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



The symbols used are 



h = the depth of the canal. 



a = the earth's radius. 



w = the rotational speed referred to the moon (23 h. 56 m. 

 = lunar day at present). 



(j) — (ot = the longitude west of the moon. 



e = half the lag of the bodily tide. 



2E — the greatest range of the bodily tide at the equator*. 



3 



t = ~ x the moon's mass x a 2 -r- (her distance) 3 . 



The result obtained for the height of the wave relatively to 

 the bottom of the canal is 



h - h d X > 



where 



C R 

 dx 



- sw^r {(I cos e - 1 ° E ) cos 2 ( * " "*) 



+ | sin e sin 2(<j> — oit)if. 



Taking up the investigation from this point since the land 



partakes in the rise and fall of the bottom of the canal, the 



measurable height of the tide will be the difference between the 



depth of the canal and the height of the water above the bottom 



d£ 

 of it, which will be — h ~- , or 



aW-gh 1(1 C ° S 6 ~ i 9 J C ° S 2 ^~ (ot ^ + l sin e sin 2 & ~ ^ } ' 



h 



For -^—5 r write H, for 2 (6 — cot) write 6. 



aW—gh vr / 



Then the height of the tide will be expressed by 

 -#jcos(0-e)-g^cos-0 



= — ITJcos 6 (cos e — v — ) + sin#sineL 



* Elsewhere Prof. Darwin uses E as the ratio of the bodily tide in the case of 

 viscosity to the like in the case of fluidity. 

 + Loc. cit. p. 26. 



