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.

!We zi mnbrrs of the fianbmr gustitutionI DEDICATE

THIS LITTLE BOOK.

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.

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.

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

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

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

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

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

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

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

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

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

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

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 .

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 .

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

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

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 .

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

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

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

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

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

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

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

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

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,

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

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.

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 .

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

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