TIDES. 



tliit whilll the carlh is moving round the luii, it alfo de- 

 fcribi-s a circle round that centre of gravity, going as many 

 tiiuci round it in one revolution about the fun as there arc 

 Ijnations or courfc» of the moon round the fun in a year ; 

 ii.d therefore the earth is conllantly falling towards the 

 moon from a tangent to the circle which it defcribcs round 

 the faid common centre of gravity. Let M {Jig. ii.) be 

 tiie moon, T W part of the moon's orbit, and C the centre 

 of gravity of the earth and moon : whilft the moon goes 

 rouud her orbit, the centre of the earth defcribes the circle 

 Jgt round C, to which circle^u^ is a tangent ; and, .-liere- 

 fore, when the moon has gone from M a little beyond W, 

 the earth has moved from g to e, and in that time lias fallen 

 towards the moon, from the tangent at a to e, and fo on 

 r6uiid the whole circle. 



From the above reafoning it appears, that the parts of 

 the earth dircclly under the moon, or that have the moon 

 in their zcr.ith, and alfo thofe in the nadir, or places dia- 

 metrically oppolite to each other, will have the flood, or 

 )ii^h water at the fame time. 



Moreover, thofe parts of the earth, where the moon ap- 

 pears ia the horizon, or gc° dillant from the zenith and nadir, 

 will liave the ebbs, or lowcfl waters. 



It is evident that, by the motion of the earth on its axis, 

 the moll elevated part of the water is carried beyond the 

 moon in the direction of the rotation. The water continues 

 to rife after it has palTed direAly under the moon, though 

 the immediate aftion of the moon there begins to decreafc, 

 and comes not to its grcatert elevation till it has got half a 

 quadrant fartlic-. It continues alfo to defcend after it has 

 pafTed at 90° diftance from the point below the moon, though 

 the force which the moon adds to its gravity begins to decreafe 

 there. For ftiU the action of the moon adds to its gravity, and 

 makes it defcend till it has got half a quadrant farther ; the 

 greateft elevation, therefore, is not in the points which are in a 

 line with the centres of tlie earth and moon, but about half a 

 quadrant to the eaft of thefe points in the direftion of the 

 motion of rotation. Thus in open feas, where the water 

 flows freely, the moon, M, {Jig. 10.) is generally pafl the 

 nortli and fouth meridian, asat^, when the high water is 

 at Z and at n : the reafon of which is plain, becaufe the 

 moon afts with fomc force after flie has paft the meridian, 

 and thereby adds to the Ifbratory or waving motion, which 

 the water acquired when (he was in the meridian ; and, there- 

 fore, the time of high water is not precifely at tl-.e time of her 

 coming to the meridian, but fome time after. 



Befides, the tides anfwer not always to the fame diftance 

 of the moon from the meridian at the fame places ; but are 

 varioufly affeAed by the aftion of the fun, which brings them 

 on fooncr when the moon is in her firft and third quarters, 

 and keeps them back later when fhe is in her fecond and 

 fourtli ; becaufe, in the /ormer cafe, the tide raifed by the 

 fun alone, would be earlier than the tide raifed by the moon, 

 and in the latter cafe later. 



For the further illuftration of the principle upon which 

 lunar tides depend, wc (hall fuppofe, with Dr. Young, that 

 the earth were wholly fluid, and the fame part of its furface 

 were always turned towards the moon ; in which cafe, the 

 pole of the fpheroid being immediately under the moon, the 

 lunar tide would remain ftationary ; the greateft elevation 

 being at the points neareft to the moon and fartheft from 

 her, and the greateft deprcfiion in the circle equally diftant 

 from thefe points ; the elevation, however, being twice as 

 great as the deprellion, on account of the fmaller furface to 

 which it is confined. The aftual height of this elevation 

 would probably be about 40 inches, and the depreffion 20, 

 making together a tide of five feet. If alfo the waters were 



\2 



capable of afTuming inftantly fuch a form as the equilibrium 

 would require, the fummit of a fpheroid equally elevated 

 would dill be direftcd towuids the moon, notwithftanding 

 the earth's rotation. This may be called the primitive tide 

 of the ocea.1 : but on account of the perpetual change of 

 place whicli is required for the accommodation of the fur- 

 face to a fiinilar pofition with refpeft to the moon, as the 

 earth revolve.;, l!ie form muft be materially difl'erent from 

 that of fuch a fpheroid of equilibrium. The force employed 

 in producing this accommodation, may be eftimated by 

 conlidering tlic adual furface of the fea as that of a wave 

 moving on the fpheroid of eq'uihbrium, and producing in the 

 water a fuflicient velocity to preferve the aftual form. We 

 may deduce, fays Dr. Young, from this mode of confidering 

 the fubjeft, a tlieory of the tides which appears to be more 

 fimple and fatisfaftory than any which has yet been publi(h- 

 ed : and by comparing the tides of narrower feas and lakes 

 with the motions of pendulums fufpended on vibrating cen- 

 tres, we may extend the theory to all pofTible cafes. 



If the centre of a pendulum be made to vibrate, the vibra- 

 tions of the per.diilum itfelf, when they have arrived at a ftate 

 of permanence, w'ill be performed in the fame time with 

 thofe of the centre ; but the motion of the pendulum will be 

 either in the fame direftion with that of the centre, or in a 

 contrary direftion, accordingly as the time of this forced 

 vibration is longer or (horter than that of the natural vibra- 

 tion of the pendulum ; and in the fanie manner it may be 

 (hewn that the tides, either of an open ocean or of a con- 

 fined lake, may be cither direft or inverted with refpeft to 

 the primitive tide, which would be prodiced, if the waters 

 always affumed the form of the fpheroid of equilibrium, ac- 

 cording to the deplli of the ocean, and to the breadth as well 

 as the depth of the lake. In the cafe of a direft tide, the 

 time of the pafTage of the luminary over the meridian muft 

 coincide with that of high water, and in the cafe of an inverted 

 tide with that of low water. 



In order that the lunar tides of an open ocean may be 

 direft, or fynchronous, its depth muft be greater than 1 3 

 miles, and for the folar tides than 14. The lefs the depth 

 exceeded thefe limits, the greater the tides would be, and 

 in all cafes they would be greater than the primitive tides. 

 But in faft the height of the tides in the open ocean is 

 always far (hort of that which would be produced in this 

 manner ; it is therefore improbable that the tides are ever 

 direft in the open ocean, and that the depth of the fea is fo 

 great as 13 miles. 



In order that the height of the inverted or remote lunar 

 tides may be five feet, or equal to that of the primitive tides, 

 the depth of the open fea muft be 6i- iniles ; and if the height 

 is only two feet, which is perhaps not far from the truth, the 

 depth muft be 3^ miles. 



The tides of a lake or narrow fea differ materially from 

 thofe of the open ocean, fince the height of the water 

 fcarcely undergoes any variation in the middle of the lake ; 

 it muft always be high water at the eaftern extremity when 

 it is low water at the weftern : and this muft happen at the 

 time when the places of high and low water, with refpeft to 

 the primitive tides, are equally diftant from the middle of 

 the lake. 



The tides may be direft in a lake 100 fathoms deep and 

 lefs than 8° wide ; but if it be much wider, they muft be 

 inverted. Suppoiing the depth a mile, they will be direft 

 when the breadth is lefs than 25° ; but if a fea, like the 

 Atlantic, were 50 or 60 degrees wide, it muft be at leaft 

 four miles deep, in order that the time of high water might 

 coincide with that of the moon's fouthing. 



Hitherto we have confidered the motion of the water as 



free 



