and Honolulu (PI. LVHI, Fig. 3-4 ; PI.
LIX, Fig. 1-3). The times of arrival of the waves in the
standard times of these stations and the periods of the waves
are given in the foUowino" table : — ■

Ecudor Waves

Valparaiso Waves

Stations

Beginning

Periods

Beginning

Periods

San Francisco
San Diego
Honolulu

4" 45-^' p.m.
8" 25'" p.m.

16.7'", 33.5"'
24.8'", 26.8'"

7" 34'" a.m.
6*' 25'" a.m.
7" 52'" a.m.

25.3'"
32.2'", 43'"
26.2'"

Thus, if we compare the periods of several sea waves observed
at these American bays, it may also be concluded that the
periods of the different sea waves observed at each bay are
proper to the bay. Honolulu affords the best example ; a simple
wave of the period varying from 23'" to 28'" has always been
found for s( a waves originated near the Pacific coast of America

*) The Ikle-gange recorrls utilized are those furnished by Dr. Tittmann.

96 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

or of Japan. As we have seen, this period nearly coincides
with that of the proper fundamental oscillation of the inlet
leading to Honolulu.

(/) Sea waves accompanying cyclonic storms.

Hitherto we have exclusively considered the sea waves
caused by the earthquake or the submarine eruption.
There are, however, other classes of sea waves accom-
panying a cyclonic storm. Tliese latter may be subdivided
into three kinds, that is, short and long waves and abnormal
rise of sea level.

The violent short waves, the geUro as they are commonly
called, have usually periods of a few minutes, and are super-
posed by waves of still shorter periods with considerable
amplitudes. On the Pacific coast they cause, year after
year, great damages in autumn, and on the Japan Sea coast,
in winter. The waves are always associated with strong
gales ; as tliey approach a shallow shore, they increase in
amplitudes, and break on the shore one after another, leaving
damage behind them. They have probably the same origin
as the ordinary wind waves'"^' always observable on the surface
of the sea.

Examining the records of the tide-gauges, it will be observed
that tliere are many cases, in which general sea-level is ab-
normally raised for many hours, associated with a center of
low pressure existing near by. For example, the record of the
tide-gauge in Aburatsubo (PI. LX, Fig. 1), September 28, 1902,
shows a remarkable upheaval of level in 7' -10'' a.m. during low
water, the maximum heiglit above the ordinary level being about
20 cm. On examining the weather chart on the same day (PI.

*) Wheeler, Tides and Waves, Ch. X, Wind waves.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 97

XCIV), it was found that a remarkalile cyclonic center drew
across the district from the Pacific to the Japan Sea during
these hours. This general upheaval is also accompanied by the
secondary undulation proper to the bay. To take another
example, the mareogram in Takow, Formosa (PI. LX, Fig. 2),
June 27, 1904, shows an abnormal rise of sea level ; at 4'' a.m.,
the sea began to rise rapidly, attained a height of about GO cm.
above the ordinary level after half an hour and tlien gradually
returned to its ordinary level. The weather chart (PI. XCIV)
shows a persistent center of low pressure on the south of
Formosa during preceding days accompanied by lasting eastern
gale in that district, which seems to have attained its height
on the morning of 27tli. This abnormal rise of the level is
probably due to the strong gale.

There are further marked sea waves of the same kind,
which are however not recorded on the tide-gauges. On August
11, 1889, a deep cyclonic center rapidly approached from Kii
sea to the Bay of Mikawa and reached that district with a
high velocity. When tlie center was passing over the bay,
strong gales upheaved the sea level by a few meters for an
interval of about 1 hour. The short waves, superposed on tliis
abnormal rise of the level, broke on the coast, leaving great
catastrophes behind them. On August 28, 1902, a cyclonic
center was threatening the southern coast of Tokaido. At the
same time, another center of low pressure, appearing in the
vicinity of tlie Benin Island, drew towards the Bay of
Sagami and crossed over the central part of Honshiu. When
the center arrived at the coast, strong gales heaped up the
water and flooded the shore of Odawara and its vicinity.
Associated with the upheaval of the level, the short waves

1)8 K. HONDA, T. TER ADA, Y. YOSHIDA, AND D. ISITANI.

rolÜDg into the shore caused great damage to the town/''

There are a few examples, in whicli abnormal rise of sea
level occurred, when neither a cyclone nor an earthquake was
recorded. For example, on March 4, 1001, the mareogram at
Ilososhima (PI. TjX, Fig. 3) shows an upheaval of about 20 cm.
during 7" -10" a.m. In tlie weather cliart on tliis day (PI. XCTY-
XCV), no cyclone is indicated, though a low pressure seems to
have prevailed over the Pacific and gales are recorded in several
other stations in southern Japan. On this occasion, the second-
ary undulation was unusually faint.

As for the remaining kind of sea waves,f namely long
waves witli considerable amplitude accompanying cyclonic storms,
we have many remarkable examples, some of wliich we shall
describe. On the morning of September 28, 1900, a center
of intense cyclonic disturbance passed over the southern coast
of Kii (PI. XCV). Tlie tide-gauge record at Kushimoto (PI.
LXI. Fig. 1), the southernmost promontory of Kii, shows a rise
of general level amounting to about 40 cm. from 3' to 0'' a.m.,
upon which very remarkable long wave with a maximum am-
plitude of 80 cm. were superposed. The period of the most
conspicuous wave is about 10'". It is a remarkable fact that
on this occasion, the long wave with considerable amplitude
lasted only for 3 or 4 hours, during which the general level
was upheaved ; they soon subsided into ordinary small waves
witli tlie rapidly disappearing cyclonic center. A similar case
occurred on August 28, 1890, though without considerable up-
heaval of the general level. To take another example, on the

*) Many examples of the upheaval of sea level observed in Europe and America will
be found in Wheeler's " Tid s and waves," Chapter VIII.
t) Wheeler, " Tides and waves," Chapter XI, p. 1^7-UO.

