TIDES. 



If the particles of the earth did not gravitate towai-d 

 C3ch other, but toward the moon only, the dillances be- 

 Tvvixt tlie parts of the cjrth that are fuppoicd to be neareit 

 the moon, and the central parts, would continually increafc, 

 becaufe of their greater celerity in falling ; and the dillancc 

 betwixt the central parts, and tlie parts that arc fartheft. 

 from the moon, would increafe continually at the fame 

 time ; thefe being left behind by tiie central paits, which 

 they would follow, but with a lefs velocity. Thus the 

 figure of the earth would become more and more oblong, 

 tiiat diameter of it which pointed toward the moon conti- 

 nually increafing. 



But there is another reafon why the earth would foon 

 aiTunie an oblong fpheroidal form, if its parts were allowed 

 to fall freely by their gravity towards the moon's centre ; 

 for the lateral parts of the eartii, or thofc which arc at the 

 diftance of a quarter of a circle from the point which is 

 direftly below the moon, and the central parts defcending 

 with eqn.il velocities toward the fame point, viz. the centre 

 of the moon, in approaching to it, would manifeftly ap- 

 proach, at the fame time, to each other ; and their diftance 

 becoming lefs, the diameters of the earth paffing through 

 them would be diminifhed, fo that the diameters of the 

 earth that point toward the moon would increafe, and thofe 

 diameters of the earth that are perpendicular to the line 

 joining the centres of the earth and moon, would decrcafe 

 at tlie fame time, and render the figure of the earth ftill 

 more oblong for this reafon. 



Let us now allow the parts of the earth to gravitate to- 

 wards its centre ; and, as this gravitation far exceeds the 

 aftion of the moon, and much more exceeds the differences 

 of her aftions on different parts of the earth, the effeft re- 

 fulting from the inequalities of thefe aftions of the moon, 

 will be only a fmall diminution of the gravity of thofe parts 

 of the earth which it endeavoured in the former fuppofition 

 to feparate from its centre, and a fmall addition to the 

 gravity of thofe parts which it endeavoured to bring nearer 

 to its centre ; that is, thofe parts of the earth which arc 

 neareft to the moon, and thofe which are fartheft from her, 

 will have their gravity toward the earth fomewhat abated ; 

 whereas the lateral parts will have their gravity increafed ; 

 fo that if the earth be fuppoled fluid, the columns from 

 the centre to the neareft, and to the fartheft parts muft 

 rife, till, by their greater height, they be able to balance 

 the other columns, whofe gravity is either not fo much 

 diminifhed, or is increafed by the inequalities of the aftion 

 of the moon. And thus the figure of the earth muft ftill 

 be an oblong fpheroid. 



Let us now confider the earth, inftead of falling toward 

 the raoon by its gravity, as projefted in any direftion, fo as 

 to move round the centre of gravity of the earth and 

 moon ; it is manifeft, that the gravity of each particle to- 

 ward the moon will endeavour to bring it as far from the 

 tangent, in any fmall moment of time, as if the earth were 

 allowed to fall freely toward the moon ; in the fame man- 

 ner as any projeftile, at our earth, falls from the line of 

 projeftion as far as it would fall by its gravity in the per- 

 pendicular in the fame time. Confequently the parts of the 

 earth neareft to the moon will endeavour to fall fartheft 

 from the tangent, and thofe fartheft from the moon will en- 

 deavour to fall leaft from the tangent, of all parts of the 

 earth ; and the figure of the earth, therefore, will be the 

 fame as if the earth fell freely toward the moon ; that is, 

 the earth will ftill afFeft a fpheroidal form, having its longeft 

 diameter direfted toward the moon. 



In order to underftand this theory, it muft be carefully 

 confidered, that it is not the aftion of the moon, but the 

 Vol,. XXXV. 



inequalities in that a^ion, tliat produce any variation from 

 the fpherical ficure ; and that if this aftion were the fame 

 in all the particles as in the central parts, and operating in 

 the fame direftion, no fiich change would enfue. 



For the farther illuftration of the preceding obfervations, 

 we muft perceive that the waters at Z [Plate I. Grot^raphy, 

 fig. lo.) on the fide of the earth ABCDEFGH, next 

 to the moon M, are more attraftcd than the central parts 

 of the eartli, O, by the moon, and tiie central parts are morp 

 attraftcd by her than the waters on the oppolite fide of the 

 earth at n ; and therefore the diftance between the earth's 

 centre and the waters on its furface, under and oppofite to 

 tlie moon, will be increafed. For let H, O, and D be three 

 bodies, all equally attrafted by the liody M, and they will 

 all move equally fall toward it, their mutual diftances from 

 each other continuing the fame. If the attradlion of M is 

 unequal, then that body wliicli is moft ftrongly attrafted 

 will move fafteft, and this will increafc its diftance from the 

 other body. Confequently, by the law of gravitation, M 

 will attradl H more ftrongly than it docs O, by which the 

 diftance between H and O will be increafed ; and a fpec- 

 tator in O will perceive H rifing higher toward Z. In hke 

 manner O, being more ftrongly attrafted than D, will move 

 farther toward M than D does ; and therefore the diftance 

 between O and D will be increafed ; and a fpeftator in O, 

 not perceiving his own motion, will fee D receding farther 

 from him towards n ; all effefts and appearances being the 

 fame, whether D recedes from O, or O from D. 



Suppofe now there is a number of bodies, as A, B, C, D, 

 E, F, C H, placed round O, fo as to form a flexible or 

 fluid ring ; then, as tlie whole is attrafted toward M, the 

 parts at H and D will have their diftance from O increafed ; 

 whiUl the parts at B and F, being nearly at the Came dif- 

 tance from M as O is, will not recede from one another ; 

 but rather, by the oblique attraftion of M, they will ap- 

 proach nearer to O. Hence the fluid ring will form itfelf 

 into an ellipfe ZIBLnKFNZ, whofe longer axis n O Z 

 produced, will pafs through M, and its fhorter axis, B O F, 

 will terminate in B and F. Let the ring be filled with fluid 

 particles, fo as to form a fphere round O ; then, as the 

 whole moves toward M, the fluid fphere, being lengthened 

 at Z and n, will affume an oblong or oval form. If M is 

 the moon, O the earth's centre, ABCDEFGH the fea 

 covering the earth's furface, it is evident that, vvhilft the 

 earth by its gravity falls towards the moon, the water di- 

 reftly below her at H will fwell, and gradually rife toward 

 her ; and alfo the water at D will recede from the centre, 

 (or, ftriftly fpeaking, the centre recedes from D, ) and rife 

 on the oppofite fide of the earth ; whilft the water at B and 

 F is depreffed, and falls below the former level. Hence, 

 as the earth turns round its axis from the moon to the 

 moon again in about 24|- hours, this oval of water muft Ihift 

 with it ; and thus there will be two tides of flood and two 

 of ebb in that time. 



Some perfons have found a difficulty in conceiving how, 

 agreeably to the principles above ftated, the earth can fall 

 towards the moon by the power of gravity, when the moon 

 is full, or in oppofition to the fun ; fince the earth revolves 

 about the fun, and muft continually fall towards it ; and if 

 the earth is conftantly falhng towards the moon, they muft 

 at laft come together. In order to obviate this difficulty, 

 it has been fuggefted, that it is not the centre of the earth 

 that defcribes the annual orbit round the fun, but the com- 

 mon centre of gravity of the earth and moon, the diftance of 

 which from the earth's centre, dividing 240,000 miles, the 

 moon's diftance from the earth, by 40, the excefs of the 

 earth's weight above that of the moon, is 60CO miles ; and 

 4 K that 



