-
THE ROMAN CE OF SCIEN CE .
TIME AND TIDE ,3 110m m “: of the$0011.
BEING TWO LECTURES DELIVEREDIN THE THEATRE OF THE LONDON IN STI 'I UTION ,
ON THE AFTERNOONS OF NOVEMBER 19AND 26, 1888 .BY
S IR IROBERT S . BALL, LL .D. ,AUTHOR OF STARLANDLOWNDEAN PROFESSOR OF"ASTRON OMY AN D G EOMETRY IN THE l'N lVERQ lTY
OF CAMBRIDGE .
SE COND EDI T/01V, RE VI S ED .
PUBL ISHED UNDE R THE D I R EC TI ON OF THE COMM IT TE E OFGEN ERAL L I TERATUR E A\ D EDUCAT I ON APPO I NTED
BY THE SOC ILTY FOR P ROMOT I NG CHR I ST IANKNOWI EDGE .
L O N D O N
SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE .N E W Y o s E J . B . YOUNG CO.
1892.
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!We zi mnbrrs of the fianbmr gustitutionI DEDICATE
THIS LITTLE BOOK.
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PREFACE .HAV ING been ho n o u red o n ce a g a in with a
request tha t I sho u ld lecture before the London
In sti tut ion,I chose for my subj ect the Theo ry of
Tida l Evolution . The kin d reception which these
lectures received has led to thei r publication i n
the present vol ume . I have taken the opportun ity
to supplemen t the lectures as actual ly del ivered
by the i n sert ion of some add itional matter. I am
indebted to my frien ds M r . Close and M r . Ram
baut for thei r kind n ess in read in g the proofs .
ROBERT S . BALL.
Ob ser u a lo ry, Co . DUBL IN ,Apr il 26, 1889.
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PREFACE TO THE SECOND EDITION .IN the presen t E d it ion I have taken the
opportun i ty of mak i n g sundry verbal correct ions .
I may also remark that the reader i s presumed
to be acquain ted wi th such ord i nary astronomica l
facts as would be contained i n a book of the
scope of my l i ttle volume
ROBERT S . BALL.
1s t, 1892.
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TIME AND TIDE .LECTURE I .
IT i s my privi lege to address you thi s a fternoon
o n a subject in which science and poetry are
blended in a happy conj unction . If there be a
M o n about the earl i er chapters ofany branch of h istory
,how great must b e the
i nterest which attaches to that most primeval of
al l terrestria l h i stories which rel ates to the actual
beginn ings of th is glob e on which we stand .
In our efforts to grope into the d im recesses of
this awful past,we wan t the ai d of some stead fa st
l ight which shal l i l lumine the dark places wi thou t
the treachery of the wi l l-o’-the-wisp . I n the
absence of that steadfas t l ight, vague con j ectu res
as to the begin n ing of th i n gs cou ld never be
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10 TIMEAND TIDE .en ti tled to any more respect than was due to
mere matters of specu lat ion .
Of late,however
,the requ i red l ight has been to
some considerable exten t forthcoming, a n d the
attempt has been made,with no l i ttle success, to
elucidate a most i nterest i n g and wonderfu l chapter
of an exceed in gly remote h istory . To chron icle
th is h istory i s the object of the presen t l ectures
before thi s I nst i tu tion .
First,let us be fu l ly aware of the extraord inary
remoteness of that period of wh ich ou r h i story
treats . To attempt to defin e that period chrono
logical ly wou l d be utterly fu ti l e. When we have
stated that i t i s more ancien t than a lmost any other
period which we can d iscuss, we have expressed
al l that we are real ly en ti tled to say . Yet thi s
conveys n o t a l ittle . I t di rects us to look back
through al l the ages o f modern human h istory,
through the great days of ancien t Greece and
Rome,back through the times when Egypt and
Assyri a were names of ren own,through the days
when N i neveh and Babylon were mighty a n d
populou s c i ties i n the zen i th of thei r glory. Back
earl ier sti l l to those more ancien t nations of wh ich
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TIMEAND TIDE . I Iwe kn ow hardly an yth in g, a n d sti l l ea rl ier to
the prehistoric man,of whom we know less back,
fi n al ly,to the days when man first trod o n th i s
planet,untold ages ago . Here is i n deed a por
tenton s retrospect from most poin ts of v i ew, but
i t i s on ly the commen cement of that which our
subj ect suggests .
For m a n i s bu t the fi n al product of the lon g
an terior ages durin g whi ch the development of l i fe
seems to have un dergon e an exceed in gly gradual
elevation . Our retrospect now takes i ts way alon g
the vistas opened up by the geologists . We look
through the protracted tert iary a ges,when mighty
an imals,now gen era l ly exti n ct
,roamed over the
conti n en ts. Back sti l l earl i er through those w o n
d r o u s secon dary periods, where swa mps or ocean s
often covered wha t i s now dry lan d, and where
mighty repti les of uncouth forms stalked a n d
crawled a n d swam through the old world a n d the
new . Back sti l l ea r l ie r through those vital ly s ig
n ifica n t ages when the sun beams were bein g
ga rnered a n d la id aside for man ’s u se i n the great
forests,which were afterwards preserved by bei n g
transformed in to seams of coal . Back st i l l earl ier
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12 TIMEAND TIDE .through endless thousan ds of years, when lust rous
fishes abounded i n the oceans back again to those
periods characteri zed by the lower types of l i fe ;
a n d sti l l earl ie r to that in cred ibly remote epoch
when l i fe i tsel f began to dawn on ou r awaken i ng
globe . Even here the epoch of our presen t h istory
ca n hardly be said to have been reached . We
have to look through a long succession of ages
sti l l an teceden t. The geologist, who has hi therto
gu ided ou r v i ew,can not render us much further
ass istan ce but the phys ic i st i s at hand—he teaches
us that the warm globe on which l i fe i s beginn i ng
has passed in i ts previous stages through everyphase of warmth
,of fervou r
,of glowin g heat
,o f
i ncandescen ce, a n d of actual fusion ; a n d thus at
last ou r retrospect reaches that particu lar period
o f our earth’s past h i story which i s spec ial ly
i l l ustrated by the modern doctri ne of Time a n d
Tide.
The presen t i s the cl ue to the past. I t i s the
stea dy appl i cat ion of this pri n c iple which has led
to such epoch-mak in g labou rs as those by which
Lyel l i nvestiga ted the origin of the earth’s crust,
Darwin the origin of spec ies,Max Mu l ler the origin
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TIME AND T IDE . 13
of language. I n ou r presen t subj ect the course
i s plain . Study exactly what i s going on at
presen t, a n d then have the cou rage to apply con
s is ten t ly a n d rigorously what we have learned
from the present to the i nterpretat ion of the
past.
Thus we begin wi th the ripple of the tide on the
sea-beach which we see to-day. The ebb a n d the
flow of the tide are the present ma n i festat ions of
an agent whi ch has been constan tly atwork. Letthat present teach u s what tides must have done i n
the i ndefin ite past .
I t has been known from the very earl i est t imes
that the moon and the ti des were connected
together—con nected , I say, for a great advan cehad to be made in human knowledge before i t
wou ld have been possible to u n derstand the true
relat ion between the tides and the moon . I ndeed,
that relation i s so far from bein g of an obvious
character,that I th in k I have read of a race who
fel t some doubt as to whether the moon was the
cause of the t ides,or the t ides the cause of the
moon . I shou ld , however, say that the moon i snot the sole agent engaged i n produci n g thi s
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14 TIME AND TIDE .
period ic movement of our waters . The sun also
arouses a t ide, but the solar t ide i s so smal l in
for ou r pre—s_
en t p urpose we m ay _le_a ve i t o u t Of
con siderat ion . We must, however, refer to the
solar t ide at a later period of ou r d iscou rses,for
i t wi l l be found to have played a splen did pa r t
at the i n i t ial stage of the Ea rth-Moon Histo ry,
whi le in the remote future i t wi l l again ri se i n to
prominen ce .
I t wi l l be wel l to set forth a few prel imin ary
figures which shal l expla i n how it comes to pass
that the efficiency of the s u n as a t ide -producin g
agent i s so greatly i n ferior to tha t of the moon .
I n deed,con siderin g that the sun has a mass so
stupendous,that i t con trols the en ti re plan etary
system,i t seems stran ge that a body so insign ifi can t
as the moon can raise a bigger tide on the ocea n
than can the s u n , of wh ich the m a ss i s
t imes as great as that of our s a tel l i te
This apparen t paradox wi l l d isappear when w e
en un ciate the law accord in g to which the effic ien cy
of a tide -produci n g agen t i s to be estimated . This
law is somewhat d ifferen t from the fami l iar form i n
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TIME AND TIDE . 15
whi ch the la w of gravitat ion i s expressed . The
gravi tation between two d istan t masses i s to be
measured by mul tiplyi n g these masses together,
and d ivid in g the product by the squ a r e of the d is
tan ce. The la w for express ing the effic i en cy of a
tide-producin g agent varies not accord ing to the
i nverse a cco_rdin g __t o the in verse cu b e
of the distan ce. Thi s d i fferen ce i n the expressionM
of the law wi l l suffi ce to accou n t for the superiori ty
of the moon as a t ide-producer over the s u n . The
moon ’s d istan ce o n an average i s about o n e
386th part of that of the sun , a n d thu s i t i s easy
to show that so far as the mere attract ion of gravi
t a t io n i s concern ed , the efficien cy of the sun’s force
on the earth i s abou t on e hu n dred a n d seven ty-five
t imes as great as the fo r ce with which the moon
attracts the ea r th . That i s of course calcu lated
u n der the la w of the i nverse square . To determi n e
the tidal effi cien cy we have to d ivide th is by three
hun dred a n d eighty-s ix , and thus vLeh s ee that the
tidal effi cien cy of the sun i s less than hal f that ofH
the moon .