SECONDARY UNDULATIONS OF OCEANIC TIDES. 99

afternoon of September 28, 1902, a remarkable cyclonic center
crossed over the northern part of Ilonshiii (PI. XCW) and the
tide-gauge at Ayukawa showed remarkable secondary luidulation
with the period of about 7'" (PL LXI, Fig. 3), which lasted for
more than 12 hours. The maximum amplitude recorded was
about 1 m., nearly at the time of arrival of the cyclonic center.
It is to Ije remarked that in these examples the periods of long
waves with remarkable amplitudes are nearly equal to those
peculiar to the bays.

In the above examples, the beginning of the remarkable
undulation is well defined and its connection with the presence
of cyclonic center is very clear. On the other liand, there are
examples in which remarkable secondary undulations lasted for
a very long time during cyclones passing along our land, the
beginning being not (j[uite marked. Generally speaking, the
duration of large secondary undulations seems to depend on the
width as wt^I as the velocity of the cyclonic area.

There are also cases, in wdiicli a remarkable undulation
appeared, when neither a cyclone nor an earthquake was
reported. As we have already remarked, the mareograms of
Nagasaki afford mauy good examples of this sort of undulation.
To take another example, the Kushimoto mareorgram (PL LXII,
Fig. 1) on February 8, 1904, is marked with a considerable
undulation with the periods of 13'", 20"'-2G"\ etc., which lasted
from the morning till the next day, the greatest amplitude being
nearly GO cm. The weather chart indicates no cyclone and no
wind in the neighbourhood of the district, but low pressures
reigned over the northern part of Hokkaido and also over the
Pacific in tlie south of Ilonshiu (PL XCY), while high pressure
prevailed over the continent. The remarkable undulation seems

100 K. HONDA, T. ÏERADA, Y. YOSHIDA, AND D. ISITANI.

to be associated with unstable distribution of pressure, in which
case a sudden local change of pressure may be possible.

It is to be remarked tliat at a station, the period of the
most prominent undulations accompanying a cyclonic storm are
sometimes different for different cases. Thus, in Kushimoto, the
most prominent undulations of the sea wave of February 8,
1904, were of 21" -24'", while the period recorded at the time of
cyclone on September 28, 1900, was about 10"\ Again, during
the cyclone on November 17, 1900, the Ayukawa tide-gauge
(PI. LXII, Fig. 2) showed a remarkable undulation with the
period of 22"\ superposed by waves of shorter period pecuhar
to the bay, while in the cyclone of September 28, 1902, the
proper period of the bay are most pronounced.

Thus far, we have confined our description on the records
obtained on the Pacific coast. Now, the records of tide-gauges
situated on the coast of Japan Sea show somewhat different
aspects, when compared with those of the Pacihc coast. The
former is generally characterized by extremely small tides
usually superposed by conspicuous secondary undulations (PL
LXII, Fig. 3 ; PI. LXIIl, Fig. 1-4), whether the station be on
the open coast or in a bay. During a cyclonic storm, the
amplitude of secondary waves is generally increased and the
undulation lasts for a considerable time. Comparing the records
for different stations widely apart from each other, the remark-
able fact is generally found that periods of conspicuous waves
for different stations and for different occasions are nearly
similar. It is not seldom that a series of waves recorded at
one station on one occasion is quite a facsimile of that obtained
in another station on another occasion. Taking the wave with
the period of 20"\ whicli is very prevalent, its wave length

SECONDARY UNDULATIONS OF OCEANIC TIDES. 101

corresponding to the mean depth of the sea, is calculated to be
about 100 km., \vhJcli is not very small, if compared with the
dimensions of Japan Sea. The distance from Korea Strait to the
northern end of Hokkaido is only ten times this wave length.
Hence if a train of waves be generated in or propagated into
any part of this confined l)asin, it may be propagated impartially
along the entire coast without considerable dissipation and affect
all the tide-gauges on the coast. Such a train of waves may
also undergo repeated reflections and refractions, before it is
quite dissipated away, and cause the variety of records for
different stations.

The similarity of the periods of waves accompanying
cyclonic storms may, in some measure, be observed on the
Pacific coast also. Besides, at different stations, though char-
acterized by the undulations peculiar to their own, the mare-
ograms present not unfrequently a common feature with respect
to the periods of exciting waves ; a fact which suggests the
similarity of waves generated by and propagated from cyclonic
regions. Another interesting fact is that the wave length of
the most prevalent cyclonic waves is generally comparable with
the dimensions of tlie area of the cyclonic depression. Though
we are not yet enabled to solve the problem on the exact basis
of hydrodynamics, it results from all probabilities that a baro-
metric fluctuation at a cyclonic center, acting in an impulsive
manner, may give rise to a train of long waves propagated
from thence, and that their wave lengths are comparable with
the variations at the center. N. Denison has sought to attribute
the secondary undulation to Helmholtz's " Luftwogen," but the
periodic variation of surface pressure is not the only means of
producing a train of waves. A single impulse often snflices to

102 K. HONDA, T. TER AD A, Y. YOSHIDA, AND D. ISITANI.

generate a long train of regular waves.

Before concluding this section, a brief chronological sketclr''
of remarkable sea waves in Japan, recorded in connection with
earthquakes, will be given below : —

1. Nov. 29, 684: A.D. A vast area of laud iu the province of
Tosa was lost under the sea ; sea waves resulted.

2. Nov. 27, 850. Sea waves ou Japan Sea coast of northern Japan.

3. July 18, 869. Great waves on the coast of Sanriku.

4. Aug. 26, 887. Sea waves on the coast of Settsu aud neigh-
bo nriug provinces.

5. May 22, 1240. Sea waves ou the coast of Kamakura iu the
province of Sagami.

6. Aug. 3, 1361. Sea Avaves on the coast of Settsu and Awa ;
gi'eat loss of life aud property. It is recorded that on the coast of Settsu,
the sea has receded for about an hour before the coming in of the wave
crest, aud also that the narrow strait of Naruto was drained dry.

7. Jan. 21, 1408. Sea wave recorded, but doubtful.

8. Sept. 20, 1498. Sea waves on the coasts of Ivii, Ise, Mikawa,
Suruga, Izu, Sagami ; great loss of life.

9. Sept. 21, 1510. Sea waves on the coast of Settsu.

10. (3ct. 10, 1510. Sea waves on the coast of Tôtômi. (Earthquake
not recorded).

