342 



Rev. 0. Fisher, On the hypothesis of a [May 30, 



Suppose, as is usual in the canal theory, that AP is developed 

 into a straight line, and that the earth is at rest, and the moon 



moving westward above AP. Then, if AP = x, the attraction 

 of the moon on the water at P will be in the direction to diminish 

 x, and will be negative. The moon's differential horizontal attrac- 

 tion at P will therefore be 



daM . 0/ , . 

 - -22J3- sm 2 (4> - at \ 



which for shortness write — fi sin 2-v/r. 



Let, as before, the depth of the canal be h, and its width 

 unity, i.e. one foot, and let y be the height of the tide above the 

 undisturbed water. 



Then we have for the accelerations on a unit particle of water 

 atP 



X = — fj, sin 2-yjr, 

 Z = -g. 

 And x = a^r, .'. dx = ad\}r. 



Now the work on a unit particle 



= p I {Xdx + Zdz) 



= p I (— /xa sin 2-^rd^r—gdz) 



= p (^cos2f-gz"j + C. 