When the solar tide a n d the l un ar t ide are acti ng
in un ison , they con spi re to produce very h igh
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16 TIME AND TIDE .
t ides and very low t ides,or, as we cal l them , spring
tides . On the other hand , when the su'
n i s so
placed as to give us a low tide whi le the moon i s
producin g a h igh t ide,the n et resu l t that we
actual ly experience i s mere ly the excess of the lunar
t ide over the solar t ide these are what we cal l n eap
t ides . I n fact, by very carefu l and lon g-continued
observation s of the rise and fal l of the tides at a
part icu lar port, i t becomes poss ible to determin e
with accuracy the relative ranges of spri ng t ides
and neap t ides ; and as the spring t ides are pro
d u ced by moon plus sun, whi le the n eap tides
are produced by moon minus s u n , we obtain a
means of actual ly weigh ing the relat ive ma sses of
the sun a n d moon . This i s o n e of the remarkab l e
facts which ca n be deduced from a prolonged study
The d emonstrat ion of the law of the tide-pro
d u cin g force i s of a mathematica l character, a n d
I do not i n tend i n these lectures to enter i n to
mathematical calcu lat ion s . There i s, however, a
s imple l ine of reason in g which,though i t fal ls shor t
of actual demon strat ion,may yet suffice to give a
plausible reason for the law.
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18 TIMEAND TIDE .i nversely as the cube of the d i stance between i t
m WnVMEHrfim e—fm-
i ty we may make the assumption
that the whole of the earth i s submerged beneath
the ocean,and that the moon revolves i n the plane
of the equator. We may a lso en t i rely n eg lect for
the presen t the tides produced by the s u n , a n d we
shal l al so m a ke the further assumption that fri c
tion i s absen t . What fri ction i s capable of doing
we must,however
,refer to later on . The moon
jw illact on the ocean and deform it
,so that there
wi l l be h igh tide alon g one merid ian,and high
tide a lso on the opposi te merid ian . This i s i ndeed
o n e of the paradoxes by which students are
frequently puzzled when they begi n to learn
about the tides . That the moon should pul l the
wate r up i n a heap on one side seems plaus ibl e
enough . High tide wi l l of course be there ; a n d the
student might n atural ly th ink that the water being
drawn in th is w a y i n to ‘a heap on one side, there
wi l l of course be low tide on the Opposi te side of
the earth. ~Anatu ral assumption, perhaps, butnevertheless a very wrong one . There are at
every moment two opposite parts of the earth in
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TIMEAND T IDE . 19a cond ition of h igh water ; i n fa ct ,
’
this wi l l be
obvious i f we remember that every day,or
,to speak
a l i ttle more accurately , i n every twen ty-fou r hours
and fifty-one mi n utes, we have on the average
two high t ides at each local i ty . Of cou rse th i s
cou ld n o t be i f the moon raised on ly one heap
of h igh water,because
,as the moon on ly appears
to revolve arou n d the ea rth on ce a d a y, or, more
accurately,on ce in that same average period of
twen ty- fou r hours a n d fifty-o n e mi n utes, i t wou l d
be imposs ibl e for u s to have high tides succeed ing
each other as they do i n pe r iods a l i tt le lon ger
tha n twelve hours,i f on ly o n e heap were carri ed
roun d the earth .
The fi rs t quest ion then i s,as to how these two
opposite heaps of water are placed in respect to
the posi tion of the moon . The most obvious ex
planation wou l d seem to be,that the moon shou ld
pu l l the waters up into a heap d i rectly un dern eath
i t,a n d that therefore there should be h igh water
underneath the moon . As to the other side,the
presence of a h igh tide there M y,to be accounted fcg flb ym tlfi fact that the moon
pu l led the earth away from the waters on the more
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20 TIMEAND TIDE .remote side, j ust as i t pu l led the waters away from
the more remote earth on the s ide underneath the
moo n ."
I t i s,however
,certai n ly not the case that
the h ig h t ide i s s i tuated in the s imple positionthat thi s law wou ld in d icate, and which we ha ve
represented i n Fig . I,where the ci rcu lar body is
the earth,the ocean su rround ing which i s d i storted
by the action of the t id es.
F lc . l.
We have here taken an ova l to represent the
shape i nto which the water i s supposed to be
forced or drawn by the t ida l action of the tide
producing body. This may possibly be a correct
representation of what would occur on an idea l
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TIMEAND TIDE. 21globe en t i rely covered wi th a friction less ocean
But as our earth i s not covered en t i rely by water,
a n d as the ocean i s very far from being fri ctionless,
the ideal t ide i s n o t the t ide that we actual ly kn ow ;n o r i s the ideal t ide represen ted by thi s ova l even
an approximat ion to the actual t ides to which
our oceans arg su lject . I n deed , the ova l does notrepresen t the facts at al l
,and of thi s i t i s on ly
n ecessary to adduce a s in gle fact i n demonstrat ion .
I take the fundamen tal i ssue so often debated,as
to whether I n the ocean vibrati ng with i deal t ides
the h igh water or the low water shou ld be under
the moon . Or to put the matter o therw Is e when
we represent the d i splaced water by a n oval,I s
the lon g axi s of the oval to be turn ed to the
moon,as gen eral ly supposed , or i s i t to be d i rected
at right angles therefrom I f the ideal t ides were
i n a ny degree represen tat ive of the actual t ides, so
fun damental a quest ion as this could be at once
an swered by an appeal to the facts of observation .
Even i f fri ct ion i n some degree masked the phe
n o m en a , surely o n e wou ld th in k that the state o f
the actual tides should st i l l enable u s t o an swer
thi s question .
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TIMEAND TIDE .Bu t a study of the t ides at d ifferen t ports fa i l s
to real i ze th i s expectat ion . A t some po rt s, n o
doubt,the t ide
_is h igh whe n the moon i s o n the
merid ian . I n tha t . ca se, of course, the high water
i s under the moon , as apparen tly ought to be the
case i nvariably,on a superfici al view. But, on
the other hand,there are ports where there i s
often low water when the moon i s crossi ng the
merid ian . Yet other ports might be ci ted i n
which every in termed iate phase cou ld be observed .
I f the theory of the tides was to be the s imple one
so often described,then at every port noon should
be the hour of hig h water’
o n the day o f the n ewa “ u—n—n qmoon or of the fu l l moon , because then
exciting b Odies are o n the merid ian at the same
t ime. Even i f the friction retarded the great t idal !
wave un iformly,the h igh t id e o n the days of fu l l
or change shou ld always occur at fixed hou rs but,
unfortun ately,there i s n o such del ightfu l theory
of the t ides as thi s would imply. At Green ock
no doubt there isn hig h lva ter at or abou t n oon on
the day of fu llQ LchaIIg e ; and i f i t cou ld be s imi
la r iy said that o n the day of fu l l or change there
w a s h igh water everywhere at local n oon,then
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TIME AND T IDE. 23
the equ i l ibrium theory of the tides,as i t i s cal l ed
,
would be beau ti fu l ly simple . Bu t th is i s n o t the
case . Even around our own coasts the d is cre
p a n cies are such as to u tterly d iscred i t the theory
a s OREr in g a ny
—“practical At Aberdeen
the h igh t ide does not appear ti l l an hour l aterthan the doctri n e wou ld suggest. I t i s two hou rs
late at London , three at Tyn emou th, four at Tralee,five at Sli o, and si x at Hu l l . Thi s l ast port
would be i ndeed the haven of refuge for those
who bel i eve that the low t ide ought to be un der
the moon . At Hu l l th i s i s n o doubt the ca se ; a n d
i f at al l other pl aces the water behaved as i t does
at Hul l,why then
,of course
,i t wou ld fol low that
the law of low water un der the moon was general ly
true . But then th is wou ld not tal ly with the con
dit ion of affai rs at the other pla ces I have named ;a n d to complete the cycle I shal l add a few more .
At B ristol the h'
g h wa ter does n o t ‘g et u p untilseven hours after the m o o n
_h a s p a ssed the merid ian
,
at Arklow-
the delay i s eight hou rs, at Yarmouth
i t i s n i n e, at the Needles i t i s ten hours, whi le
l astly, the moon has n ea r ly got back to the
meridian a gain ere i t has succeeded in draggin gI
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24 TIME AND TIDE .
up the tide on whi ch Liverpool’
s great commerce
Nor does the resu l t of studyi n g the tides along
other coasts beside our o w n decide more con clu
s ivelyon the mooted poin t. Even ports i n the vast
ocean give a very un certain response. Kerguelen
I sland a n d San ta Cru z seem t o_p1;oye_t_hat
the h igh tide occu rs un der the moon , bu t u n fo r t u
n a telybOth Fij i a n d Ascens ion seem to presen t u swith an equal ly satis fa ctory demonstrati on
,that
beneath the moon is the invariable home of low
water.
I do not mean to say that the study of the t ides ’l
i s i n other respects such a con fused subj ect as the
facts I have sta ted would seem to i n dicate: I t
becomes rather pu zzl in g, n o doubt, when we com
pare the t ides at one port with the t ides elsewhere .
The la w a n d order a r e, then , by n o means co n
spicu o u s , they a re often hardly d iscern ible . Bu t
when we con fine ou r attention to the tides at a
s ingle port, the problem becomes a t once a very
in tel l igible o n e. Indeed , the in vest igation of the
t ides i s an easysubject, i f we a r e con ten ted wi th
a reason ably approximate sol ution shou ld,how
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26 TIME AND TIDE .
and how comes i t to pass that these pred ict ions are
i n variably correct
We fi rst refer to that won derfu l book, the N a u
t ica lAlm a n a c. I n that vol ume the movemen ts ofthe m oon are set forth wi th fu l l det a i l ; and amon g
other parti cu lars we can learn o n page iv of every
mon th the m ean t ime o f the moon ’s merid i a n
passage. I t appears that on the day in question
the moon crossed the merid i a n at I 1h . 23m . Thus
we see there w a s high water at D u bl in at 10h.