11. July 25, 1562. Sea waves on tlie coast of YatsusLiro, Higo ;
three waves counted ; (no recorded of earthquake).

12. Jan. 18, 1586. Great sea waves on the coast of central part
of Honshiu.

13. Sept. 1, 1596. Sea waves on the coast of Bungo ; three waves
counted ; a few square miles of land fell beneath the sea level.

14. Jan. 31, 1605. Sea waves on the coast of Satsuma, Tosa, Kii,
Ise, Tôtômi, Izu, Sagami, Awa, Ka/usa, Shimôsa, Hachijô-jiraa. Drain-

*) The chief material were taken from the Eeport of the Earthquake Investigation
Committee, No. 46.

SECONDARY ÜNDI^LATIONS OF OCEANIC TIDES. 103

iug of tlie sea before the arrival of high water is recorded on the coast
of Awa, Kaznsa, Shimosa, Totomi, Ise ; in the last province the sea had
receded for about two hours before the arrival of the wave crest. Coasts
of Seto-naikai and the Bay of Osaka were safe.

15. Dec. 2, IGll. Sea waves on the coast of Sanriku and Hokkaido.

10. Nov. 26, 1614, Sea waves on the coast of Echigo.

17, March 1, 1633, Sea waves on the coast of Atami in Izu.

18, Oct, 30, 1662, Sea waves on the coast of Hiuga and Ôsumi ;
several square miles of laud lost under sea,

19, April 13, 1677. Sea waves on the southern coast of Eikuchiu ;
at Mijako, three large waves counted in the interval ca. 10'' p.m. -2'' a.m.

20, Dec. 30, 1703, Sea waves on the coast of Sagami, Awa, and
Kazusa ; four waves counted,

21, Oct. 28, 1707, Remarkable great sea waves devastated the
Pacific coasts of Kiushiu, Sliikoku, and also of Honshiu up to Izu to the
north. In Susaki, Tosa, eleven or twelve waves were counted in the
interval about 3'' p.m. 4'' a.m. ; at Ivcclii, the w^ave reached so far into
the land as several km.; at the same district, the third wave was the
highest. Coasts of the Bay of Osaka were also damaged by waves.

22, Aug. 29, 1769. Sea wave in Satsuma,

23, Feb, 10, 1792. Sea wave at Shimabara in Hizen, accompanj--
iug the eruption of Mt. Unsen""' ; it is recorded that the high tide
occurred seven or eight times a day. On this occasion a portion of the
mountain was split up and fell into the sea forming a number of small
isles. Inundated area, however, was confined to the coast of the Sea of
Tsukushi.

24, June 29, 1799. Sea wave at Miyakoshiura, Kaga.

25, July 10, 1804, Sea waves at Ivisakata ; a portion of the sea
upheaved into land,

26, Dec. 12, 1833, Ssa wave in Sado : draining of the sea was
observed before the arrival of the high water,

*) F. Omori, Nota 'on the eniption of the Unsen-daké in the 4th year of Kansei (1792)
Proc. Tokyo, Math.-Phys. Soc. 4, p. 32, 1907.

104 K. HONDA, T. TERADA, Y. YOSHIDA, AND D. ISITANI.

27. Fob. 9, 1834. Sea wave on the coast of Tsliikari ; three -vyaves
coTintecI.

28. 1835. Sea wave at Hanasaki.

29. April 25, 1843. Sea waves on the coasts of Oshima, Knshiro
and Nemnro ; two large waves conuted in ß'^ a.m. -10'' a.m.

30. Dec. 23 and 24, 1854 (Ansei). Notoiions sea waves on the
Pacific coast.

31. Aug. 23, 1856. Sea waves occurred on the coast of Oshima
and Ibnri in Hokkaido.

32. June 4, 1893. Sea waves in Kurile Islands (Chishima) ; at
Shibetori periods of 5 waves estimated were 20™-30"\

33. March 22, 1894. Sea waves on the coast of Nemuro ; periods
of more than ten waves were estimated to have been 20"'-30"\

34. June 15, 189(). Great sea waves on the entire coast of Sanriku.

35. Aug. 5, 1897. Sea waves on the coasts of Sanriku.

§ 9. OSCILLATION OF LARGE BAYS AND
ANOMALY OF TIDES.

Thus far, wc have generally treated of secondary undula-
tions, the periods of which are much shorter than those of the
principal tidal components, viz. the diurnal and semidiurnal. We
will now proceed to consider those undulations of much longer
periods, which commonly exist in the tides near the end of
long inlets or estuaries.

Exaggeration of oceanic tides which takes places in shallow
seas and in estuaries, has often been explained merely by the
law of amplitude given by Green.* Airyf attenipted to explain
anomalies of tide observed in some rivers by the consideration
that for a wave of fmite amplitude different parts of the wave

*) Green, Camb. Trans. 6, 1837; Math. Papers, p. 225.
t) Airy, Tide and waves, Art. 198

SECONDARY UNDULA-TIONS OF OCEANIC TIDES; 105

profile travel with different velocities ; but his argument has
been proved unsastainable.'" Again, inferior tidal components,
known as compound tides or overtides, which become conspicuous
only in shallow basins, have been explained by the analogy of
combination tones in acoustics. f It seems to us, however,
the theory alone is not sufficient to account for the facts that
in some gulfs or bays the amplitudes of superior tides are often
comparable with those of the proper tidal components and also
that most pronounced compound tides are different for different
bays or gulfs. FerrelJ attempted to explain some irregularities
of oceanic tides by considering oceans as making stationary
oscillation as in the case of seiches in lake. Recently E. A.
Harris,'^ '=' according to a similar view, constructed a cotidal
chart of the world. In his theory, water on the globe is divided
into several distinct portions, each of which has the proper period
of its own stationary oscillation. This point have been subjected
to criticism, by Gr. H. Darwin. He applied his theory also to
the explanation of tidal plienomena in many bays and straits,
the standing oscillations of which are forced by tidal waves
incident on their mouths. He considered, however, exclusively
the forced oscillation with diurnal and the semidiurnal periods,
and has not considered those oscillations peculiar to each bay.

