454 Lord Kelvin on the Front and Rear of a 
electrolyse a gram-molecule of a substance, the energy spent 
= 96,000 x 107 V ergs, and this is the equivalent of 165,000 
calories. Hence 
96,000 x 10’ V=165,000 x 4°2 x 10’ 
and VY = volis, 
in good agreement with the estimates of Townsend, H. A. 
Wilson, J. Stark, and Langevin. 
Sir John Cass Technical Institute, 
Jewry Street, E.C. 
XLIV. On the Front and Rear of a Free Procession of 
Waves in Deep Water. (Continued from Phil. Mag., 
June, 1904.) By Lord KELVIN*. 
§ 11. & hse present communication is substituted for another 
: bearing the same title, which was read before the 
Royal Society of Edinburgh on January 7th, 1887, because the 
result of that paper was rendered imperfect and unsatisfactory 
by omission of the exponential factor referred to in § 10 of 
my paper of February Ist, 1904. I shall refer henceforth 
to the last-mentioned paper as §§ 1... . 10 above. 
§ 12. I begin by considering processions produced by 
superposition of static initiating disturbances, of the type 
expressed in (12) of § 4 above ; graphically represented by 
fig. 1; and leading to motion investigated in §§ 1-3, 5-10. 
The particular type of that solution which I now choose, 1s 
that chosen at the end of § 4, which we, with a slight but 
useful modification ¢, may now write as follows :-— 
= pies : 
1 I eR ) ae 
co 2 =n / = 003(F by )e _ (17). 
where p= ,/(2?+.7), and Vax ta ee) 
Here —€ denotes the upward vertical component of the 
displacement of the fluid at time ¢ from its undisturbed 
position at point (a, <), which may be either in the free 
surface or anywhere below it. Taking t=0 in (17), we 
* From the Proceedings of the Royal Society of Edinburgh for 
June 20, 1904. Communicated by the Author. 
+ The substitution of $y, for 3r— tantly / pte , saves considerable 
p—2 
labour and use of logarithms; especially when, as in our calculations, 
Ze 