I4m . , a n d l b . 9m . la ter, that i s, at 11h. 23m , the
moon crossed the merid ian .
Let us take an othe r i nstan ce. There i s a h igh
tide at PM . o n the 2sth August , a n d aga i n
the i n fa l l ible N a u t ica lAlm a n a c te l ls us that themoon crossed the merid ian at 5h. 44m . , that is, at
2h . 4m . after the h igh wa ter.
I II the fi rst case the moon fol lowed the t ide in
about a n hou r,a n d in the secon d case the moon
fol lowed in abou t two hours . Now i f we are to be
sat isfied with a very rough t ide rule for D ubl in,
we m a y say ge n eral ly i s a lways a high
tide a n hou r a n d a hal f before the moon crosses
the'
m_
erid ian . This would n o t be a very accurate
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TIME AND TIDE . 27
rule,but I can assure you of th is
,that i f you go
by i t you wi l l never fai l of fi n d i n g a good tide to
en able you to en j oy your swim . I do not s a ! r th i s
ru le would en able you to con s truct a respectab le
tide-table. A sh ip -owner who has to creep up the
river, a n d to wh om the i n ches of water are often
material,wil l requ ire far more accurate tables than
thi s simple ru le cou ld give. Bu t we enter i n to
rather compl icated matters when we attempt to
g ive any real ly accurate methods of computation .
On these we shal l say a few words presen t ly.
What I fi rst want to do, i s to impress upon you i n
a s imple way the fact of the relat ion between the
tide and the moon .
To give another i l l ustrat i on , let u s see how the
tides at Lon don Bridge are related to the moon .
On J a n . I st, 1887 , i t appeared that the t ide was
high at 6h. 26m . RM a n d tha t the moon had
crossed the merid ian 56m . previously ; on the 8 th
Jan. the tide was high at o h. 43m . P .M. , and the
moon had crossed the merid ian 2h . I m . previously,
Therefore we wou l d have at London B ridge h igh
water fol lowi n g the moon ’s tran s i t i n som ewhere
a bou t a n hour and a hal f.
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TIMEAND TIDE .I choose a day at random , for example—the
12th Apri l . The moon crosses the upper merid ian
at 3h . 39m . A.M . , and the lower merid ian at 4h6m . P.M. Addin g an hour a n d a hal f to each
would give the h igh t ides at 5h. 9m . A.M . a n d5h . 36m . P.M. ; as a matter of fa ct, they are 4h.
5 8m .A.M . a n d 5h. z o m . P .M .But these i l l ustrat ions are suffi cien t. We find
that at Lon don , i n a gen eral w a y, high water
appears at Lon don B ridge about an hour and a
hal f after the moon has passed the merid ian of
Lon don . I t so happens that the interval at Dubl i n
i s about the same,zle. an hou r a n d a hal f ; only
that i n the latter case the high water precedes the
moon by that in te i va l in stead of fol lowi n g i t. We
may employ the same s imple process at other
places . Choose two days abou t a week d istan t ;
fin d o n each occasion the in terva l between the
tra n s i t of the moon a n d the t ime of h igh water,
then the mean of these two d ifferen ces wi l l a lwa ys
g ive some notion of the i n terval between high
water and the moon ’s trans i t. I f then we take
from the N a z/lz'
ca lAlm a n a c the t ime of the moon ’st ran s i t, a n d apply to it; the correction proper for the
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TIME AND TIDE. 29
port,we shal l alwa ys have a sufficien tly good tide
table to gu id e us in choosing a su i tab le t ime for
tak ing our swim or ou r walk by the sea-side ;
though i f you be the captain of a vessel,you wil l
n o t be so imprudent as to enter port wi thout
tak in g cou n sel of the accurate t ide- ta bles,for wh ich
we are i n debted to the Admi ral ty .
Every o n e who visi ts the sea-side,or who l ives
at a sea-port, shou ld know thi s constan t fo r the
t ides,which affect h im and his movemen ts so
materia l ly. I f he wi l l d iscover i t from his own
experien ce,so much the better.
The fi rst poi n t to be ascertained i s the time of
h igh water. Do not take thi s from any loca l table
you ought to observe i t for you rsel f. You wi l l go
to the pier head,or
,better sti l l , to some place where
the ri se a n d fal l of the mere waves of the sea wi l l
n o t embarrass you i n your work. You must note
by your watch the t ime when the t ide i s h ighest.
An accurate way of doing th i s wi l l be to have ascale on which you can measure the height at
in tervals of five minu tes abou t the time of high
water . You wi l l then be able to conclude the
time a t wh ich the t ide was actual ly at i ts h ighest
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30 T IME AND TIDE .
poin t bu t even i f no great accuracy be obtainable ,
you c a n sti l l get much i n teresti ng in formation , for
yo u wil l wi thout much d iffi cu lty be right within
ten min utes or a quarter of an hou r.
The correct ion for the port i s properly cal led the
establ ishmen t, th is bei n g the average time of
h igh water on the days of fu l l a n d chan ge of the
moon at the part icu lar port i n question .
We can con s iderably amen d the elementary
notion of the tides wh ’ch the former method has
given us,i f we ad o pt the plan described by D r.
Whewel l in the fi rst fou r ed i t ions of theAdm ir a ltyM a n u a l of S cien lific I n qu iry. We speak of the
in terval between the tran si t o f the moon and the
t ime of high water as the l un i-tida l i n terval . O f
course at fu l l a n d change thi s i s the same th in g as
the establ ishmen t,but for other phases of the moon
the establ i shmen t must receive a correct ion before
b ein g used as the lu n i-tidal in te rval . The correction
is given by the fol lowi n g table
Ho u r o fMo o n 's t r a n s it a fter Su n6
—60 mCo rrec t io n o f esta b l ishm en t t o fin d l u ni -tida l in terva l
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TIME AND TIDE . 3I
Thus at a port where the establ i shmen t was 3h .
25m . , let us suppose that the trans i t of the moon
took place at 6 PM . then we correct the establ i sh
men t by —60m . , and fin d the l un i -t idal i nterval to
be 2h. 25m . , a n d accord i n gly the h igh water takes
place at 8h . 25m . PM .
Bu t even th is method i s on ly an approximation .
The study of the tides i s based o n accurate o b s er v
ation of thei r ri se a n d fal l on d i fferent places
round the ea rth . To show how these observation s
are to be made, a n d how they are to be d iscussed
a n d reduced when they have been made,I may
refer to the last ed i tion of theAdm ir a lty M a n u a lof Scien t ifi c I n qu i ry, 1886. For a complete study of
the tides at a ny port a sel f-r eg is tei in g t ide-gauge
should be erected, o n which not alone the heights
a n d times of high a n d low water shou ld be depicted ,
but also the con tin uous curve which shows at a nyt ime the height of the water. I II fact, the whole
subject of the practi cal observat ion a n d d iscuss ion
a n d predict ion of t ides i s fu l l of val uable in struct ion ,
a n d may be c i ted as o n e of the most complete
examples of the modern scientifi c methods .
I n the first place,the tide-gauge i tsel f i s a
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32 TIME AND T IDE .
del i cate instrument ; i t i s actuated by a float which
ri ses a n d fa l l s wi th the water, due provi sion bein g
made that the mere in fluence of waves shal l n o t
make i t to osci l late i n conven i ently . The motion of
the float when su i tably reduced by mechan i sm
serves to gu ide a pen ci l,whi ch, a ctin g o n the paper
rou n d a revolvin g drum , gives a fa i thfu l a n d u n
in term itti n g record of the height of the wa ter.
Thus what the tide-gauge does is to presen t to
us a lon g curved l ine of which the summits corre
spo n d to the heights of h igh water, whi le the
depressions are the correspond i n g poin ts of low
water. The long u n du lation s of this curve are, how
ever,very i rregular. At spri n g tides, when the s u n
a n d the moon con spire, the elevation s ris e much
higher and the depression s s in k much lower than
they do at neap t ides,when the high water raised
by the moon i s reduced by the act ion of the sun .
There are also many minor i rregulari t ies which
show the tides to be n o t nearly such simple phe
n o m en a as migh t be at fi rst supposed . But what
we might hast i ly th in k of as i rregu lari t ies are, i n
truth , the most i nteresti ng parts of the whole
phenomena . Just as i n the observations of the
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34 TIME AND TIDE.
harmon i c analys i s. The pri nciple of the method
may be very simply described . Let u s fix our atten
tion o n a n y parti cu lar“ t ide, for so the variou s
elements are denoted . We can always determ in e
beforehan d,with as much accuracy as we may
r equ i re, what the period of that t ide wi l l be. For
in stan ce,the period of the l un ar semi-di urn al t ide
wil l of course b e hal f the average t ime Occupied
by the mo on i n travel l in g roun d from the merid i a n
of a ny place un ti l i t regains the same merid ian ;
the period of the l unar d iurn al t ide wi l l be
double as great ; a n d there are fortn ightly tides,
a n d others of periods st i l l greater. The essenti a l
w in t to n ot ice i s, that the pe riods of these t ides
are given by purely astron om ica l con s ideration s,
and do n o t depen d upon the actual observat ion s of
the height of the water.
We measure ofl' o n the cu rve the height of thetide at i ntervals of an hour. The larger the
number of such measu res that are avai lable the
better bu t even i f there be on ly three hun dred
and sixty or seven hun dred a n d twenty co n secu
t ive hours , then , a s shown by Professor G . H .
Da rwin in theAdm ir a lty M a n u a l already referred
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TIME AND TIDE . 35
to, i t wi l l sti l l be poss ible to obtain a very com
peten t kn owledge of the tides in the particu lar
port where the gauge has been placed .
