Calometric Absolute Measurements. 33 



According to the law of magneto-induction, with the mul- 

 tiplier " closed " 



the oscillation-period ■> 



ti i 



IT 



% = 



/MH B/M 2 G 2 Ay 

 V-K+k(2K^ + 2k) L- • ( 2 ) 



and the logarithmic decrement of the amplitudes 

 / M 2 G 2 . A 



\2Kw ' 2K 



)• 



In these equations, K denotes the moment of inertia, and M 

 the magnetic moment, of the magnet ; H the horizontal com- 

 ponent of the earth's magnetic force ; B the torsion-moment 

 of the suspension-wire ; A the rotation-moment with which 

 the wire and the surrounding medium act upon the magnet 

 moved with the angular velocity 1 ; G the electromagnetic 

 force with which the multiplier, when the current 1 flows 

 through it, acts on the magnetic unit of mass concentrated in 

 one polar point ; and w the absolute value of the resistance of 

 the multiplier (in electromagnetic measure). 



From equations (1) and (2) result the further equations 



A-2 



and 



Ti 



7T 2 + Xf 



TI 



M 2 G 2 

 2Kw> 



t 2 + K 

 ^ — ? 



and from these we get, for the absolute resistance w the ex- 

 pression 



w = 



G 2 M 2 T X 



which, according to equation (1), can be replaced by 



M\ 1 7T 2 + \? 



-<*(S) 



2T 1 .(l + 0)' 



v 



B 



where 6 denotes the quantity ™tt. If the resistance of the 



multiplier has been found equal to n Siemens mercury units, 

 Phil. Mag. S. 5. Vol. 5. No. 28. Jan. 1878. D 



