TIDES. 



•ncM,. .> neurcU thf rarth. The height to which the water 

 .> f..und to rife, upon coalU of the open and deep ocean, is 

 aifrtcable enough to lhi« computation. 



Dr. Horlley eftimates thr force of the moon to that ot 

 the fun as 5.0469 to I. Newton Princip. lib. in. fed. 1... 

 prop. l6, ^7,apuJ Newt. Op. Ed. Hordey, vol. 111. p. 104. 

 &c and "Maclauri.i's Di(T. de Caufa Phylica Fluxus & 

 Rertuxus Maris, apud Phil. Nat. Princ. Math. Comment. 

 le Seur & Jacquier, torn. iii. p. 272. 



V It mull be obfcrvcd that the fpring-lides do net 

 happen precifely at new and full moon, nor the neap-tides 

 at the quarters, but a day or two after, (at lead two, and 

 commonlv three tides after,) becaufc, as in other cafes, fo 

 in this, the cffeft is not greateil or lead when the immediate 

 influence of the caufe is greated or kail. Ah '■ g- the 

 gn-ateft heat is not on the folilitial day, when the immediate 

 aflion of the fun is greatcft, but fomc time after. 



That this may be more clearly underllood, let it be con- 

 fidcred, that though the aftions of the fun and moon were 

 to ceafc this moment, yet the tides would continue to have 

 t'r-.tir courfc for fome time ; for the water, where it is now 

 highell, would fubfide, and flow down on the parts that are 

 lower, till, by the motion of dcfcent, being there accumu- 

 hted to too great a height, it would neceffarily return again 

 to its firft place, though ioi a lefs meafure, being retarded 

 by the refiftance arifiiig from the attraftion of its parts. 

 Thus it would for fome time continue in an agitation like to 

 that in which it is at prcfent. The waves of tlie fea, that 

 continue after a ftorm ceafes, and every motion almofl of a 

 fluid, may illuftrate this. 



The refinance of fluids, in general, fays Dr. Young, is 

 as the fquare of the velocity, confequently it muft be rhuch 

 greater for the lunar than for the folar tide, in proportion 

 to the magnitude of the force ; and the acceleration of the 

 lunar tide produced by this caufe muft be greater than that 

 of the folar : hence it may happen, that when the lunar Lde 

 occurs two or three hours after the tranfit. of the moon, the 

 folar tide may be three or four hours after that of the fun, 

 fo as to be about an hour later, at the times of conjunftion 

 and oppotition, and the tides will be higheft when the moon 

 paflTes the meridian about an hour after the fun ; while at 

 the precife time of the new and full moon, the lunar tide 

 will be retarded about a quarter of an hour by the effeft of 

 the folar tide. 



4.. The different diftances of the moon from the earth 

 iiroduce a fenfible variation in the tides. When the nioon 

 approaches the earth, her aftion on every part increafes, 

 and the differences of thataftion on which the tides depend, 

 mcreafe. For her aftioii increafes as the fquaies of the 

 diflancis decreafe ; and though the differences of the dif- 

 tances themfelves be equal, yet there is a greater difpropor- 

 tion betwixt the fquarcs of lefs, than the fquares of greater 

 quantities i e. g. ^ exceeds 2, as much as 2 exceeds i ; but 

 the fquare of 2 is quadruple of the fquare of i, whilft the 

 fquare of 3 (ijja. 9) is little more than double the fquare 

 of 2 [viz. 4). 



Thus it appears, that by the moon's approach, her aftion 

 on the neareft parts increafes more quicltly than her ac- 

 tion on the remote parts ; and the tides, therefore, increafe 

 in a higher proportion as the diftancesof the moon decreafe. 

 Sir Ifaac Newton (hews, that the tides increafe in propor- 

 tion as the cubes ef the diftances decreafe, fo that the moon, 

 at half her prefent diftance, would produce a tide eight times 

 jfreater. 