The art ! for such in deed i t may be described! of
harmon i c an a lysis con s ists i n deduci n g from the
hourly observation s the facts with regard to each
of the con st ituent t ides . This art has been carried
to such perfect ion,that i t has been reduced to a
very simple series of ar i thmetical operation s .
I ndeed i t has now been found poss ible to cal l i n
the aid of ingen ious mechan i sm,by which the
labou rs of computation are en t i rely superseded .
The poin ter of the harmon i c an alyzer has merely
to be traced over the curve which the tide-gauge
has drawn,a n d i t i s the fun ction of the mach i n e
to decompose the compos ite u n dulat ion in to i ts
parts, and to exh ibi t the several con st i tuen t t ides
whose confluence gives the total resu l t .
As i f n oth i n g shou ld be left to complete the
perfection of a process which,both from its theo
ret ica la n d i ts practical s ides,i s of such importance
,
a ma ch in e for pred ict in g tides has been design ed,
constructed,a n d i s n o w i n ordin ary use . When
by the aid of the harmon ic an alysis the effectiven ess
C 2
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36 TIME AND TIDE .
of the several con st i tuen t tides affect in g a port
have become fu l ly determin ed , i t i s of course
possible to pred i ct the tides for that port . Each
tide ” i s a simple period ic ri se a n d fal l,an d we can
compute £07 565, fu ture t ime the height of ea ch
were i t.
acting alon e. These heights can al l be
added together, a n d thus the height of the wa ter“
m a m a .“
I n th is way a t ide- tabl e i s formed,
a n d such a table when complete wi l l express not
alon e the hours a n d heights—
o f high water on every"
8 51971565 the height o f the wa ter at a n y i n terven ing
The computation s n ecessary for this purpose are
no doubt s imple,so far as thei r pri n ciple i s co n
cern ed ; but they are exceed i n gly tedious, a n d
a ny process must be welcomed whi ch afl'o rd smitigation of a task so l aborious . The theory of
the t ides owes much to S i r Wi l l iam Thomson in
the methods of observa tion a n d in the method s of
reduction . He has n o w completed the practi ca l
parts of the subject by i n ven ting a n d con stru ctin gthe famous t ide- predi ct i n gen g ine.
The pri n ci ple Bf th is eng in e i s comparat ively
s imple . There is a chain which at o n e end i s
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0L,M m h w Vm ' v m
‘
TIME AND TIDE . 37
fixed,a n d at the other en d carries th e pen ci l whi ch
i s pressed again st the revolving drum on which
the pred ict ion i s to be in scribed . Between i ts
two en ds the chain passes u p and down over
pu l leys . Each pul ley correspon ds to one of the“ t ides
,
”a n d there are abou t a dozen al together,
some of which exercise bu t l i ttle effect. Of course
i f the centres of the pu l leys were al l fixed the pen
cou ld not move, bu t the cen tre of each pul ley
describes a c i rcle wi th a radius proport ion al to the
ampl itude of the correspon d in g tide, a n d i n a
t ime proportion al to the period of that ti de . When
these pu l leys are al l set so as to start at the proper
phases, the motion i s p roduced by tu rn i n g rou n d
a han dle which sets al l the pul leys in motion , a n d
makes the drum rotate . The tide curve i s thus
rapid ly drawn out ; a n d so exped itious i s the
mach in e, that the tides of a port for a n enti re year
can be completely worked ou t i n a couple of
hours .
While the student or the phi losopher who seeks
to ren der a ny accoun t of the tide on dyn amica l
groun ds i s greatly embarrassed by the d ifli cu lt iesin troduced by fri ct ion , we, for ou r presen t purpose
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38 TIME AND TIDE .
in the study of the great roman ce of modern
science open ed up to us by the theory of the t ides,
have to welcome fri ct ion as the agen t whi ch gives
to the tides thei r sign ificance from ou r poin t of
vi ew.
There i s the greatest d ifferen ce between the
height of the ri se and fal l of the tide at d i fferen t
local i ties . Out i n m id-ocean , for i n stan ce, a n i sla nd
l ike St . Helen a i s washed by_a t ide on ly about
three feet in range ; an en closed sea l ike the
Caspian Is sub j ect to no apprec iable t ides whatever,
while theMed i ter ran ean,n otwithstand ing i ts co n
n ect io n with the At l a n t ic,15 st i l l on ly subject to
very in con siderable t ides,varyi n g from one foot to
a few feet. The s tatemen t that wa ter always fi n ds
i ts own level must be received,l ike man y another
proposit ion in nature,with a con s iderable degree of
qual ificat ion . Lon g ere o n e t ide cou ld have foun d
i ts way through the Strai ts of G ibral tar in suffi cien t
vol ume to have apprec iably a ffected the level of the
great i n lan d sea, i ts effects wou l d have been obl i
t er a t ed by succeed i n g tides . O n the other han d,
there are certai n local it ies whi ch expose a fun n el
shape open in g to the sea in to these the great tidal
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TIME AND TIDE; 39
wave rushes,and as i t passes on wards towards the
narrow part, the waters become pi led up so as to
produce t idal phen omena of abnormal proportion s .
Thus,in our own islan ds
,we have in the B ri sto l
Chan n el a wide mouth in to which a gr eat t ide
enters,a n d as i t hurr ies up the Severn i t produces
the extraord in ary phen omenon of the Bore. The
B ri stol Chan nel also concen trates the great wave
which gives Chepstow and Card i ff a t ida l ran ge of
thi rty- seven or thi rty-eight feet at spri n gs,and
forces the sea up the r iver Avon so as to give
B ri sto l a won derfu l t ide. There i s hard ly any
more in terestin g spot in our i slands for the o b serv
ation of tides than i s foun d on Cl i fton Suspen sion
Bridge. From that beaut i fu l structure you look
down o n a poor and not very attract ive stream,
wh ich two hours later becomes tran sformed in to a
river of ample volume, down which great sh ip s are
n avigated . But of al l places in the world, the most
colossa l t idal phenomena are those in the Bay of
Fun dy . Here the At lan t i c passes in to afi
lg pflg ,—5chan n el whose sides gr adu a l ly
.
con verg e. When
the great pu lse of the t ide rushes up thi s channel,
it is'
gr a du a lly accumu lated i nto a mighty volume
”AM U3 4 _0lrWW1n ! t v-n V, a VA
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NMVWM W m WU
4o TIME AND TIDE.
at the upper en d , the ebb a n dflo w of which atsprin g tides exten ds through a n aston i sh i n g ran ge
of more than fi fty feet .’
The discrepan cies between the tides at d ifferen t
pla ces a re chiefly due to the loca l formation s
of the coasts a n d the sea-beds . Indeed , i t seems
that i f the whole earth were covered with an
un i form a n d deep ocean of water, the t ides wou ld
be excessively feeble . On no other supposi t ion
can we reason ably accoun t for the fact that ou r
barometri c records fai l to afford us a ny very
d i stin ct eviden ce as to the existen ce of t ides i n
the atmosphere . For you wil l,of cou rse
,remem
ber that our atmosphere may be rega r ded as a deep
a n d vast ocean of ai r, which embraces the whole
earth,exten d in g far above the loft i est summits of
the moun ta in s .
I t i s o n e of the profou n dest of nature’s laws that
wherever friction takes place,en ergy has to be
con sumed . Pe rhaps I ought rather to s a y‘
t r a n s
formed,for of course i t i s n o w wel l k n own tha t
con sumption of energy in the sen se of absolute
loss i s imposs ible. Thu s,when en ergy is expen ded
in movin g a body i n opposi tion to the force of
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42 TIME AND TIDE.
wi l l see the water copiously charged with sed imen t
which the t ide i s beari n g alon g . En gin eers are
wel l awa re of the po ten cy of the t ide as a vehicl e
for transport in g stupen do us quantities of san d or
mud . A san d-bank impedes the n avigation of a
river ; the remova l of that san d-ban k wou ld be a
task,perhaps
,con ceivably possible by the u se of
steam dredges and other appl ian ces,whereby vast
quan ti ties of san d could be raised a n d tran sported
to where they can be safely deposi ted in deep water.
I t i s sometimes poss ible to effect the des i red end
by applyi n g the power of the t ide. A sea-wal l
j udic iously thrown out can be made to con cen trate
the tide in to a much narrower channel . I ts dai ly
osci l lat ion s wi l l be accompl ished with greater
vehemen ce, a n d as the tide rushes furiously back
wards a n d forwards over the obstac le, the i n cessan t
action wi l l gradual ly remove i t, and the i mped i
men t to naviga tion may be cleared away. Here we
actual ly see the t ides performin g a piece of defi n i te
and very laborious work , to accompl ish wh ich by the
more ord i n a ry agen ts would be a stupendous task .
I n some places the t i des are actual ly harnessed
so as to accompl ish useful work. I have read that
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TIMEAND TIDE. 43underneath old London B ridge there u sed formerly
to be great water-wheels, which were tu rn ed by
t he t ide as i t rushed up the river, a n d turn ed a gai n ,
though i n the Opposite way,by the ebbin g t ide .
These wheel s were,I bel ieve
,employed to pump up
water, though i t does n o t seem obviou s for what
pu rposes the water would have been su i table.
I n deed in the ebb a n d flow al l round our coasts
there i s a poten tial source of energy wh i ch has
gen eral ly been al lowed to run to waste,save per~
haps in o n e or two places i n the south of Englan d .
The tide could be ut i l i zed in various ways . M a n y of
you wi l l remember the floa ti n g mi l ls o n the Rhin e.
