ON ELECTROLYSIS IN ITS PHYSICAL AND CHEMICAL BEARINGS. 141 
Maxwell’s theory is given in the Glasgow volume of the British Association for 
1876. 
Recently Dr. Fison seems to have promulgated the same objection, and conse- 
quently Professor Fitzgerald wrote to Professor Chrystal about it. In reply he 
received a very interesting letter, which he has passed on to me, and from which I 
extract the portion referring to this subject. 
OLIVER J. LODGE, 
Letter from Professor Chrystal to Professor Fitzgerald. 
. . . The problem which I set myself in the Ohm’s law experiment was to sbow 
that when a Wheatstone’s bridge is balanced for any electromotive force in the 
battery circuit, it is balanced for every, or, to put it safely, for widely varying, 
electromotive force. 
The theoretical part of the paper, for which Maxwell was responsible, I do not 
remember ever having examined from a scep- 
tical or logical point of view. Fig. 4. 
It now appears to me that we ought to reason 
as follows :— 
In order to find the necessary condition 
upon the resistance-function E/C, let us make 
matters as simple as possible by considering a 
bridge in which two arms, R, R, are of equal 
resistance, of the same metal, and alike in every 
respect. Let the two other resistances § and T 
be made of two different metals, say of Cu and 
Fe. Let the length and section of S be / and ; 
and the length and section of T be /’ and @’. 
The specific resistance must in each case be a 
function of the current intensity (current per 
unit of section). Temperature is supposed kept 
constant, of course. Let the whole current 
flowing through § and T when there is a balance be i, the specific resistances of 
S and T will be > (é/w) and ¥ (i/w’) respectively. 
The condition for balance will therefore be 
CHEN @ Cpeay = CE peshy wy C4] aahy Oe. AES ae ay; 
and this equation must, by the result of the experiment, hold for all values of ‘i? 
Let us suppose that we alter the length of the iron wire S to Z’’, then there will 
be a corresponding section, w’’, for which there will again be a balance ; so that we 
must have 
(Uw!) @ (éfo") = (Uo) W(ifo’) . o¥G2)3 
and this again must hold for all values of 7. 
Combining (1) and (2), we get ; 
PAY TP VEE (1 UAT CHES Ne ae me 8 
From this equation we can readily determine the form of the function ¢. 
If we put p=0"/w, A=1!'w/lo!’, x =i/w'', we get 
o(Mar)=A > (#); 
whence, putting # = mu x, we get 
p (Mev) =r p (mar) =A*G (a); 
p (Hw) = AY (@); 
and, in general, 
P (nv) = A"d (@). 
Hence, putting «=1, we get 
$ (u") = Ang (1). 
Now u is unrestricted, therefore we may put 
z=", n=log z/log uw. 