The moon defcribcs an ellipfe about the earth, and in her 

 ixarcft diftance produces a tide fenfibly greater than at her 

 7 



greatell dillancc from the earth : and hence it is, that two 

 great fpring-tidcs never fucceed e.ich olh-r immediately ; 

 for if the moon be at her neareft dillance from the earth 

 at the change, fhe muft be at her greateft diftance at the 

 full, having, in the intervening time, fiiiifhed half a revolu- 

 tion ; and, therefore, the fpring-tide then will be much lefs 

 than the tide at the change was : ;ind for the fame reafou, 

 if a great fpring-tide happens at the time of full moon, the 

 tide at the enfuing change will be lefs. 



5. The fpring-tides are greateft about the time of the 

 equinoxes, i. e. about the latter end of March and Sep- 

 tember, and leaft about the time of the folftices, i. f. to- 

 ward the end of June and December ; and the neap-tides 

 are leaft at the equinoxes and greateft at the folftices ; {o 

 that the difference betwixt the fpring and the neap-tides is 

 much lefs confiderable at the folftitial than at the equinoc- 

 tial feafons. In order to illuftrate and evince the truth of 

 this obfervation, it is manifeft, that if either the fun or moon 

 were in the pole, they could have no efFeft on the tides, for 

 their aftion would raife all the water at the equator to the 

 fame height, and any place of the earth, in defcribing its 

 parallel to the equator, would not meet, in its courfe, with 

 any part of the water more elevated than another, fo that 

 there could be no tide in any place. 



The efTeft of the fun or moon is greateft when in the 

 equinoftial ; for then the axis of the fpheroidal figure, 

 arifing from their aftion, moves in the greateft circle, and 

 the water is put into the greateft agitation ; and hence it is 

 that the fpring-tides produced, when the fun and moon ai-e 

 both in the equinoftial, are the greateft of any, and the 

 neap-tides are the leaft of any, about that time. 



But the tides produced when the fun is in either of the 

 tropics, and the moon in either of her quarters, are greater 

 t!' 'n thofe produced when the fun is in the equinoftial, and 

 the moon in her quarters, becaufe, in the firft cafe, the moou 

 is in the equinoftial, and in the latter cafe, the moon is in 

 one of the tropics ; and the tide depends more on the aftion 

 of the moon than that of the fun, and is, therefore, greateft 

 wh?n the moon's aftion is greateft. 



Hff^vever, it is necefTary to obferve, 6. That, becaufe 

 the f"i!n is nearer the earth in winter than in fimimer, i. e, 

 in Febru-vry and Oftober than in March and September, 

 t^: greaOjft fpring-tides are after the autumnal, and before 

 tit' vernal c^ainox. 



; . Since the greateft of the two tides happening in every- 

 diurnal revolution of the moon, or lunar day, i. e. about 

 24'' 50™, is that in which the moon is neareft the zenith, or 

 nadir ; for tliis rcaibn, while the fun 'is in the northern IJgns, 

 the greater of the two diurnal tides in our climates, is that 

 arifing from the moon above the horizon : when the fun is 

 in the fouthern figns, the greateft is that nrifing from the 

 m.oon below the horizon. 



In proof of this obfervation, let it be confidered, that 

 when the moon declines from the equator toward either 

 pole, one of the greateft elevations of the water follows 

 the moon, and defcribes nearly the parallel on the earth's 

 furface which is under that \vhich the moon, on account of 

 the diurnal motion, feems to defcribe ; and the oppofite 

 greateft elevation, being antipodal to that, muft defcribe a 

 parallel as far on the other fide of the equator ; fo that 

 while the one moves on the north fide of the equator, the 

 other moves on the fouth fide of it, at the fame diftance. 

 Now the greateft elevation which moves on the fame fide of 

 the equator, with any place, will come nearer to it than the 

 oppofite elevation, which moves in a parallel on the other 

 ide of the equator ; and, therefore, if a place is on the fame 



fide 



