OP ARTS AND SCIENCES. 127 



and the effect of the earth and local attraction are eliminated. By 

 this method of observation, no telescope and scale are needed. It is 

 only necessary to bring the point of the bar which passes through the 

 movable coil to a fixed point. The mercury iu the pivot cups serves 

 to dampen the vibrations of the movable part of the apparatus ; and 

 it was found that readings could be taken quicker than by galvano- 

 metric methods. 



Theory of Instrument. 

 ("Maxwell's Electricity," Vol. II. page 329.) 



™ F tan 0. 



G 1 =■ 



Gg cos /3. 

 Where 



G = current. 



F = directive force. 



G and g =■ constants of fixed and movable coils. 



8 = angle of coil with magnetic meridian. 



If the torsion head of the instrument can be adjusted so that the 

 deflection is zero, and d = — 8 



F 



we have G 2 = — sin 8. 



The value of F was determined by several methods. Since 



Ft 2 = n 2 A, 



where t is time of vibration, 

 and A = moment of inertia, 



it is necessary to determine both the time of swing and the inertia. 

 The times of swinging were obtained by means of a chronograph upon 

 which seconds were recorded by the side of the records produced by 

 breaking an electric circuit at the instant the movable coil passed the 

 middle of its vibrations. The moment of inertia was first determined 

 experimentally by adding known cylindrical weights, and determining 

 the new time of vibration. 

 We thus have 



-4-*( ( l + «,t l ._-|i) 



and k = w ( I' 2 -f- -- ) 



where k = moment of inertia of added cylindrical weights ; w = 

 weight of cylinders in milligrammes ; I = distance of point of suspen- 



