PHYSICAL ASTRONOMY. 



34*0. Let AB, (fig. 28.) be the total rise of the 

 tide at any place ; and let the circle ADBF be 

 described on it. If we suppose this circle pla- 

 ced vertically, with the point B at the level of 

 low-water, the tide will rise or fall over equal 

 arches, in equal times ; that is, if the arches BD, 

 DH, HA, be equal, the times in which the wa- 

 ter will rise from B to D, from D to H, &c. will 

 be equal ; and the same in the ebbing of the tide. 



Mecanique Celeste, torn. n. p. 221. 



If the arch BD be proportional to the interval be- 

 tween any instant and the time of low-water, BE 

 the versed sine of that arch, will be the height to 

 which the water will have risen. 



Near the high and low water, the differences of the 

 depths from those of the high or low water, are 

 as the squares of the times. 



341. The total rise of the water in the tides 

 of the syzygies, is to the total rise at the quadra- 

 tures nearly as 2 to 1 ; and hence the effect of 

 the Moon is also nearly to that of the Sun as 



3 to 1. 



. 



This is known from observation, and hence the mass 

 of the Moon, in respect of that of the Sun, and 

 consequently in respect of the mass of the Earth, 

 may be found. 



For 