They are vesse ls l ike paddle steamers anchored i n
the rapid curren t. The flow of the river makes the
paddles rotate, a n d thus the machi n ery i n the
i n te rior i s worked . Such craft moored i n a rapid
tide-way cou ld also b e made to con vey the power
of the tides in to the mechan i sm of the mi l l . O r there
i s st i l l another method which has been employed,
a n d which wi l l perhaps have a futu r e before i t i n
those approachin g t imes when the coal - cel lars of
England shal l be exhausted . Imagin e on the sea
coast a large flat exten t which i s i n un dated twice
every day by the tide . Let us bu i ld a stout
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44 TIME AND TIDE .
wal l roun d this area , a n d provide i t wi th a sl u i ce
gate . Open the gate as the t ide r ises, a n d the
great pond wil l be fi l led ; then at the m oment o f
h igh water close the sl u ice a n d the pon d - fu l l wi l l
be impoun ded . I f at low t ide the slu i ce be open ed
the water wi l l rush tumu l tuously ou t . Now suppose
tha t a water-wheel be provided , so tha t the rapid
rush of water from the exi t shal l fal l upon i ts
bl a des ; then a sou rce of power i s obviously the
resu lt .
At presen t,however, such a con trivance wou ld
fin d bu t few a dvocates, for of cou rse the com
m er cia l aspect of the question i s that wh ich wi ll
decide whether the scheme is practi cable a n d
econ omica l . The issue in deed ca n be very simply
stated . Suppose tha t a given quan t i ty of power be
requ i red—le t u s s ay that of o n e hu n dred horse . Then
we have to con s ider the condition s u n der wh ich a
con trivan ce of the k i n d we have sketched shal l yiel d
a power of thi s amoun t . Si r Wi l l i am Thomson,
in a very in terestin g address to the B rit ish Asso
c ia t io n at York in 188 1,d iscussed this quest ion
,
a n d I sha l l here make use of the fa cts he brought
forward on that occasion . He showed that to
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TIME AND TIDE . 45
obtain as much power as cou ld be produced by a
steam -en gin e of o n e hun dred horse power,a very
large reservoir wou ld be requ i red . I t i s doubtfu l
i n deed whether there would be man y local i ties o n
the earth which wou ld be su i table for the purpose.
Suppose,however
,a n estuary cou ld be fou n d
which had a n area of forty a cres ; then i f a wal l
were thrown across the mouth so that the t ide
could be impoun ded , the total amou n t of power
that could be yielded by a water-wheel worked by
the in cessan t influx a n d efflu x of the tide wou ld beequal to that yielded . b y the o n e hun dred horse
en gin e,runn in g con tin uously from one en d of the
year to the other.
There are man y dra wbacks to a tide-mi l l of
thi s description . I n the fi rst place, i ts s ituat ion
would natural ly be far removed from other con
ven ien ces n ecessary for m a n ufa ctu ri n g purposes .
Then too there i s the great i rregul a ri ty in the
way in which the power i s ren dered a vai lable . At
certa in periods duri n g the twen ty-four hours the
mi l l would stop run n in g,a n d the hours when this
happen ed wou ld be constan t ly chan gi n g. The
i n conven ience from the man u facturer’s poi nt of
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46 TIME AND TIDE.
view of a deficiency of power during neap t ides
might not be compen sated by the fact that he had
a n excessive supply of power at sp rin g-ti des.
Before tide-mil l s cou ld be su itable for m a n u fa c tu r
in g pu rposes, some mean s mu st be fou n d for stor in g
awa y the en ergy when i t i s redundan t, a n d a pply
in g i t when i ts presen ce i s requ i red . We shou ld
want in fact for great sou rces of energy some con
t r iv a n ce wh ich shou ld fu lfi l the same function as
the accumu lators do in a n electri cal i nsta l lat ion.
Even then,however
,the fi n an cia l con sideration
remai n s,as to whether the cost of bu i ld i n g the dam
and maintain ing the tide-mi l l i n good order wi l l
not o n the whole exceed the origi n al pri ce a n d
the charges for the mainten an ce of a hun dred
horse power steam-en gin e . There can n ot be a
doubt that in th i s epoch of the earth ’s h istory,
so lon g as the price of coal i s on ly a few shi l l in gs a
t o n , the tide-mi l l , even though we seem to get i ts
power withou t curren t expense,i s vastly more ex
pen sive than a ste a m-engin e . I n deed,Si r Wi l l iam
Thomson remarks,that wherever a su i ta ble t ida l
basin cou ld be found , i t would be nearly as easy to
reclaim the land altogether from the s ea . And i f
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TIME AND T IDE . 47
t his were in a ny local ity where man u factures were
possible,the commerci a l value of forty acres of r e
claimed lan d would greatly exceed al l the expen ses
attend in g the steam-en gin e . But whe n the t ime
comes,as come i t apparen tly wil l
,th a t the price of
coal shal l have ri sen to several pounds a ton,the
econ omical aspect of steam as compared with other
pr ime movers wi l l be greatly al tered ; i t wi l l then
no doubt be found advan ta geous to u ti l i ze great
sources of en ergy,such as N iagara and the t ides
,
which i t i s n o w more pruden t to let r u n to waste.
For my a rgumen t,however, i t m a tters l i ttl e that
the t ides are n o t con stra i n ed to do much usefu l
work. They are always doin g work of some k i n d ,
whether that be merely he a t in g the part icles of
water by fri ct ion,or va guely tran sportin g sa n d
from o n e part of the ocean to the other. Usefu l
work or usel ess work a re al ike from the presen t
poin t of view. We kn ow that wor k ca n n ever be
don e u n l ess by the con sumption or tran sformat ion
of en ergy. For each u n i t of work that i s don e
whether by a ny mach i n e or con tr ivan ce , by the
muscles of m a n or a ny other an imal , by the win ds,
the waves,or the t ides
,or in any other way
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48 TIME AND TIDE .
whatever—a certain equ iva len t quan ti ty of en ergymust have been expen ded . When , therefore, we see
a nywork bein g performed , we may alwa ys look for
the source of en ergy to which the machi n e owes i t s
efficien cy. Every machine i l lustrates the old story,that perpetu a l motion i s impossible . A mechan i cal
device,however in gen i ous may be the con struction ,
or however accurate the workman sh ip , ca n n ever
possess what i s cal led perpetu a l motion . I t i s
needless to en ter i n to detai ls of a n y proposed co n
t r iva n ce of wheels, of pumps , of pul leys ; i t i s
sufficien t to say that n oth in g in the shape of me
cha n ism can work without fri ct ion , that frict ion
produces heat , that heat i s a form of energy, a n d
that to replace the en ergy con sumed in producing
the heat there must be some source from which
the machi n e i s replen i shed i f i ts motion i s to be
con tin ued i n defi n i tely .
Hen ce, as the tides may be regarded as a machine
doi n g work,we have to ascerta i n the origin of that
en ergy which they a re con tinual ly expen ding . I t
i s at th is poin t that we fi rst begi n to feel the diffi
cu lt ies in heren t i n the theory of t idal evol ut ion . I
do n o t mean d iffi cu l t ies i n the sense of doubts,for
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50 TIME AND TIDE .
clock may be exten ded to the great bod ies of the
un iverse. The moon i s a giganti c globe separated
from o u r earth by a distance of m iles .
The attract ion between these two bodies always
tends to bri n g them together. No doubt the
moon is not fa l l i ng towards the earth as the de
scen ding clock-weigh t i s doing . We m ay, i n fa ct,
consider the moon,so far as ou r presen t obj ect i s
concerned,to be revolvi n g almost i n a ci rcle
,of
which the earth i s the centre . I f the moon , ho w
ever,were to be stopped
,i t wou ld at once com
mence to rush down towards the earth,whi ther it
would arrive wi th a n awfu l crash i n the course of
four or five d a ys . I t i s fortun ately true that the
moon does n o t behave thus ; bu t i t has the ab i l i ty
of do ing so,a n d thus the mere separat ion between
the ea rth a n d the moon i n volves the ex isten ce of
a stupen dou s quan t i ty of energy,cap a ble un der
certa in cond itions of u n dergoin g tran sformat ion .
There is al so an other source of mechan i ca l en ergy
besides that we have j ust referred to. A ra pidly
movin g body possesses,i n v i r tue of i ts motion
,a
store of read i ly avai lable energy,a n d i t i s easy to
show tha t en erg y of th i s type is capable of tran s
-
TIMEAND TIDE . SIformation in to other types . Thin k of a can non
bal l rush in g through the ai r at a speed of a thousan d
feet per secon d i t i s capable of wreak in g d isaster
wherever i ts blow may fal l,simply because i ts
rapid motion is the vehicle by which the en ergy
of the gun powder i s t ran sferred from the gun to
where the blow is to be struck. Had the can non
been d i rected vertical ly upwards, then the pro
ject ile, leaving the muzzle wi th the same in i tialveloci ty as before
,would soar up a n d up
,with
gradual ly a bat in g speed,u n t i l at last i t reached a
turn in g-poin t,the elevation of wh ich would depen d
upon the in i t ial veloc i ty. Poi sed for a momen t at
the summit,the ca nnon -bal l m a y then be l iken ed
to the clock-weight, for the en ti re en ergy which
i t possessed by i ts motion has been t ra n sformed
in to the Stat ical en ergy of a ra ised weight . Thus
we see these two forms of en ergy are mutual ly
i nterchan geable . The raised weight i f al lowed to
fa l l wi l l acqui re veloci ty, or the rapid ly movin g
weight i f di rected upwards wi l l acqu i re alti tude.
The quan t i ty of en ergy whi ch ca n be con veyed
by a rapidly moving body i n creases greatly with
it s speed . Fo r instan ce, i f the speed of the bodyD 2
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52 TIMEAND TIDE.be doubled
,the energy wi l l be in creased fourfold ,
or,i n general
,the en ergy which a movin g body
possesses may be said to be proportio n al to the
square of i ts speed . Here then we ha ve an other
source of the energy presen t in ou r ea rth-moon
system ; for the moon i s hu rryin g alon g I n i ts
path with a speed of two- th i rds of a mi le per
secon d,or about twice or th r ee t imes the speed of
a can n on -shot . Hen ce the fact that the moon
i s con t in uously revolvi n g i n a ci rcl e shows us that
i t possesses a store o f en ergy which i s n in e t imes
as great as that which a can n on -bal l as massive
as the moon,a n d fi red with the ord in ary veloci ty
,
would receive from the powder which d ischarged i t.
