On Transcendental and Algebraic Solution. 379 
At the commencement of the experiment, the deviation of the 
galvanometer caused by the terrestrial current was read off at 
19-2 divisions. 
The above experiments disclose nothing at variance with the 
known laws of galvanism; but it nevertheless appeared to me 
advisable to make them known, as they afford a simple expla- 
nation of certain phenomena which Professor Thomson has de- 
scribed*, and which he seems to attribute to entirely different 
causes. 
LVIII. On Transcendental and Algebraic Solution. By JamMEs 
Cocks, M.A., F.R.A.S., F.C.P.S., Barrister-at-Law, of the 
Middle Temple. 
Saga fe=0 be an algebraic equation of the nth degree, all 
the coefficients of which are functions of one parameter a. 
By differentiation we obtain a result of the form 
oe =Fr = +fe=0. 
But, since F and f are rational functions, 
de fe 
da ‘Fe 
Ue ee Oe ee 
~ Fa.Fu,.Fa,..Fa, 
where R is a rational and integral function of z And 
Ra=A,a"-!+A,a"-?+..+A,, 
where A is a function of a. Moreover 
2 
= Poa’. espace a 
Hence, repeating this process, we are conducted to the system _ 
= Raz, 
@ —Re= Aya +A,2™-?4+..+A,, 
d? 
eg le 14 Boa"-?+ .. +B,, 
Biot 
eT oe G,2"-1 + G,a"-2+ ..4+G, ; 
and if we assign n—2 indeterminates A, u,..v so as to satisfy 
* Report of the Twenty-ninth Meeting of the British Association for the 
Advancement of Science (Transactions of the Sections), p. 26. 
+ Communicated by the Author. 