Now according to our view, any bay or gulf, either small
or large, may be considered as a resonator which oscillates
with its own period, if it be excited by waves in the external
sea having the synclironizing component. If the proper period
of the bay happens to coincide nearly with one of the tidal

*) McCowen, Phil. Mag. (5), 35, 1892.

t) W. Thomson, Proc. Roy. Soc. 7. G. H. D.irwio, Brit. Ass. Rep. 188.

I) Ferrel, Tidal Researches, Rep. Coast and Geodetic Survey, Washington, 1874.

**) R. A. Harris, Manual of Tides.

106 K. HONDA, T. TER ADA, Y. YOSHIDA AND D. ISITANI.

components, that component will become more or less prominent,
according to the degree of proximity of tlie proper and the
exciting period. Again, it is possible that astronomical com-
ponents of superior orders, compound tides resulting from
the combination of several astronomical components or many
indefinite components arising from meteorological causes, may
sometimes become prominent by the resonance of bay water,
though almost insensibly small in open sea. Moreover, the case
may occur, in which a solitary wave of wide extent caused by
some disturbances either meteorological or geotectonic, excites
the oscillation of a long period proper to a bay. These oscillations
in a bay will more or less deform the tidal curve and cause an
anomaly of tides peculiar to that bay. According to this view,
the proper periods as given by our formula were calculated for
different bays or gulfs, which are notorious for abnormal range
of tide, and also those for which some remarkable irregularities
of tide was observed in the mareograms given in the Report of
the Krakatoa eruption often cited.

The results of calculations, together with their bearings
upon the tidal irregularities for a number of bays, will be given
below.

(a) Bay of Fundy, Canada. Near the end of this bay,
spring tides range 15m., while near its entrance the rise is only
2.5 m. to 3.5 m. For the calculation, the mouth line was taken
from Cape Cod to Cape Sable ; and the end of the Bay was taken
at Port Greville. Then /=460km., h=Ul m.; hence 7^=13.0".
If the mouth line be taken l^etween Yarmouth and Machias, the
calculated period is 11. ß''. In any case, the proper period of this
bay would be very near 12 hours. The abnormal high tide may
then partly be explained by the coincidence of the proper period

SECONDAKY UNDULATIONS OF OCE.\NIC TIDES. 107

with one of the semidmrnal tides, though the tidal phase is
slightly retarded toward the end of the Bay and therefore the phe-
nomenon can not be wholly attributed to the standing oscillation.

(&) Bay of Bengal. Near the mouth of this bay, the tidal
range is small, being less than half a meter at the southern
coast of Ceylon, while in the bay, the range is 1-2.7 m., in-
creasing abruptly near the end of the Bay. Since the tidal
phase is nearly the same for the great part of the bay, principal
part of the tide in the Bay is probably due to the standing oscil-
lation of it. Taking the mouth line from the eastern coast
of Ceylon to the northern end of Sumatra, and the end of the
Bay at Akyab in Burma, we obtain /= 1500 km. and A == 1950 m.,
which gives 2'=12.0'\ coinciding with the period of semidiurnal
solar tide.

(c) Madura Strait, Java. Mareograms of Ujong Sourabaya
and Karang Kleta reproduced in the Krakatoa Eeport of the
British Association show very marked irregularities of tide in
the narrow strait of Sourabaya, which connects the end of wide
Strait of Madura with the Java Sea. Since the width of the
Strait of Sourabaya is extremely small in comparison with that
of the Madura Strait, we may consider the latter strait as a
rectangular bay, having its end inside the former strait. The
effect of narrow opening at the end of a bay is only to shghtly
reduce the effective length of the bay, or in other words to
shorten the period of oscillation by a small amount. The length
of the Madura Strait, considered as a bay is about 1(30 km.
As for the mean depth of the basin, no chart of a sufficient
scale is at hand, so that we may only roughly estimate it from
the data collected from different maps'-' available. In any case,

*) Maps of Encyclopedia Britanica, Bergbaus' Physikal. Atlas, etc.

108 K. HONDA, T. ÏEILIDA, Y. YOSHIDA AND D. I«ITANI.

however, the mean depth can not differ mueli from 30 m. The
period calculated from these data is 8.8''. In order to see, if
any long wave corresponding to this result of calculation exists
actually in record, the mareogram of Karang Kleta was analysed
by means of the tide-rectifier. Eliminating tlie great parts of
diurnal and semidiurnal components, the remaining curve reveals
to us an evident trace of waves with the mean period of 8.0''
(PI. LXIV, Fig. 1).

The exciting cause of this wave is probably the compound
tide usually denoted by MK, the period of winch is about 8.2'',
nearly coinciding with the proper period of the Madura Strait.
(d) Port Adelaide, Australia. A mareogram (PI. LII, Fig.
3) of this Port given in the Krakatoa Peport shows remarkable
change of diurnal inequality on successive days. On eliminating
the principal parts of diurnal tides, the resulting curve shows
apparent beats of semidiurnal tides (PI. LXIA'', Fig 2). The
period of the characteristic component which forms beats with
the usual semidiurnal tides, is about 10.9'', as estimated from
the rectified curve. It is probably to be attributed to the
standing oscillation of the St. Vincent Gulf. Taking the mouth
line from Trowbridge Point to Cape Jevis, and the end of the
Gulf at Wakefield, w^e have /=140km. The estimated mean
depth is 21.5 m. Hence 7 = 10.8'', which coincides very well
with the observed period.

(e) Port Phillip, Austraha. Mareogram (PI. LII, Fig. 4)
of Williamstown given in the above quoted Eeport, shows some
irregularities of tide which suggests the existence of very long-
undulation peculiar to the bay. The curve was rectified (PI.
LXIV, Fig. 3) and a period of 8.3'', was detected. Xow the
period of seiches in this nearly enclosed basin can by no means

SECOND.\EY UNDULATIONS OF OCEANIC TIDES.

109

become so long as 8'', unless the mean depth of the Port be
less than one meter. This period is probably due to the un-
dulation of the whole basin with its narrow neck communicating
with open sea. For the calculation of the period corresponding
to tliis mode, the necessary data were estimated from the chart
given in Harris' Report: >S:=13.7 x 10' m'., /=2.95km., 5 = 4.08
km., 7^:== 18.4 m. and ;.= 200km. The period calculated from
these data is 8.39" which almost coincides with the observed
period.