Thus we see that the moon is en dowed with
two sources of en ergy,o n e of whi ch i s due to i ts
separat ion from the earth , a n d the other to the
speed of i ts motion . Though these a re d istin ct,
they are con n ected together by a l in k which i t i s
importan t for u s to comprehen d . The speed wi th
wh ich the moon revolves around the earth i s c o n
n ected with the moon’s d istan ce from the earth.
The moon might, for in sta n ce, revolve in a larger
circle than that which i t actual ly pursues ; bu t i f
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TIME AND TIDE . 53
i t d id so the speed of i ts motion would have to be
appropriately lessen ed . The orbit of the moon
m ight have a much sma l ler radiu s than i t has at
presen t, provided that the speed was suffi cien tly
i n creased to compen sate for the i n creased a t
tract ion which the earth would exerci se a t the
l essened d istan ce. I n deed , I am here o n ly sta t in g
what every o n e i s fami l ia r wi th u n der the form of
Kepler’s Law,that the square of the period i c time
i s in proportion to the cube of the mean distan ce .
To each di stan ce of the moon therefore belon gs a n
appropriate speed . The en ergy due to the moon ’s
posi tion a n d the e n ergy due to i ts motion are
therefore con n ected together. On e of these quan
t it ies can n ot be al tered without the other u n der
goi n g chan ge . I f the moon ’s orbit were in creased
there wou ld be a gain of en ergy due to the
en larged di stan ce,a n d a loss of en ergy due to the
d imin i shed speed . These wou ld n o t , however,
exactly compen sate . On the whole, we may
represen t the total en ergy of the moon as a sin gle
quan ti ty,which i n creases when the d i stan ce of
the moon from the ea rth i n creases,a n d l essen s
when the d istan ce from the earth to the moon
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54 T IME AND TIDE.
lessen s . For simpl ic i ty we may speak of this as
moon -en ergy.
Bu t the most importan t con sti tuen t of the store
of en ergy i n the earth-moon system i s that co n
tributed by the earth i tsel f. I do n o t now speak
of the en ergy due to the veloci ty of the earth in
i ts orb i t rou n d the sun . The moon in deed part ic i
pates in this equal ly wi th the earth,but i t does
not affect those mutual act ion s between the earth
and moon with wh ich we are at presen t concerned .
We are, i n fact, d iscuss in g the action of that piece
of machin ery the earth-moon system ; and i ts
action i s not affected by the circumstan ce that
the en ti re mach in e i s bei n g bod i ly tran sported
aroun d the sun In a great an n ual voyage. This
has l i ttle more to do with our prese n t argumen t
than has the fact that a man is walk in g about to
do with the motion s of the works of the watch in
h is pocket. We shall, however, have to al l ude to
th is subj ect further o n .
The energy of the earth which i s s ign ifican t in
the earth-moon theory is due to the earth’s rota
t ion upon i ts axi s . We may here a gain use as
a n i l lustrat ion the action of machi n ery ; a n d the
-
TIMEAND TIDE . 5 5spec ia l con triva n ce that I n o w refer to i s the
pun chin g-engi ne that i s used i n our ship-bu i ld in g
works. I n preparin g a plate of i ron to be riveted
to the side of a sh ip,a n umber of holes have to be
made al l round the margi n of the plate . These
holes must be half an in ch or more i n d iameter,
a n d the plate i s sometimes as much as,or more
than , hal f a n in ch in thickn ess . The holes are pro
du ced in the metal by forcin g a steel pun ch through
i t ; a n d th i s i s accompl ished wi thou t even heati n g
the pl a te so as to soften the i ron . I t i s n eedless to
s ay that an in ten se force must be appl ied to the
punch . On the other ha n d, . the distan ce through
which the punch has to be moved i s comparatively
smal l . The pun ch i s attached to the en d of a
powerfu l l ever,the other en d of the lever i s ra ised
by a ca m,so as to depress the pun ch to do its
work. An essen tial part of the machi n e i s a smal lbut hea vyfly-wheel con n ected by gearing withthe cam .
Thisfly-wheel when rapid ly revolvin g conta in s with i n i t, i n vi rtue of i ts mot ion , a large
store of en ergy which has gradual ly accumu lated
durin g the time that the pu n ch i s not i n action .
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56 TIME AND TIDE.
The energy i s no doubt original ly suppl ied from
a steam-engine . What we are espec ial ly concerned
with i s the action of the rapid ly rotatin g wheel as
a reservoi r i n which a large store of en ergy can be
conven i en tly main tained u n t i l such time as i t i s
wanted . I n the action of pun ch ing, when the
steel d ie comes down upon the su rface of the plate,
a large quan t i ty of en ergy i s sudden ly demanded
to force the punch again st the i n ten se res istan ce
i t experien ces ; the energy for th is purpose i s drawn
from the store i n thefly-wheel , which exper ien ces no doubt a check i n i ts veloci ty, to be r e
stored again from the en ergy of the en gi n e du ri n g
the i n terval wh ich elapses before the punch i s
cal led o n to make the next hole.
Another i l l ustration of thefly-wheel o n a splend id scale i s to be seen in steel works
,where
rai lway l in es are bei n g man u factu red . A white
hot ingot of stee l i s presen ted to a pa i r o f power
fu l rol lers,which grip the steel
,a n d sen d i t through
at the other s ide both compressed a n d elon gated.
Tremen dous power i s requ i red to meet the sudden
deman d o n the machin e at the cri t ical moment.
To obtain th i s power an en gin e of immen se
-
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-
5 8 TIME AND TIDE.fly-wheel con tai n i n g a quan t i ty of energy great incorrespon den ce wi th the earth
’
s mass . The amou n t
of en ergy which can be stored by rotation also
depen ds upon the square of the veloci ty with
which the body tu rn s rou n d ; thu s i f our earth
turned round i n hal f the t ime which i t does at
presen t,that i s
,i f the day was twelve hours i n stead
of twen ty-fou r hours, the energy con tain ed in
vi rtue of that rotation wou ld be four t imes i ts
presen t amoun t .
Revert i ng now to the earth-moon system , the
energy which that system con tain s con sists essen
t ia llyof two parts—the moon-energy, whose compo
s i te character I have al ready explained,a n d the
earth -en ergy,which has i ts origin solely in the
rota t ion of the earth on i ts ax is . I t i s n ecessary
to observe that these a re essen ti al ly d i sti n ct—therei s n o necessary relation between the speed of
the earth’
s rotation a n d the d istan ce o f the moon ,
such as there i s between the d istan ce of the moon
a n d the speed with which i t revolves in i ts o rbi t.
For completeness, i t ought to be added that
there i s al so some energy due to the moon ’s rota
t ion on i ts axis, b u t th i s i s very smal l fo r two
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TIME AND TIDE. 59
reasons : fi rst, because the moon i s smal l compa r ed
with the earth, and secon d , because the an gular
veloci ty of the moon i s also very smal l comp a red
with that of the earth . We m a y therefore d ismiss
a s i n sign ifican t the con tribut ion s from this source
to the sum total o f en ergy.
I have frequently used i l l ust rat ion s derived from
machinery,but I want n o w to emphasi ze the
profound d ist in ct ion that exi sts between the rotation
of the earth a n d the rotat ion of afly-wheel i na mach in e shop . They are both, n o doubt, en ergy
holders,but i t must be born e in mind
,that as thefly-wheel doles ou t i ts en ergy to supply the wants
of the machin es wi th which i t i s con nected,a resti
t u t io n of i ts store i s con tin ual ly goin g on by the
a cti on of the en gin e, so that o n the whole the
speed of thefly-whee l does not slacken . Theearth , however, must be l i ken ed to afly-wheelwh ich has been discon nected wi th the en gine . I f
,
therefore,the earth have to supply cer tai n deman ds
o n i ts accumulat ion of en ergy,i t can on ly do so
by a d imin ution of i ts hoard,and this i nvolves a
sacrifice of some of i ts speed .
I n the earth-moon system there i s no en gine
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60 TIME AND T IDE .
at han d to restore the losses of energy which are
i nevitable when work has to b e ~ do n e . But we have
seen th a t work i s don e ; we have shown , in fact ,
that the tides are at presen t doin g work,a n d have
been doin g work for as lon g a period in the
past as our imagin a ti on can exten d to . The
en ergy which th is work has necess ita ted can on ly
have been drawn from the exi sti n g store in the
system ; that en ergy con s ists of two parts -the
moon -en ergy a n d the earth’
s rotation energy. The
problem therefore for us to con sider i s,whi ch of
these two ban ks the tides h a ve drawn o n to meet
thei r con stan t expen d itu re . This i s n o t a quest ion
that c a n be decided offhan d in fa ct,i f we attempt
to decide i t i n a n offhan d man n er we shal l
certain ly go wron g . I t seems so very plaus ible
to say that as the moon causes the tides,therefore
the energy which these t ides expen d shou l d be
con tributed by the moon . Bu t th i s i s not the case.
I t a ctu a l ly happen s that though the moon doescause the t ides
,_yet _ when those t ides con sume
en ergy they draw i t n o t from the d istan t moon,
but from the wa st“ supply which they find readyo
to thei r han d,stored up in the rotation of the ea rth .
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TIME AND TIDE . o r
The demonstrat ion of thi s i s not a very simple
matter ; i n fact, i t i s so far from being simple that
man y phi losophers,i n cl ud in g some emi nen t on es
too,whi le admi tti n g that of course the tides must
have drawn thei r en ergy from o n e or other or both
of these two sources,yet fou n d themselves u n able
to assign how the dem a nd was d istributed between
the two con ce ivable sources of supply.
