Prof. Thomson on the Mechanical Theory of Electrolysis. 433 



7. If we substitute the expressions (3), (4) and (6), (7) for 

 the three terms of the original equation (].), we have 



v^-^^if^-ee,, .... (8 



from which we deduce 



.= t^2^fi^ (.) 



8. It appears from this result that the value of 7 will be posi- 

 tive or negative according as the angular velocity of the disc 

 exceeds or falls short of a certain value D., given by the equation 



"=p|; (10) 



and therefore we conclude that^ when the angular velocity has 

 exactly this value, the electro-motive intensity of the disc is just 

 equal to the intensity of the reverse electro-motive force exerted 

 on the fixed wires, by the electro-chemical apparatus with which 

 they are connected. 



9. If we adopt as the unit of electro-motive intensity that 

 which is produced by a conductor of unit length, carried, in a 

 magnetic field of unit force, with a velocity unity, in a direction 

 which is both perpendicular to its own length and to the lines of 

 force in the magnetic field, it is easily shown that the electro- 

 motive force of the disc, in the circumstances specified above, is 

 given by the equation 



i=*|r2Fa> , *H.(11) 



Hence if I denote the electro-motive force of the disc when it 

 just balances that of the chemical apparatus, we have by (10) 



IzrJ^'e. (12-) 



This equation comprehends a general expression of the conclu- 

 sion long since arrived at by Mr. Joule, that the quantities of heat 

 developed by difierent chemical combinations are, for quantities 

 of the chemical action electrically equivalent, proportional to the 

 intensities of galvanic arrangements adapted to allow the combi- 



y is infinitely small. Consequently what is denoted in the text by R will 



be equal to — +B, and will therefore be infinitely great when y is infi- 

 y 



nitely small. The modification required for such cases will be simply to 

 use B in place of R, and to diminish the value of I found in the text (12) 

 by JA ; but the assumption that R does not become infinite in any of the 

 circumstances considered is, I believe, quite justifiable in the two special 

 cases which form the subject of the present communication. — W. T. Nov. 1, 

 1851. 



