44 REPORT — 1876. 



figure, fey introducing two new pieces of copper and two more mercury-cups, 

 the arrangement independently of the bridge being very nearly symmetrical : 

 let the reading now be x' . 



Assuming that the resistances of the movable cups and bows at the two 

 ends are equal, =-lc in one case, =7^' in the other, then 



P + 7c-+rt + Z-.r _ A 

 P + Ar+rt + Z-.r A 



Similarly, 



r + Q4-27.- + « + ^ + ^ A + B 



P + 7c-- + 7> + .r' ^ __A^ . 



p + (i + 27c:'+« + 6 + Z ~ A + li' 

 r ^ Tc^a^l-x 1 f -, _ 2X-+a + 6 \ 

 ■ ■ I ' P J I P+Q+T J 



-|i + --p- I r~ p+a+z /' 



• 1 U ^^• + «+lllf _ 7c: + |(« + ^>) 

 • -^-h- P P 



-i+ p ^p , 



.•.rt-6=a,'+.'j;'-10000. 



A variety of experiments were made with the coils arranged sometimes in 

 one way, sometimes in the other, and closely agreeing values of « — 6 were 

 found varying from 52 to 58. 



Correction for want of Syminetr)/. 



Referring back to fig. 4, we see that in the arrangement for multiple- 

 arc experiments the connexions are not quite symmetrical. Tlic copper bows 

 were all nearly of the same length and thickness : let the' resistance of one 

 of them be 2h. Let also the average resistance of a mercury-cup be 2r. 

 Then we get for the addition to ^(l3 + y + S + e), 



i(2b + 10r) + b + r, 

 for the addition to a 2h + 4r. Hence a — :^(/3 + y +2-|-e) is too great owing 



. .(>,'>' 

 to the connexions byp+^- 



Various experiments were made to find the value of h-{-r, and all gave 

 very nearly the same result. The following is a specimen :— A copper bow 

 very slightly longer than those in the connexions was inserted l)y means of 

 an additional mercurj'-cup, first on the right then on the left of the bridge ; 

 the readings were 5032 and 4982, the diflTercnce being 50 ; 



.•.2(6 + r) = 50, 



h r 

 •••2+2=12. 



The correction was actually taken to be 10. 



Limits of Temperature Effects. 

 The coils were arranged for a multiple-arc experiment ; the balance was 