We are in debted to Professor Purser of Belfast
for ha vin g in dicated the true dyn a mical prin c i pl e
o n which the problem depen ds . I t in volves
reason i n g b a sed simply on the laws of motion a n d
o n elemen tary mathematics,but n o t in the least
involvin g quest ion s of a stron omical observat ion .
I t would be impossible for me in a lectu re l ike
th is to give a ny explan ation of the mathema tical
prin ciples referred to . I shal l , however, en deavour
by some i l lustrat ion s to set befo r e you what th is
profoun d prin ciple rea l ly i s. Were I to give i t the
old name I should cal l i t the law of the co n s erv
ation of areas the more modern wri ters,however
,
spea k of i t as the con servation of momen t of mo
men tum, a n expression which exhibits the n ature
of the prin ciple in a more defin i te man n er.
-
TIMEAND TIDE .I do not see how to give a ny very accurate
i l l u stration of what th i s law m ean s,but I must
make the attempt,and i f you th i n k the i l l ustration
ben eath the d ign i ty of th e subj ect, I ca n on ly
plead the d iffi cu lty of mathem a ti cs as an excuse.
Let us suppose that a bal l - room is fairly fi l led
wi th dan cers, or those w i l l i ng to dan ce, a n d that
a merry waltz i s being played ; the couples have
formed,a n d the floor i s occupied wi th pa i rs who
are wh irl in g rou n d a n d roun d in that del ightfu l
amusemen t . Some couples drop out for a whi le
a n d others strike in ; the fewer couples there are
the wider i s the ran ge arou n d which they can
wa l tz , the more n umerou s the couples the less
in d ividual ran ge wi l l they possess . I Wan t you to
real i ze that i n the progress of the dance there i s
a certai n total quan ti ty of spin at a n y momen t
in progress ; thi s Spi n i s partly m a de up of the
rotation by which each d a n cer revolves roun d his
partn er,a n d partly of the ci rcu lar orbi t abou t the
room which each couple en deavours to desc r ibe .
I f there are too many couples o n the floor for the
gen eral en j oymen t of the dan ce,then both the orbi t
a n d the a n gular veloci ty of each couple wi ll b e
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TIME AND TIDE. 63,
restricted by the i nterference wi th their neighbours .
We may,however, assert that so long as the dance
i s i n fu l l swin g the total quan tity of sp in,partly
rotational a n d partly orbital,wi l l remai n con stan t .
When there are but few couples the u n impeded
rota t ion a n d the large orbits wi l l produce as much
spin as when there i s a much larger number of
couples,for in the l a tter case the d im i n i shed
freedom wil l lessen the quan ti ty of spin produced
by each i n dividual pai r. I t wi l l sometimes happen
too that col l is ion wi ll ta ke pl a ce,but the sl ight
d iversions thus aris in g on ly in crease the general
merriment,so that the total quan t ity of spin may
be sustain ed,even though one or two couples
are placed tempora ri ly li a r s a ’e co m éa t . I have
in voked a ball - room for the purpose of bri n gin g
out what we may cal l the law of the con servation
of spin . No m a tter how much the i n d ividual per
formers may chan ge,o r n o matter what v icis s i
tudes arise from thei r col l i s ion a n d other mu tual
action s,yet the total quan ti ty of spin remains
Let us look at the earth-moon system . The
law of the conservat i on of moment of momen tum
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64 TIME AND TIDE.
may,with suffi cien t accuracy for ou r presen t
pu rpose,be in terpreted to mean that the tota l
quan t i ty of spin in the system remain s un al tered .
I n our system the spin i s threefold ; there i s
fi rst the rotation of the earth on its axi s, there i s
the rotation of the moon o n i ts ax is,a n d then
there i s the orbi tal revolu tion of the moon around
the earth . The law to which we refer asserts that
the total quanti ty of these three spin s,each est i
mated in the proper w a y, wil l remain un altered .
I t matters n o t that t ides m a y ebb a n d flow, or that
the d istribu tion of the spin sha l l va ry, bu t i ts tota l
amou n t rem a in s inflexib ly con stan t. On e cons t it u en t of the total amoun t —that i s, the rotationof the moon o n i ts axi s— i s so ins ign ifican t
,that
for ou r presen t pu rposes i t may be en ti rely d is r e
garded . We m a y therefore assert that the amoun t
of spin in the earth , due to i ts rotation rou n d i ts
axi s,added to the amoun t of spin in the moon
due to i ts revolut ion round the earth,remain s
un al terable. I f o n e of these quan ti t ies change by
in c r ease or by dec r ease,the other must correspon d
in g ly chan ge by decrease or by i ncrease . I f, there
fore, from a ny cause, the earth began to Spin a l i t tl e
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66 TIME AND TIDE .
Were the ea rth a n d the moon both rigid bodies,
then there cou ld be of course no t i des on the
earth , for i f rigid i t i s devoid of ocean . Th e
rotat ion of the earth on i ts axis wou l d therefore
be absolu tely withou t chan ge,and therefore the
necessary condi tion of the conservat ion of s p’n
would b e very simply attain ed by the fact that
nei ther of the con st ituent parts chan ged . The
earth,however
,not being en t i rely rigid
,and bein g
subject to tides,th i s s imple state of th i n gs can not
con tinue ; there must be s ome chan ge in progress.
I have al ready shown that the fa ct of the
ebbi n g and the flowing of the t ide necessi tates an
expen d i ture of en ergy,and we saw that thi s energy
must come either from that stored up in the earth
by i ts rotat ion , or from that possessed by the
moon in vi rtue of its d istance a n d revolu tion . The
law of the conservat ion of spin wi l l enable us to
decide at on ce as to when ce the t ides get their
en ergy. Suppose they took i t from the moon,the
moon would then lose i n en ergy,a n d consequen tly
come nearer the earth . The quan t i ty of spin con
tr ibu ted by the moon wou l d therefore be lessen ed,
and accordingly the spin to b e made up by the
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TIME AND TIDE. 67
earth wou ld be increased . That means , of cou rse,
that the veloc i ty of the earth rotatin g on i ts axi s
must be in creased , and th i s aga in wou ld n eces s i
tate an i ncrease i n the earth ’s rotation a l energy.
I t: can be shown , too, that to keep the total spi n
rig ht, the en er g y of the earth would have to gain
more than the moon wou ld have lost by revolving
in a small er orbi t . Thu s we find that the tota l
quant i ty of energy i n the system would be i n creased .
Thi s woul d lead to the absurd resu l t that the act ion
of the t ides manufactu red energy in our system .
Of course, such a doctrin e can n ot be true ; i t wou ld
amoun t to a perpetual motion ! We might as
wel l t ry to get a steam-en gine which wou l d
produce en ough heat by friction n o t on ly to
supply i ts own boi lers,bu t to sati s fy the therma l
wan ts of the whole pari sh. We must therefore
adopt the other al ternative. The tides do not
draw th ei r energy from the moon ; they draw i t
from the store possessed by the earth in vi rtue
of i t s rotation .
We ca n n o w state the end of th i s rather long
discussion in a very simple a n d brief manner.
Energy ca n on ly be yielded by the earth at theE 2
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68 TIME AND TIDE .
expense of some of the speed of i ts rota tion . The
t ides mu st therefore cause the ea rt h to revolve
more slowly i n other words,t/zc t ides a r e in cr ea s ing
t/ze lcng tk of Me day.
The earth therefore loses some of i ts veloci ty
of rotat i on con sequen tly i t does less than i ts due
share of the total quan t ity of spi n,a n d an increased
qu a ntity of spi n must therefore be accompl ished
by the moon ; bu t th is can on ly be don e by an
en largement of i ts orb i t. Thus there are two gr eat
consequen ces of the tides in the earth-moon system
the days are gett in g lon ger, the moon i s reced ing
further.
These poi n ts are so importan t that I shal l try
and i l l u strate them in an other way, which w i l l
show,at al l even ts
,that o n e a n d both of these tidal
phenomena commend themselves to ou r common
sense . Have we n o t shown how the tides in thei r
ebb a n dflo w are in ces s a n tly ‘p r o du cm g friction ,a n d have we n o t al so l iken ed the earth to a great
wheel ? When the driver wan ts to stop a rai lway
trai n the brakes are pu t o n,a n d the brake i s merely
a con trivan ce for applyin g fri ction to the ci rc um
feren ce of a wheel for the purpose of checki ng its
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TIME AND T IDE. 69
motion . Or when a great weight is bein g lowered
by a crane,the motion i s checked by a ban d which
appl ies fri ction on the c i rcumferen ce of a wheel
arra n ged for the special purpose. Need we then
be su rprised that the frict ion of the t ides acts l ike
a bra ke o n the ea rth , a n d gradual ly ten ds to check
its mighty rotation ? The progress of l en gthen in g
the day by the t ides i s thus read i ly i n tel l igible . I t
i s n o t quite so easy to see why the ebbi n g a n d the
flowi n g of the tide o n the ea rth shou ld actual ly
have the effect of mak in g the moon to retrea t th is
phen omen on i s in deferen ce to a profoun d law of
n ature,which tel l s u s that act ion and reaction are
equal a n d opposite to'
each other . I f I might
ven ture o n a very homely i l lustrat ion , I may say
that the moon,l ike a troublesome fel low, i s co n
s t a n t ly an noyin g the earth by draggin g i ts wa ters
backward and forward by mean s of t ides and the
ea rth,to free i tsel f from thi s i rri tat i n g in terferen ce,
tries to push off the aggressor a n d to make h im
move further away.
