284 Mr. T. Gray on arranging Wheatstone* 's Bridge 

 is approximated to to a degree determined by the equation 



n a b 

 g it 



where C is a constant very near unity. 



By the aid of Kirchhoff's corollaries to Ohm's law we 

 readily obtain the following equation to the current passing 

 through the galvanometer when E is the electromotive force 

 of the battery. 



n-_l EQR-6c) m 



ab(c + R) + cR(a + b)+g(a + c)(b + R) ' ' V ; 

 +/{(« + b)(c + R)+g(a + b + c+JR)} 



Along with this equation we have the condition 



°;-h (2) 



Substituting C — for b in equation (1) and putting 1 — C = i, 

 we get c 



p _ ERaci 



~ CaR{(c + R)a + cR + g(a + c) +/(c + R) +/#} 



+ ae{cE +/(c + R) +/#} + cR{g(a + c) +/#} + c 2 fg 



We have to find when this quantity is a maximum, R being 

 supposed constant. It will be found more convenient to take 

 the reciprocal of G and solve for a minimum. We have 



g =R+%+/)+ ! + (B+y)(°+/) + K±f c+ 9(c±f) 



+ % + a, . . (3) 



neglecting C and making i very small. 



Differentiating this quantity with respect to a and c respec- 

 tively, we obtain 



d_m_ R + g + c g{R(c +/) + <;/} m 



da a " c Ra 2 ' ' ' W 



^ 2 Ez _ g{R( c +f) + cf} { , 



da 2 G Z R? > W 



A^ ,_( B+^X «+/) , (« + g)(B+/) , 6 v 



do G " c 2 " " + Ra ' " W 



^ 2 E*_ (B+g)(a+/) 7 . 



dc 2 G c 



rZ 2 Ez _ fR+g 

 da . dc G 



EF- t^~ + ~l£?~ J (8 ) 



