Mr. Woolhouse on the Deposit of Submarine Cables. 345 
at, 
— (78% 4 eal {" al2abr(a!) + ¥ F(a')f'(a!) + = = 
TT a 
This equation also holds for the surface of separation, For 
the next surface de niveau within ae fluid it becomes 
2¢(a—h) Pip (a—h) ny ox ‘a a ! ! 
com t+ Gane sl) eeet) seve) 
+(Feyte ao 
Expanding as before, and ie we find 
$0)+ cee He) — EO (1 rem a) 
Fray * foray 
which is identical with equation in 
The foregoing investigation is of course only an application to 
the equation (12) of the principles which I stated more generally 
in your Number for December. I regret that Archdeacon Pratt 
has obliged me to occupy your pages with a second discussion of 
a question which in fact belongs to the elements of the integral 
calculus. 
I am, Gentlemen, 
Your obedient Servant, 
Trinity College, Dublin, Joun H, JELuert. 
April 1860. 
XLIX. On the Deposit of Submarine Cables. 
By W. 8S. B. Woornovss, F.R.A.S., FSS. &e. 
To the Editors of the Philosophical Magazine and Journal, 
GENTLEMEN, 
M* attention has recently been drawn to the dynamical 
theory of the submergence of telegraphic cables, which 
has already been discussed both theoretically and practically, at 
some length and with considerable skill, by Messrs. J. A Long- 
ridge and C. H. Brooks, in a valuable paper read before the 
Institution of Civil Engineers, Feb. 16, 1858. The mathema- 
tical theory originally laid down in this excellent paper has since 
been established, by a different form of process, in an elegant 
paper by Mr. G. B. Airy, the Astronomer Royal, inserted in 
your valuable Journal for July 1858, Independently of the 
practical importance of the subject as an engineering operation, 
the investigation of the several relations appertaining to it is not 
devoid of mathematical interest. Indeed I have found the in- 
quiry to be so inviting as to lead me not only to simplify, but 
to extend the investigations of the general problem somewhat 