An other way in which we ca n i l l ust rate the
retrea t of the moon as the i n evita ble con sequen ce
of t idal fri ction i s shown i n the adj oin in g figure, i n
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7 0 TIME AND TIDE.
which the large bo dy
E represents the earth ,
and the smal l body M
the moon . We may for
simpl ici ty regard the
moon as a poin t, and
as thi s attracts each
particle of the earth ,
the total effect of the
moon o n the earth may
be represen ted by a
sin gle force . By the
la w of equal ity of action
and reaction,the force
of the earth on the
moon i s to be r ep re
sen ted by an equa l and
Opposite force . I f there
were n o t ides then the
moon’
s force wou ld of” Lee course pass through the
earth’s centre ; bu t as the effect of the moon i s to
slacken the earth’s rotat ion,i t fol lows that the total
force does not exact ly pass through the l i ne o f the
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TIMEAND TIDE. 7 1ea rth
’
s centre, but a l i ttle to o n e s ide, i n order to
pu l l the opposi te way to that i n which the ea rth
is turn in g,and thus bring down i ts speed . We
may therefore decompose the ea r th’
s tota l fo r te
on the moon i n to two par ts,one of wh ich tends
d i rectly towa rds the earth ’s centre,whi le the other
acts tangen t ial ly to the moon’
s orb it . The central
force i s of course the main gu i d i ng power which
keeps the moon i n i ts path ; bu t the in cessan t
tan gent ial force con stan t ly tends to send the moon
o u t further and further,and thu s the growth of i ts
o rbi t can be accounted for .
We therefore con cl ude final ly,that the t ides are
mak ing the day lon g er and sending the moon away
further. I t i s the developmen t of the con sequen ces
of these laws that special ly deman ds our atten tion
i n these lectures . We must have the coura ge to
look at the facts u nflin chin g ly, a n d deduce fromthem al l the won drous consequences they i nvolve.
Thei r poten cy arises from a characteristi c feature
—they are u n i n termitt in g . Most of the greatastron omical chan ges wi th wh ich we are ord i n ari ly
fa mil iar are real ly periodic : they gradual ly in
crease in o n e d i rection for years , for centuries, or
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7 2 TIME AND TIDE .
for untold ages bu t then a change comes , and the
i n crease i s changed in to a decrease,so that after
the lapse of becomi n g periods the origin al state
o f thin gs i s restored . Such period i c phen omen a
aboun d i n astron omy. There i s the an n ualflu ct uation of the season s ; there i s the eighteen or n in e
teen year period of the moon ; there i s the great
period of the precess ion of the equ i n oxes,amou n t
ing to twen ty-s ix thousa nd years ; a n d then there
i s the stupendous An n us Magn us of hu n dreds of
thousan ds of years , duri n g which the earth’s orbi t
i tsel f breathes in a n d out i n respon se to the attrae
t ion of the plan ets . B ut these period ic phenomen a,
however important they may be to us mere
creatures of a day, a r e i n sign ifica n t i n thei r effects
on the grand evolu ti on through which the celestia l
bod ies are pass in g. The real ly poten t agen ts i n
fashion i n g the un iverse are those which,however
s low or feeble they may seem to be, are in ces
sant in thei r act ion . The effect which a cau s e
i s competen t to produce depen ds n o t alon e
Upon the i n ten s i ty of that cause, but also upon
the t im e'
d u r in g which i t has been in operation .
From the phen omen a of geology, as wel l as from
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7 4 TIME AND TIDE .
which the studen t of natu re shou ld most n arrowly
watch,for they are the real arch i tects of the
u n iverse .
The tidal consequences which we have al ready
demon strated are emphatical ly of th is non -pe
r io dic class—the day i s a lways len gthen i n g, the
moon i s always retreati ng . To—day i s longer than
yesterday ; to-morrow wi l l be lon ger than to -day.
I t can n ot be sa id that the change i s a great one ;
i t i s in deed too smal l to be appreciable even by
our most del icate observation s . I n one thousan d
yea rs the alteration i n the length of a day is on ly
a s n a ll fract ion of a secon d ; but what may be a
very smal l matter i n one thousand years can b e
come a very large one in man y mi l l ion s of years .
Thus i t is that when we stretch ou r View through
immen se vistas of time past,or when we look for
ward through immeasurable ages o f t ime to come,
the al terat ion i n the len gth of the day wi l l assume
the most startl ing proportion s, a n d i nvolve the
most momentous consequences.
Let us first look back. There was a time when
the day, in stead of bein g the twen ty-four hours we
now have, must have been only twenty- three hours,
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TIME AND TIDE . 7 5
How man y mi ll ion s of years ago that was I do
n o t preten d to say , n o r i s the poi n t material for
our argumen t ; s uffice i t to say, that assumin g, as
geology assu res us we may assume, the existen ce
of these aeon s of mi l l ions of years,there was on ce
a time when the d ay was n o t on ly o n e hour
shorter,bu t was even several hours less than i t i s
at presen t . Nor n eed we stop our retrospect at a
day of even twen ty,or fi fteen
,or ten hours
lon g ; we shal l at on ce proj ect our glan ce back to
an immeasu rably remote epoch,at wh ich the ea rth
was spin n i n g round in a t ime on ly one s ixth or
even less of the len gth of the presen t day. There
i s here a reason for our retrospect to halt,for at
some even tful period,when the day was abou t
three or four hours lon g,the earth must have been
in a con dition of a very cri tical kind .
I t i s wel l kn own that fearful acciden ts occasion
al ly happen where large gri n ds tones are bein g
driven at a h igh speed . The veloci ty of rotation
becomes too great for the tenac i ty of the stone to
w i thstan d the stress ; a rupture takes place, the
ston e fl i es i n pieces, and huge fragments are
hurled around . For each particu lar grin dston e
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7 6 TIMEAN D TIDE .there i s a certa i n spec ial velocity depend in g upon
i ts actual material s a n d character, at which i t would
i nevitably fly in pieces . I have on ce before l ikened
our earth to a whee l ; now let me l iken i t to a
grin dstone. There i s therefore a certai n cri t ical
veloci ty of rotation for the earth at wh ich i t wou ld
be on the brin k of rupture . We can n ot exactly
say,i n ou r ign oran ce of the in ternal con st i tution
of the earth,what len gth of day would be the
shortest possib le for ou r earth consisten tly wi th
the preservat ion of i ts i n tegri ty ; we may, how
ever,assume that i t wi l l be abou t three or four
hours,or perhaps a l ittle less than three The
exact amou n t, however, i s n o t real ly very materi a l ;
i t wou ld be sufficien t for ou r argumen t to assert
that there i s a certain min imum len gth of day for
which the earth c a n hold together. I n our retro ~
spect,therefore
,through the abyss o f t ime our
view must be bounded by that state of the earth
when i t i s revolvi n g in this cri t ical period . With
what happened before that we shal l n o t at presen t
con cern ou rselves . Thus we look back to a time at
the begi n n in g of the presen t order of thin gs,when
the d a y w a s on ly some th r ee or four hours lon g.
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T IMEAND TIDE. 7 7Let us n o w look at the moon , a n d ex a mi n e
where i t must have been during these past ages .
As the moon i s grad ual ly gett ing fu rther and fur
ther from u s at presen t, so, look in g back in to pa st
t ime,we find that the moon was n earer a nd n earer
to the earth the further back our view exten ds ;
in fact, con centrat in g our atten t ion solely on essen
t ia l features, we m a y say that the path of the
moon i s a sort of Spira l which win ds round and
round the earth,gradual ly gettin g larger, though
with extreme slowness . Lookin g back we see th is
spiral gra dual ly coi l in g in a n d i n , u n t i l in a retro
spect of m i l l ion s of years,i nstead of i ts d i stan ce
from the earth bein g miles,i t must have
been much less . There was a time when the
moon was on ly m i les away ; there was
a time man y mi l l ion s of years ago,when the moon
was on ly mi les away. Nor n eed we here
stop our argumen t we may look further a n d
fu rther back,a n d fol low the moon ’s spi ra l path as
i t creeps i n a n d i n towards the earth,unti l at last
i t appears actual ly in con tact with that great globe
of ours, from which i t i s n o w separated by a quarter
of a mil l ion of mi les .
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7 8 TIME AND TIDE .
Surely the tides have thus led us to the know
ledge o f an astound ing epoch in ou r earth ’s past
history, when the earth i s spin n ing round in a few
hou rs, and when the moon i s, practical ly speaki n g,in contact wi th i t . Perhaps I should rather say,
that the material s of ou r present moon were i n th i s
s i tuation , for we would hardly be en ti tled to assume
that the moon then possessed the same globular
form i n wh ich we see i t now . To form a j ust
apprehen sion of the true n atu re of b o'
fh bod ies a t
thi s cri tica l epoch,we must study thei r con curren t
h istory as i t i s d isclosed to us by a total ly d i fferen t
l ine o f reason in g .
D rop,then
,for a moment al l thought of t ides ,
a n d l et u s brin g to our a id the laws of heat, which
wi l l d isclose certain facts i n the ancien t history
of the earth-moon system perhaps as astou n d i ng
as those to which the ti des have con ducted us .
I n o n e respect we may compare these laws of heat
wi th the laws of the t ides ; they are both al ike
non -periodic,thei r effects are cumulat ive from age
to age,and imagin ation can hardly even impose
a l im i t to the m a gn ificen ce of the works they can
accompl ish . Our argumen t from heat i s founded
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TIME AND TIDE . 7 9
o n a very simple matter. I t i s qu i te obvious that
a heated body tends to grow cold . I am not now
speak i ng of fi res or of actual combust ion whereby
heat i s produced ; I am speaking merely of such
heat as would be possessed by a red-hot poker
a fter bein g taken from the fi re, or by an i ron casti ng
after the metal has been run i n to the mould . I n
such cases as thi s the general law holds good ,
that the heated body tends to grow cold . The
cool in g may be retarded no doubt i f th