158 HENEY A. EOWLAND 



of the tangent galvanometer for the length of needle is almost elimi- 

 nated. When the method of recoil is used, we must substitute - ~TA 



for the term involving /, and sin $A f -f- sin %B' in the place of sin ^ 6' 

 A' and B' being the greater and smaller arcs in that method. This is 

 on the supposition that X is small. 



The ratio of G" to G must be so large, say 12,000, that it is difficult 

 to determine it by direct experiment, but it is found readily by measure- 

 ment or indirect comparison. 



It is seen that in this equation the quantities only enter as the first 

 powers, and that the only constants to be determined which enter the 

 equation are M, G and G", which all vary in simple proportion to the 

 linear measurement. It is to be noted also that the only quantities 

 which require to be reduced to standard measure are M and T, and 

 that the others may all be made on any arbitrary scale. No correction 

 is needed for temperature except to M. Indeed, I believe that this 

 method exceeds all others in simplicity and probable accuracy and its 

 freedom from constant errors, seeing that every quantity was varied 

 except G" and G, whose ratio was determined within probably one in 

 three thousand by two methods. 



Having obtained the resistance of the circuit by this method, we 

 have next to measure it in ohms. For this purpose the resistance of 

 the circuit was always adjusted until it was equal to a certain German 

 silver standard, which was afterward carefully compared with the ohm. 

 This standard was about thirty-five ohms. 



By this method, the following data are needed. 



1. Eatio of constants of galvanometer and circle. 



2. Eatio of the tangents of the two deflections of tangent galvano- 

 meter. 



3. Eatio of the deflection to the swing of the other galvanometer. 



4. Mutual potential of induction coils on each other. 



5. Time of vibration of the needle. 



6. Eesistance of standard in ohms. 

 For correction we need the following : 



1. The logarithmic decrement. 



2. Distance of mirror from scale. 



3. Coefficient of torsion of suspending fibre. 



4. Eate of chronometer. 



5. Correction to reduce to standard metre. 



