OHM ON THE GALVANIC CIRCUIT. 499 



<p m n , X ($ 7)1 n 



i{m ^ — na.) k' {m^ — na.y 



passes into 



0= xco-j^ + vl/w [xz + ^{l—z)'\—Ka}{n — m) -j^. ( i ) 

 dx -^ 'ax ^ ' 



This equation undergoes no change, as indeed is required by 

 the nature of the subject, -when m, a, z, and n, ^,\ — z are re- 

 spectively interchanged, and, at the same time, the sign of <$ 

 is changed, as accordmg to the remark made in the preceding 

 paragraph, must take place, since by this transformation the 

 direction of the decomposition is transferred from one consti- 

 tuent to the other. 



36. In order to be able to deduce from this equation the 

 mode of the ditFusion of the two constituents in the fluid, i. e. 

 the value of z, we ought to know the pow er of conduction k, and 

 the electroscopic force u at each point of the portion in the act 

 of decomposition, the values, however, of which, are themselves 

 dependent on that diflrusion. Experience, as yet, leaves us in 

 uncertainty respecting the change of conductibility, which 

 occurs %vhen two fluids are mixed in various proportions with 

 one another, and likewise with respect to the law of tensions, 

 which is followed by different mixtures of the same consti- 

 tuents in various proportion ; for, if we do not err, no ex- 

 periments have been instituted relatively to the latter law, and 

 the law of the change produced in the conducting power of 

 a fluid, by the mixture of another, is not yet decidedly esta- 

 bUshed by the experiments of Gay Lussac and Davy. For this 

 reason we have been inclined to supply this want of experience 

 by hypothesis. We have, it is true, constantly endeavoured to 

 conceive the nature of the action in question, in its connexion 

 with those with whose properties we are better acquainted ; 

 but, nevertheless, we w ish the determinations given to be re- 

 garded as nothing more than fictions, which are only to remain 

 until we become by experiment in possession of the true law. 



With regard to what relates to the change in the power of 

 conduction of a l)ody, by mixture with another, we have been 

 guided by the following considerations. We suppose two adja- 

 cent parts of a circuit of the same section w, whose lengths are 

 V and w, and whose powers of conduction are a and b ; then, 

 when A is the sum of the tensions in the circuit, and L the re- 

 duced length of the remaining portion of the circuit, the mag- 



