124 Mr. L. Schwendler on the General Theory 



d- d'=0, 



«"- d" = 0, 



a!a"-g'g" = 



is one of the simultaneous solutions of the two equations *. 



Thus, substituting for d' its value a 1 , and for d" its value a", 

 we get 



ui 



G' — Wi --£ 



»-* ^— j-i * / ?i . n\ , ii in 



(c" -J- a") {a 11 +g") [a! +y } ) [d + q') 



G"=Wi ,,. twl £# 



The first equation has clearly a maximum with respect to a', 

 and the second with respect to a"; namely, 



— =0, which gives a'=g', 



and 



__=(), which gives d ] =g". 



Thus it follows generally that*0 = d -=.g represents a maximum 

 of the currents; and this, in consequence of the immediate ba- 

 lance, gives at last 



a = d=g=f, 



the known regularity-condition, which thus has also to hold 

 good in order to make the two currents G' and G" simultaneous 

 maxima. 



The first problem for the bridge method has therefore now 

 been generally solved ; and the results are expressed by the fol- 

 lowing formulae : — 



a=d=f=g=w + /3, 



=h(v^+1-i) 



where 



T r_q _l_±j, 

 3~ 3 



When the insulation is perfect (i= oo), the results revert to 

 those originally obtained in the special solution, viz. : — 



* The other solutions, however, which are possible from a mathematical 

 point of view, are impossible with respect to the physical problem ; for the 

 quantities, being all electrical resistances, must be taken with the same 

 sign, say positive. 



