120 REPORTS ON THE STATE OF SCIENCE. 



Balance was effected by shunting Pt with 122,000 ohms. The cohnector 

 completing the branch d was then removed and balance again established 

 by shunting « with 0,500 ohms. The balance still held good when the 

 connector was restored in position. Hence, if R' and a' represent the 

 shunted values of R and «, 



P^P + a'^a'^ R;+L_ 



Q q + ii ft S + L' + L"' 



the probable error of these ratios being of the order O'OOOl per cent, in 

 the present instance. The value of d (for measurement see the following 

 table) is equal to 0-000128 ohm, and is less than P. Hence 



Q(R' + L) _l-00000,x(l-OOOOl6 + 0-00011o) 

 ^"S + L' + L" 10-000l8 + 0~^0601, " ^^^"^^» ^* ^^ ^ ^' 



The manner in which d, L, and(L' + L") were evaluated will be seen from 

 the accompanying table. This is a good instance of a measurement 

 involving a number of connecting pieces which must be evaluated in 

 position. 



(g) The Differential Galvanometer.^- — This method is usually used for 

 comparing resistances which are nominally equal. It is not convenient 

 for their evaluation from the unit by means of a ratio of 1 to 10. 



The difference of the currents through the galvanometer coils is 

 i(Pgr — QG)/G(Q+^) where G and g are the resistances of the galvano- 

 meter circuits (see hg. 4). This is equal to zero when "P lQ = G/g. When 

 this latter condition holds there will in general be a deflection owing 

 to want of symmetry of the galvanometer coils. If P=l and Q=10, 

 then the ballast resistance in circuit with ff or G may be adjusted until 

 there is no deflection. In such a case, if two other coils, P'^0'1 and 

 Q'=1'0, are substituted for P and Q (G and g remaining as before), and 

 ten times the previous current sent through them, there will be no deflec- 

 tion when P/Q=P7Q'. In general, however, the maximum permissible 

 current is VlO times that previously employed, and any want of 

 symmetry in the galvanometer coils does therefore introduce an error. In 

 , addition, the substitution of P' and Q' for P and Q changes the values of G 

 and g, because these latter include the potential leads of the resistances 

 and also the contact resistances introduced. If G and g are comparatively 

 large, the error is reduced, but so also is the sensitiveness. In the same 

 way, errors are introduced in the comparison of nominally equal 



' See Heai'isidc's Papers, vol. i. Also C. W. S. Crawley, Journ. Inst, of Electrical 

 Engineers, April 1904. 



