On the Measurement of some Standard Resistances. 411 

 very small, and we have very approximately 



B = l+i(a + /8 + 7). 



Now it is comparatively easy to adjust the three 3-ohm 

 coils to equality, and an accurate 3-ohm standard is not 

 required. 



Hence, if B' be the resistance of the combination when all 

 the coils are in series, then 



B'=3 + a + 3+/3 + 3 + y=9B. 



Or the resistance of the arrangement in series is very ap- 

 proximately 9 times that when in multiple arc. 



The arrangement of mercury cups is shown in fig. 1. A 

 number of holes about '75 centim. diameter are bored through 











Fig 



1. 



















o 7 



o A 



o B cf 







D 



o 











d d 

















d 



o A ' o s ' o c 



' o s 





















^0' A' 



o o 





cf 



' cf 



















a sheet of ebonite. Thick strips of copper of the form shown 

 in the figure are cemented to the under side of the ebonite, 

 the surface of the copper in contact with the ebonite being 

 amalgamated, and the cups thus formed contain mercury. 



In the multiple-arc position the 3-ohm coils are connected 

 with AA',BB', CO respectively; in the series position they 

 connect DD', EE', FF', while a coil of 1 ohm is placed across 

 GrGr'. The cups I,, II. serve to connect the system to the 

 bridge. 



Let the resistance of the short rods used for this purpose 

 be U, and the resistance of the 10-ohm coil whose value is 

 required be X. 



The first operation is to compare by Carey-Foster's method 

 the Beetle in the multiple-arc position and a standard 1-olnn 

 coil S ; let x v be the shift on the bridge-wire. 