Beside the above enumerated examples, there are many
bays or straits, the forms of which seem favourable for their
own standing oscillation of long periods, and in which the
ranges of tides are comparatively large. The periods of these
oscillations w^ere estimated as follows : —

Bay or Strait.

T in Hours

Adriatic Sea.

15

Mozambique Cliaiiuel.

7

Bristol Bay, Alaska.

15 and 28

Hecate Strait, British Cohimbia.

7

Hudson Strait, Canada.

11

Bristol Channel, England.

5

Gulf of St. Malo, France.

7

In conclusion, we wish to express our best thanks to Prof.
H. Nagaoka under whose supervision the entire work has been
carried out and who gave us much useful instruction throughout
the course of our investigations. Equal thanks are due to Prof.

110 K. HONDA, T. TEBADA, Y. YOÖHIDA ANL> i>. ISITANJ.

F. Omori who favoured lis with valuable instruction and with
the records of numerous earthquake sea waves. We also wish
to express our thanks to Assist. Prof. A. Imamura, and to Mr.
M. Sugiyama of the Military Staff, who kindly placed valuable
mareograms at our disposal. Lastly, our cordial thanks are
due to Messrs. S. Iwamoto, N. Watanabe, T. Hirata, Y. Inouye
and T. Fukuda who have been zealous cooperators in the course
of our observations.

NAME LIST OF STATIONS,

Aburatsu

Abiiratsubo

Adasliika

Akasliiseto

Akkeshi

Araai

Aodashi

Aoraori

Ariake

Atami

Awa (Tosa)

Avnkawa

Bisanseto
Bokkiriso

Choshi

B

D

E

a

H

'à^.

mmmß

m=f

M^%

Etclnujima

F

Fukaliori

Fusliiki

Futami (Sado)

Futarai (Ogasawarajima) HM^

G

Hakodate

Hamanaka

Hanasaki

Heda

Heida

Hesliinia

Hiuoura

Hiroshima

Hososliima

Hosoura

Ibusuki

Ikeda

Imazn

Inuboye

Isegahama

Isenoumi

Iwasaki

Iwaya

Kagoshima

Kajiki

Karaagori

Kamaishi

Kamagasaki

Kameura

J

K

M'a

^^
ßm

ßei
t /fît

mm

m^

112

NAME LIST OF STATIONS.

Kamezaki

Karaiiso

Kanaiwa

Kanegafnchi

Karatsn

Kasliiwazaki

Katsuura

Kelung

Iviritapp

Kisliiwada

Koisliiliama

Kojiroliama

Kokabe

Koupaku

Kiikiura

Kiire

Kushimoto

Maisaka

Mera-koura

Mikawa wan

Misaki

Miyako

Miyazu

Moroiso

Mororan

Nagasaki

Naisliobama

Naootsu

Naruto

Nemiiro

M

N

mm

n ^ ^

Niigata
Niiyama
Nomi
Nonomae

Odsuclii

Ofunato

Ogeiira

Oishi

Okirai

Okuchi

Omaezaki

Omiuato

Onsliantin

Osaka

Otaui

Otaru

Piisan

O

P
R

H^

Ryôislii

@^

Eyôri

'^m

mm
mm

Sagami
Sakurajima

Same

•Mii^

Sasima

^mm

Senzai

Üiltt

Sliido

m?"]

Shimizu (Surnga)

^m

SMmizn (Tosa)

ffiü

TClllit

Am

Ulli

MC

m^K

NAME LIST OF STATIONS.

113

Shimoda

Shimonoseki

Shiogama

Sliionomisaki

Shioyasumi

Shiraiwa

Sliishimi

Sliitama

Shizuura

Siinagozaki

Suruga wau

Susaki

T

Tacliimachizaki

Tago

Takonoiira

Takow

Tei

Tateyama

Toba

Tokyo

Tomikawa

Tonoura

Ta

Tsuruga

y ^Wi

mm
mfà

Ucliinourai
Ujina

Umegahama
Uwajima

^PhI

mm

Yamasakibana

#^^it

Yawataliama

mmm

Yebisu

mm

Yebisujima

Yedajima

Yonozii

Ä#w

Yosliiliama

ffl-=f

Yotsn

m^m

Ynra

tTfpJ

Yuraseto

^,fê

ît\u

BM

Wajima

iîiA^

Wasliinosu

'M)\\

Weihaiwei

s^\^m

u

Y

W

$m

t^ ta

Amm

^\

MAREOGRAMS.

PL. I-LXIV.

EXPLANATIONS.

Horizontal scale below the (liagrams gives the time, generally
in hours, if not otherwise stated. In a number of cases, actual
hours of day are shown, midnight and noon being inscribed. The
length of one hour in records of Kelvin's tide-gauge is about twice
that of our instrument.

Vertical scale gives the height of level in cm.

Jour. Sei Coll. Vol. A'XII/'. PI. I.

Jour Sei Coll. Vol XXIV. PI. II.

Jour. Sei Coll. Vol. X/iy PI- III.

Jour. Sei. Coll. Vol /XIV. PI. /K

AOM 0 R I

I WA S AK

riff, .y. Fei,. :.'. I. IOC

•■AA/Vv\,A^vvAA/WA7v\AAAAAv/xA^AAA-v'WvvvAy^^

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KAS H I WAZAK I

/•yv/. / Ally. /;■ /■;■. /:k

Fi,,. U.Au,,.JJ /J.

.r^"

,.^^^-

Jour. Sei. Coll Vol XXIi^. PI. V.

^'^^^aT'--''''-'''-'^^^^'^^

F U S H I Kl

/■/</. .T. /K'f. J.'-ld. /uni:.

W A J IMA

/>>..7,/',./,. / ;-.

Jour. Sei. Co/I. I^o/. M/K PI. VI.

KAN A I W A

Fcff. I. Aux/. ^s-~'e. liW-l.

TS U RUG A

AA/'

vVWlrW'

TO N OURA

Piy.l, Sept. ua '..'S. looo.

