TIDES. 



free from all refinance ; but wlierc the tides are dircft, they 

 rauft be retarded by the efFeft of a rcfillance of any kind ; 

 and where they are inverted, they mull be accelerated ; a 

 fmall refinance producing, in both cafes, a confiderable 

 difference in the time of high water. 



Where a confiderable tide is obferved in the middle of a 

 limited portion of the fea, it muft be derived from the cffeft 

 of the elevation or deprcflion of the ocean in its neighbour- 

 hood ; and fuch derivative tides are probably combined 

 in almoft all cafes with the ofeillations belonging to each 

 particular branch of the fea. 



Lunar tides, the rife and progrefs of which are fcientifi- 

 cally traced by Dr. Young, are fubjeft, independently of the 

 influence of the fun, to a variety of modifications, fome of 

 which we fliall fpecify in the fequel of this article. 



2. We have hitherto taken notice only of the aftion of 

 the moon in producing tides ; but it is manifell that, for 

 the fame reafons, the inequality of the fun's action on dif- 

 ferent parts of the earth would produce a like effeft, and 

 that this alone would caufe a like variation from the exaft 

 fpherical figure of a fluid earth. So that, in reality, there 

 are two tides every natural day from the aftion of the fun, 

 as there are in the lunar day from that of the moon, fubjeft 

 to the fame laws ; and the lunar tide, as we have obferved, 

 is fomewhat changed by the aftion of the fun, and the 

 change varies every day on account of the inequality between 

 the natural and the lunar day. Indeed, the effeft of the fun 

 in producing tides, becaufe of his immenfe diftance, muit be 

 confiderably lefs than that of the moon, though the gravity 

 toward the fun be much greater, the folar tide being, as 

 Dr. Young ftates it, only about two-fifths of the lunar. 

 For it is not the aftion of the fun or that of the moon, but 

 the inequalities in the aftions of each, which have any effeft. 

 The fun's diftance is fo great, that the diameter of the earth 

 is as a point compared to it, and the difference between the 

 aftion of the fun on the neareft, and that on the farthcft 

 parts, becomes, on this account, vaftly lefs than it would be 

 if the fun were as near as the moon. 



However, the immenfe bulk of the fun makes the effeft 

 ftill fenfible, even at fo great a diftance ; and, therefore, 

 though the aftion of the moon has the greateft fhare in pro- 

 ducing the tides, the aftion of the fun adds feniibly to it 

 when they confpire together, as in the change and full of 

 the moon, when they are nearly in the fame line with the 

 centre of the earth, and therefore unite their forces. Thus, 

 in conjunftion, or when the fun and moon are on the fame 

 fide of the earth, they both confpire to raife the water in 

 the zenith, and confequently in the nadir ; and when tl\ey 

 are in oppofition, that is, when the earth is between them, 

 whilft one makes high water in the zenith and nadir, the 

 other does the fame in the nadir and zenitii. Confequently, 

 in the fyzygies, or at new and full moon, the tides are the 

 greateft, and are what we call the fprlng-t'tdes. Moreover, 

 the aftion of the fun diminifhes the effeft of the moon's 

 aftion in the firft and laft quarters, becaufe the one raifes the 

 water in that cafe where the other depreffes it ; and there- 

 fore, in the quadratures tlic tides are the leaft, and are called 

 neap-tides. 



As the lunar tide is much larger than the folar tide, the 

 former muft always determine the time of high and low water, 

 which, in the fprlng and neap-tides, remains unaltered by the 

 effeft of the fun ; fo that in the neap-tides the aftual time of 

 low water is that of the folar high water ; but at the inter- 

 mediate times, the lunar high water is more or lefs accelerated 

 or retarded. The progrefs of this alteration may eafily be 

 traced by means of a fimple conftruftion. If we make a 



triangle, of which two of the fides are two feet and five feet 

 in length, the extern.il angle which they form being equal 

 to twice tlie diftance of the luminaries, the third fide will 

 Ihew prccifely the magnitude of the compound tide, and the 

 halres of the two angles oppofite to the firfl two fides the 

 acceleration, or retardation, of the times of high water be- 

 longing to the feparate tides refpeftively. Hence it appears 

 that the greateft deviation of the joint tide from the lunar 

 tide amounts to 1 1'' 48' in longitude, and the time corre- 

 fponding to 47 minutes, fuppofing the proportion of the 

 forces to remain always the fame ; t)ut in faft the forces in- 

 creafe in proportion as the cubes of the diftaiices of their 

 refpeftive luminaries diminifli, as well as from other caufcs ; 

 and in order to determijie their joint cffefts, tlit lengths of 

 the fides of the triangle muft be varied accordingly. In 

 fome ports, from a combination of circumftances in the 

 channel, by which the tides reach them, or in the feas, in 

 which they originate, the influence of the fun and moon may 

 acquire a proportion fomewhat different from that which 

 naturally belongs to them : thus at Breft, the influence of 

 the moon appears to be three times as great as that of the 

 fun ; when it is ufually only twice and a half as great. 



Sir Ifaac Newton has calculated the cffefts of tlie fun and 

 moon refpeftively upon the tides from their attraftive 

 powers. Tlie augmentation of the gravity of the lateral 

 parts of the earth, produced by the aftion of the fun, is a 

 fimilar effeft to an augmentation, eftimatcd by him on 

 another occafion, that is made to the gravity of the moon 

 toward the earth by the fame aftion, when the moon is in 

 the quarters ; only the addition made to the gravity of the 

 lateral parts is about 605 times lefs, becaufe their diftance 

 from the earth's centre is fo many times lefs than the diftance 

 of the moon from it. The gravity of thofe p.irts of the 

 earth that are direftly beneath the fun, and of thofe oppofite 

 to it, is diminiftied by a double quantity of what is added to 

 the lateral parts ; and as the diminution of gravity of the 

 one, and augmentation of gravity of the other, confpire 

 together in raifing the water under the fun, and the parts 

 oppofite to it, above its height in the lateral parts ; the 

 whole force that produces this effeft is to be confidered 

 as triple of wliat is added to the gravity of the Lateral 

 parts ; and 's thence found to be to the gravity of the 

 particles as i to 12868200, and to the centrifug.ar force at 

 the equator as i to 44527. The elevation of the waters 

 by this force is confidered by Newton as an effeft fimilar 

 to the elevation of the equatorial parts above the polar 

 parts of the earth, arifing from the centrifugal force at the 

 equator ; and, being 44527 times lefs, is found to be i foot 

 and liV^ inches, Paris meafure. This is the elevation 

 arifing from the aftion of the fun upon the water. 



Mr. Maclaurin makes this elevation to be i foot iOtVuti'^ 

 inches, of the fame meafure, which differs from the above 

 eftimate by tlie ^th part of an inch ; and the greateft ele- 

 vation, when the fun is in the equinoftial, 1 foot 1 1-^^ 

 inches. 



In order to find the force of the moon upon the water, 

 Newton compares the fpring-tides, M. the mouth of the 

 river Avon, below Briftol, with the neap-tides there, and 

 finds their proportion to be that of 9 to 5 ; whence, after 

 feveral neceffary correftions, he concludes, that the force 

 of the moon is to that of the fun, in raifing the waters of 

 the ocean, as 4.4815 to i ; fo that the force of the moon 

 is able, of itfelf, to produce an elevation of 8 feet and 7-,?-j- 

 inches, and the fun and moon together may produce an 

 elevation of about 10^ feet, in their mean diftances from 

 the earth, and an elevation of about 12 feet, when the 

 4K 2 



moon 



