Constants of a Rectangular Galvanometer. 799 



giving 



S= tl — : — , and /. l + S=_^_ — y . 

 2c + #' 2c + # 



.*. Gr = — t= + — 7-- . -^ ^ 4- y-(sin v x + sin 2 ) . 



cy/'l c v y 2 2c + x b y 



Also from fig. 7, 



b = c<y~2 cos ^! = OCcos 2 = c^/2 sin (45 -f <j>). 



The third of these equations for b gives 



*«. ( i + «_.(i + g-2!+- 



and 



OC=OK+KC=C v /2+^cos^r 



= <V'2'+*cos (45-3) 



Cv/2+-=3(l + «) 



Whence 



or 



and 



* 2( C + g) 



cosg 1=e - 7I= ^ J , 



. a 1 2c-«! 



Sm ^=72-2^' 



7 -I 



cos # 2 = TTTi = —/a (to ^ rs ^ order) ; 

 sin # 2 = — . 

 -=- (sin 1 + sin # 2 ) = 



b v x ' " cV2(2c + *) 



Hence, substituting this value in equation (iv.) for G, we 

 obtain on reduction 



C \ b'G/ 



Thus the force at in fig. 7 is approximately eqmd in 

 magnitude to that at the centre of a square of semi-side 



