108 



REPORTS ON THE STATE OF SCIENCE. 



In galvanometers, the coils of which are wound in similar channels, 

 and contain the same mass of wire, the electromagnetic force on the 

 needle, and hence the deflection, is proportional to .Tn/G,' where x is the 

 current through G. In the case considered the deflection is pro- 

 portional to 



VG WP 



G- 



a/3 



• 



Q + S 



a + /3 



(P+R)(Q + S ) 

 P+R+Q+S 



P+R+Q+S 



(B) 



This is a maximum when G 



_^ (PJ-RXQ + S) 

 a+y8^P + R + Q + S' 



the resistance of 



the ' extprnal galvanometer circuit,' and the value of this is the most 

 suitable galvanometer resistance. Substituting this value for G in (B), an 

 expression is obtained which, from the conjugate condition of the arms of 

 the bridge, may be reduced to the simple form 



iA v/P/2 



(R + S)(P + R + «) 

 PS 



(C) 



in which A—vF/'P. 



If in (B) we write g for the best galvanometer resistance and N^r for 

 the resistance of the galvanometer used, the deflection is proportional to 

 \/Ng/(N + \)^yg, and the ratio of this to the maximum (N=l) is 

 2\/N/(N + l). Prof. Schuster, in the paper referred to, gives a table 

 showing that if N=20 or 0-05, the sensitiveness is 0426 times the 

 maximum. 



The derivation of the formulae being so simple, the results alone are 

 given for the other methods considered. 



Wheatstone Bridge (fig. 2). — If a=ff=0 in the expressions obtained 



Fig. 2. 



for the Kelvin double bridge, the values are those for the Wheatstone 

 bridge.^ In this case, expression (C) may be written 



.WP/2^(l.|)(l + f) 



(D) 



' A hsolute Measurements, A. Gray, vol. ii. 



■- The values usually given for the Wheatstone bridge (see J. J. Thomson, 

 Elements of Elec. and Magnetism, p. 3C5 ; Fleming, Handlook of Elec. Laboratory, 

 vol. i., p. 233 ; A. Gray, Abs. Measurements, vol. i. p. 333), involve the resistance of 