N\

,^Ar^^'*A/■

Fùf. 5 , Jan . 7. I'^o.l.

'''^J^AYuVWl^A,MM^^wR\MA^VM^

^

Jour. Sei. Coll. Vol. //IK PI. VII.

M I Y A K 0

R Y 0 I S H I

fL.1/. A ./>'<V-. -tf-J?/, Ji)0/

Jour. Sei. Coll. Vol. yf-r/K PI. I^lll.

Jmr. Sei Co/I. Vol XXIV. PI. IX.

KO N P A K U

Jour. Sei. Coll. Vol. XXIV. PI. X.

0 F U N A T 0

r,-ff.J.Aug.S-9, 100-t.

TAKONOU RA

H 0 S 0 U RA

f^i0.4,Au^. 9~JO, 1904

4>^'H"'p

Jour. Sei. Coll. Vol. /Xli^. PI. XI.

'\>v^yV(f|W/lAt

h/^'

''^^^"^^'^'^^Ua^.

Jour. Sei. Coll. i^ol. /X/y. PI. XII.

ETC H 1 UZI MA . TOKYO

Fi. I. I. Xnr. :si>- /Kc.l. j:i<i-J.

Jour. Sc/. Co//. Vo/. /X/K P/.XIII.

KANEGAFUCHI. TOKYO.

t'iii . I . All,/. : I ::o, iiJUG

Jll_

Jour. Sa- Co«. Vol. XXI V. PI. XI K

"> .Voo,

Jour. Sei. Co/I. kp/. XXIV. PI. xy.

Joar. Sei. Coll. \/ol. X/IK PI. XVI.

Jùur. Sei. Co/I. Vo/.XXIV. PI. XVII.

S H I M 0 DA

/v>. /. .r.a„, .y-s, /ane

J^tff. 'Z. y/fifi . 5-6 .

^^J\J^

Jour^ Sei. Co/I. Vol. /XIK PI. XVIII.

S H I Z U U R A

/■',(,.J.S,-,,r..f-.> . y Vit -I.

Jour. Sei. Coll. Vol. XXI y. PI. XIX.

jcur. Sei. Coll. \^oi. xxiK PI. n.

¥

/v.»

SH 10 NOM I SAKI

Fig.i. .\u,,.i:-:,iaoa.

Jour. Sei. Coll. Vol. XXI i'. PI. XXI.

J

Jour. Sei. Coll. Vol. XXIK PI. JfÀII.

BAY OF OSAKA

A/ir/./-/ . J,Uf>2

Joar. $ci: Coll Vol JfXIV. PI. /'/Ill

Jour Sc/- Coll. Vol. xxiK PI. xxiy.

Jour. Sei Coll. \^ol .W/K PI. /KTK

Jour. Sei. Coll. i/bl. XXIK PI. XaVI.

Jour. Sei. Coll. Vol. XXIV. PI. XXVll.

Jour. Sei. Coll. M XXIi'. PI. J(XVIII.

'*'^«*^>^VV^^'^,WVVVVVVV\VV^AA^A^^ .^AAA^wV^^A.-^^

.kH'^'^

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:to 10

20 -'M 'o •'"

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Jour. Sei -Coll. Vo/. X/IK PI. XXIX.

\

Jour Sei. Coll. l/ol. Jfjfll^. PI. XXX.

J

Jour. Sei. Co/I. \/ol. XXIK PI. XXri.

J

Jour. Sei. Colt. Vol. xxiy. PI. xjaii.

KAMEU RA

J

Jour. Sei. Coll. \^ol //IK PI. /X/tlt.

Jour. Sei. Coll. Vol. XXIi^. PI XXXIIf.

YAM ASAKI BAN A

F;g..l.Si:pl.2'3, J.904.

Jour. Sei Coll. \^oi //II/. PI. xay.

Alla. ■4I.IHOJ.

Aug. I7.J.903.

VAMAS A K I BAN A

Fig. 3 { ContirMcti. I

YAMAS A K I BAN A

Joar. Sc/. Coll. Vol /XIV. PI. XXXVI.

Au^.j.l

Jour. Sei Coll. Vol. XXIK PI. J!XXVII.

.J

1 y

Jmr. Sei. Coll. Vol XXIK PI. XX/VIII.

SHIRAIWA , SUSAKI

/Vy- A ^.pi . 7, i;t(t I .

Jour. Sei. Co//, /o/. /tX/K P/. JK//r.

Jour. Sc I. Coll. Vol. XXIi^. PI. XL.

Jour. Sei. Coll. Vol. xxiy. PI. XU.

"n

Far f If/. 3, 41

Jour- Sei. Coll. Vol /XIV. PI. XLII.

I Tenu, .iCiUt for/-/gJ. 1.1

Jour. Sei. Coll. Vol XXIK PI. mil.

Jour. Sei. Co//. Ko/. ^r/K P/. XLiy.

NAGASAK I

Jour. Sei. Co/r Vol. /XIV. PI. XLV.

Jour- Sei. Coll. Vol. X/l\/. PI. XLVI

Jour. Sei. Coll. M./Xiy. PI. XLVII.

FUTAMI. OGASAWARAJIMA

W^"""""^,

F,,,.i. ./,„, .,v ,0. /-^o:.

i/^MA^Yl^^

\

Jo un S ci. Coll. \/ol. XXI K PI. XL II

KE LUN G

FI,/. /, /;■!.. y :'. j:io<:.

Pi//. ','. Aiijy. /H-Itl.

TAK 0 W

F,-<,..!. /;/. /. /■•/.

fXr,. ■/, . l„f,. /tt, /.'toi;.

Jour. Sei. Coll. Vol. /XIV, PI. XUX.

SEA WAVES FROM JAPAN

SEA WAVES FROM IQUIQUE.

SEA WAVES FROM ECUADOR.

Joun Soi. Co//. Ko/. Xf/K P/. I.

Jour. Sei. Coll. \^ol /Xl\/. PI.LI.

SEA WAVES FROM K R A K A T O A.

PORT BLAIR

N EGA PATAM

Fiff. 2 .

