the Thermal Conductivity of Water. 55 



the balancing-coil when the temperatures have become steady ; 

 we have 



2«$8OTK.rJL,+W (2) 



A as 



On increasing the thickness of the water by an amount y, 

 becomes 0', d becomes d f , r becomes r\l + fi(0 f — 0)}, while 

 the resistance of the heating-coil is increased by AR where 



AR = R«(0'-0) (3) 



If R/ is the resistance of the opposing arm of the Wheat- 

 stone bridge (equal in the experiments to 10 R at 18° 0.), the 

 heating-current 



°=S?W C '' w 



or about -j ^ of C, the constant current measured on the electro- 

 dynamometer. C thus depends on R ; and since the resist- 

 ance of the heating-coil in the other vessel does not alter, the 



1 dC 

 change of C due to change of R is ^ ,^ AR. The excess of 



temperature of the heating-coil above that of the sink after 

 the alteration of water thickness will therefore be given by 

 the equation 



0-2406/, ( , , dC AT A* XTi , 0' 



An approximate solution of (2), (3), (4), (5) gives for the 

 conductivity 



._ .% r, + J* „»* ( »*=* ^ I 



(tj?r' c ') 2r - 



where v 0'2406 



TJ/ I i i 



At 18° C. ,5 ™ = — ; and if T be the temperature of 



K 18 + R 11 



the sink, the temperature of the heating-coil is T + 0. Hence 



expressing R in terms of R 18 , we have 



, 0-1988 _. v r\ 9 , m „ ,_ 10 

 ^"A 



{ ff wEr + d } + ^rtfPU] . (7) 



A V ( tu d'r-d . ,1 . 0-199 

 0-199 C /2 R 



