J 46 PHILOSOPHICAL TRANSACTIONS. [anNO 16q7. 



March and September, or near them, are the highest, and the neap tides the 

 lowest ; which proceeds from the greater agitation of the waters, when the 

 fluid spheroid revolves about a greater circle of the earth than when it turns 

 about in a smaller circle ; it being plain, that if the moon were constituted in 

 the pole, and stood there, that the spheroid would have a fixed position, 

 and that it would be always high water under the poles, and low water 

 every where under the equinoctial ; and therefore, the nearer the moon ap- 

 proaches to the poles, the less is the agitation of the ocean, which is the 

 greatest of all, when the moon is in the equinoctial, or farthest distant from 

 the poles. Whence the sun and moon, being either conjoined or opposite in 

 the equinoctial, produce the greatest spring tides ; and the subsequent neap 

 tides, being produced by the tropical moon in the quarters, are always the least 

 tides ; whereas in June and December, the spring tides are made by the tropical 

 sun and moon, and therefore less vigorous ; and the neap tides by the equinoc- 

 tial moon, which therefore are the stronger : hence it happens, that the differ- 

 ence between the spring and neap tides in these months, is much less consider- 

 able than in March and September. And the reason why the very highest spring 

 tides are found to be rather before the vernal, and after the autumnal equinox, 

 viz. in February and October, than precisely upon them, is, because the sun is 

 nearer the earth in the winter months, and so comes to have a greater effect 

 in producing the tides. 



Hitherto we have considered such affections of the tides as are universal, 

 without regard to particular cases ; what follows from the different latitudes of 

 places, will be ea>ily understood by fig. 10, pi. 3. Let ApEP be the earth, 

 covered over with very deep waters, c its centre, p, p, its poles, ae the equi- 

 noctial, pf the parallel of latitude of a place, od another parallel at equal dis- 

 tance on the other side of the equinoctial, nh the two points where the moon 

 is vertical, and let Kk be the great circle, wherein the moon appears horizontal. 

 It is evident, that a spheroid described on nh, and Kk. shall nearly represent the 

 figure of the sea, and cf, cd, cf, cd will be the heights of the sea in the 

 places f, D, F, d, in all which it is high-water: and seeing that in 12 hours' 

 time, by the diurnal rotation of the earth, the point f is transferred to f, and 

 d to D ; the height of the sea cf will be that of the high-water when the 

 moon is present, and cf that of the other high-water, when the moon is under 

 the earth: which in the case of this figure is less than the former cf. And in 

 the opposite parallel nd the contrary happens. The rising of the water being 

 always alternately greater and less in each place, when it is produced by the 

 moon declining sensibly from the equinoctial ; that being the greater of the 

 two high-waters in each diurnal revolution of the moon, when she approaches 