MADRAS

VI 2AGA PATAM

/>.-/■ / .

f\.r\

SEA WAVES FROM KRAKATOA (Continued;

Jour. Sc/. Coll. fol. XXH^. PI. III.

^,^ r-K'

yjY^ftjvV"

WILLIAMSTOWN
PORT PHILLIP

SEA WAVES FROM KRAKATOA (Continued;
LYTTELTON HARBOUR. NEW ZEALAND

FÙ/.J -i,^. ■ia-Sef>t.. 1. JS8S.

Jour. Sei. Co//, vo/. xx/K p/. un.

HONOLULU

Fug. 2, Aug. l'i:-3.9. 1883 .

SAUCELITO, SAN FRANCISCO

Fig..3.Aiut. i'7-^0, 1883.

.fJ\fV\W^^

.-r-^\.

Jnr. Sei. Ml m //IK PI. UK

SEA WAVES OF SANRIKU

Jo(ir. Sei. Coll. Vol. XXI 1^. PI. L Y.

'S>'E.K WAVE S OF SANRIKU (Continued)

CHÖ SH 1

Fiff.Z. June 15-ll>-'f<äe.

SEA WAVES FROM ECUADOR

Jo„r. Sei. Coll. Vol. XXIK PI. LVI.

-A

'^

HAKODATE

I'ia.l. Feh. ' -:', '!><><'

^ _- / ■^, A

AYUKAWA

HOSOSHIMA

r,,i. /. /•;■/.. /

Jour. Sei. Coll. Vol. XXI K PI. I VII.

SEA WAVES FROM ECUADOR AND VALPARAISO,

Jour. Sc! Coll. ^ol. /Xiy. PI. Lvm.

SEA WAVES FROM VA LP A R A I S O A N D ECUADOR

M Soon

SEA WAVES FROM VALPARAISO.

Jour. Sei. Coll. /ol. A'XIK Fl. LIX.

SAN FRANCISCO

/•Vy. /. .il/;/. /7 m, jooi;.

HONOLULU

.3. .luff. 77 J8.

Jour. Sel. Coll. Vol. X/iy. PI. IX.

Jour. Sei. Co//. \/o/ /X/y. P/. LXI,

KUSHIMOTO

Jour Sei. Coll. Vol. /Xiy. PI. LXil.

A YUKAWA

FCd.S. Vov. /7.JHOO,
Cvr/nnlc .irorm.

0 T A R U

{7^.;^^.A^^VV^V\/^^/^

Jour. Sei. Coll. Vol. XXIV PI. LXIII

I WASAK I
Flu./. Xf-./r. /HO

WAJ I M A

Jour Sal Coll- Vcl. XXiy. PI. Ulf.

KARAN G
^■■ù,.j. A,,,,,. ;

KLETA

(.■ uv.jiisrt.

Au^.-i,ifl,

r^

Auff. 21 tl,

Auff.SSeJi

^ Aic^^ßtJi

/V.

.if,,/

Moon
Aug S»M

Mui.

.Voon Nul.

PORT ADE LAI DE
J-i.,.?..iMi,. IS ao.jsan.

Atni. S3 t/i

-

Atig 30 i A

Jfid. .Voon.

The principal tidal components are
\ eliminated in these diagrams by means
\ of the rectifier (see p. 107-109).

Jfu.

fful.

^»l.«

^--/--v.

WILLIAMSTOWN.PORT PHILLIP
J'i^.o. Au.,,. ,?s!ii.yma.

>.w^

^-s^^-^^^^-^-

-^^ ~

A,,,, -t

ail,

■<-^1 -■"!■

.■tit.!f.3llA

MAPS.

PL. LXV-LXXXVI.

EXPLANATIONS.

Stations actuiilly ubservetl ;ire marked with o, wLiile those not
yet obserYed are shown by x .

Soundings are given generally in meters, it not otherwise stated.
Contour lines are given by

Median lines and mouth lines are shown by — — .

Orientation of eaeh map is shown by an arrow which points
to north.

GENERAL MAP

Jur. Sel Coll. Vol MIK PI. LXV.

S T A T I 0 N S .

.V

A

/?ir

^,...fe-Ä^j.;'-;

f^v"-'

jf2^^f-'\

.V

r^

0

J '''

Jour. Sei. Co//. Vo/. XX/y, P/. LXVI.

Top. 1.

Otaru

1 : 69,000

Top. 2.

Nefmiro

1 : 65,300

^■:)\

I ' Gyy

'?,

Top. 3.

Hanasaki

1 : 200.000

\--JL-^

> rJ

V / ■ !^

•U / ^ ;

Top. 4.

Bokkiriso

1 : 56,300

Top. 5. . k

Hamanaka

1 : 200.000

Top. 7.

Mororan

1 : 200,000

1:l -■

//(ir/>,/n'/-A(/ x\

-,V/

\,_,

c:

Jour. Sei. Co//. Vo/. ja/K P/. LXV//.

Top. 6.

Akke.<<hi

1 : 214.000

\

\

^\

i 1 ; /

\

i^J/)

"\

^■-

J--A •

.-^'

-->','

''

Top. 8.

Hakodate

1 : 214,000

/(//■/uf/ttTf {■///■:///,■/'

Jour. Sei. Co/I. Vol XXIK PL LXVIII.

Top. 9.

Aomori

1 : 377.000

0 Omuu/ti>

Jour. Sc/. Co//. Vo/. XX/y, PL LXIX.

Top. U.

M'bjazu

1 : 200,000

Top. 10.

Yebisu

1 : 200,000

Top. 12.

Fushiki

1 : 2,000,000

Top. 11.

Futami

1 : 183,000

Jour. Sei. Co//. Vo/. XX /K P/. LXX.

Top. 1.3.

TsuriKja

7 : 21)0.000

^:À \

Top. 7.5.

Tonoura

1 : 19.500

Top. W.

Mlyako

l : 200 000

7 \ /fra^a.

Jour. Sei. Co//, /o/. XX/K P/. LXXI.

)■ /

0,/.v,

'<'/,/ Of --

^y.. n

~"'^->

" /' "-' j /

T„y>. n.

Odsuchi

1 : 200,000

y,\

/^l V0l,i/li

/iurii</,/,,.s„/,;'~:> ;

//,■/./„ Jk r^^.n

7- A ^

/ y Ryôishi

'^J i \ Top. 19.

v/^' ^Kamaishi

Aot/it.^'/i,

/l "///tf/lrt/tlf/- o)

Top. 20.

Kojiiohama

Top. 25.

Niiyama

1 : 71,300

-' li Varna o/

Top. 26.

Ayukawa

oy.y/,/ <

-/ \

Ao/i^itt/ci

^ ^--^ ^ Top. 21.

J -.■'/u7,„„,a o) --.ß^ -"'Yoshihama

Äo/t4//>t

O /,■/'/•(// rv —

Top. 22.

Okirai

/U'/.yAy-A,.

Top. 27.

Katsuura

1 : 36,400

Ä.ni,<<7i.jfr'a^- X

\ \

-rL^ ^>7 '

Top. 23.

Ryori

^\/'-''X'

Jour. Sei. Co//. Vo/. XX/y, P/. LXXI/.

Toj). 29.

Bay of Tokyo

1 : 47D.OO0

'V /'/ f/

Top. 24.

A

Ofunato

1 : 120.000

\ /

- / \ [ K

Of/tri/Uo

'^o/-oi.s-o

■■■r

) -T. ^ *

^ ^-i '^.

..ox;

) /\,^ c

' \

\

jOOV-- '

-^jV. 1 \

/' ■ \ ,'

\

/ ^' \ \

30" \ 7

_,y,' y^-

Top. 2S.

Tateyama

7W/,,^;

Jour. Sei. Co//. Vo/. XX/y. P/ LXXIII.

Top. 30.

Moroiso

1 : 12,100

Yai-sfirjJiamxt

.^^V/'/ffaK.yuhiy

^n;v. (

; t

') /

^p-'-^J-

^).-.

yp''

S' V.U;,L.„

^ ^^-

Top. 31.

Sagami Sea

1 : 461,000

---4

M /

i ^\^
i ^\

'^ /Öö

'/O.y/o/'oiti'Jh

Jour. Sei. Co//. Vo/. XX/y. P/. LXXIV.

Top. 32.

Shlmoda

1 : 68,400

Top. 33.

Merci koura

1 : 200.000

Top. 34.

Tago

1 : 13,000

Ä07.,-,,

\ /

Jour. Sei. Co//. Vo/ XX/K P/. LXXK

Top. 35.

Heda

1 : 43.S00

Top. 36.

^^^V ^f Siiruga

1 : 615,000

ÖOO 400 2oo

Top. 37.

Shlmisu

1 : 154,000

Top. 38.

Ise Sea and Bay of Mlkaioa

1 : 200.000

SAr,,y

Jour. Sei. Co//. Vo/. XX/y, P/. LXXV/.

Top. 39.

Toba

1 : 109,0<H}

Top. 40.

Kukiura

1 : .54,600

Top. 41.

Kusliimoto

1 : 97,600

.^^. '^' u

'Jh'ns/u7j,„/f,

Top. 42.

-^ Adashika

1 : 72,800

'■v^

r^

vJ,/^/,.^.V

i.i"

3 'i/tùir/o//t/j,//./

Jour. Sei. Co/I. Vo/. XX/y, PL LXXVII.

Top. 43.

Bay of Osaka

1 : 550,000

/MUtZU^C

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Top 44.

Hiroshima

1 : 302.000

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Top. 46.

Shimizu

1 : 54,600

Top. 51.

Amai

1 : 70,200

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Top. 49.

Shitama

Top. 47.

Okuchi

1 : 70,000

Top. 48.

Uwajima

1 : 308,000

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Top. 52.

Ikeda

7 .• 141,000

Top. 53.

Uchinonmi

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Shido

1 : 141,000

Top. 5(1

Hoso^hima

1 : 30,400

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Top. 55.

Äriake

1 : 341,000

Top. 58.

Aburatsu

1 : 54,600

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Kagoahima

1 : 458,000

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Karatsu

1 : 328,000

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Shishimi

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Top. 60.

Nagasaki

1 : 72,800

F„l,a/<ori

Top. 64.

Futami {Chichißma)

1 : 75,000

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Top. 63.

Sasuna

1 : 22,600

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Kelung

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Onshantin

1 : 67,800

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Pusan

1 : 91,000

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Top. 68.

Weihaiwei

1 : 109,000

Top. 69.

Sunda Strait

1 : 4,450,000

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Top. 70.

San Francisco

1 : 4U,000

PHOTOGRAPHS OF MODELS.

PL. LXXXVll-XClJ.

PI; LXXXVÏI.

Tormka^va^ 1^

X v^MSSi^ÀSW»^

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X^'MSS^^S^^

^.'«èi^

PI. LXXXVII.

Pilot. 1, Bay of Hakodate.

Phot. 2, Bay of Hnko-lato.

PL

Anmnri'

Phut. 3, Bay of Aoniui

F iff. 3

Bav of MoroiV>.
Fug. 6.

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PI. LXXXVIII

Phot. 3, Bay of Aomori.

Phot. 5, Bjiv of Moroiso.

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Phot. 4, Bay of Aomori.

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t. ■ 'îay of Siisaki.

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r::." of !^i:~Mi.r

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PI. LXXX»?

Phot. C), Bay of Susaki

Phot. 7, Bay of Susaki.

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PI. xc.

i'iiot. 8, Bay of flusoslnrna.

'^ 1?::,- of rr.sosL

J^i^.3.

PI. xc.

Phot. 8. Bay of Iîososliim<a.

Phot. 9. Biiy of Hososhima.

XCI.

Noffa^fo/iZy

Fig. JO

ay of Nagasaki.

Fi^. 11.

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PI. XCI.

Phot. 10. Bay of Nagasaki.

Phot. 11. Bay of Nagasaki.

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PI. CXII.

Phot. 12. Bay of San Francisco.

WEATHER CHARTS.

PL. XCIII-XCV.

EXPLANATIONS.

The charts were drawn according to the daily weather charts
issued hy the Central Meteorological Observatory, TokyH. Stations
referred to in the text are marked with x .

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