Siemens Mercury Unit of Electrical Resistance. 303 



of every damped needle, with the difference merely that the 

 coefficients are here given in their physical signification. 



Now the coefficient of j- determines, as is well known, the 



relation between the time of vibration and the amount of damp- 

 ing. Next, let t be the time of vibration of the damped needle, 

 and a and b the magnitudes of two successive arcs of vibration, 



so that \ = log t is the Napierian logarithmic decrement of the 



needle. Then we have q 2 c _ X 



c 

 The second term ^, depending on the resistance of the air, 



is found exactly in the same way, by observing the time of 

 vibration t and the logarithmic decrement X after breaking the 

 galvanometei % circuit. Then 



And since t and t n are connected by the equation 



_ H 



t* «f 



we get finally 



?2=2 f ( VSS- Xo) * (L) 



This is the important equation whereby the coefficient of sen- 

 sitiveness of a galvanometer, with narrow coils and with a needle 

 of any given shape, can be determined from the moment of 

 inertia and time of vibration of the needle taken in connexion 

 with the degree of damping due to the coil, if the absolute 

 resistance of the coil is known. In future this last quantity 

 can be easily ascertained by means of a Siemens's resistance- 

 scale f. 



* Weber (Zur Galvanometrie, p. 23, 25, where it must be observed that 

 £ is denoted by/and our X by X,) obtains q*=2 — (X-X ) . A!±^o 



f It is hardly needful to say that q is not the coefficient of sensitiveness 

 that comes into account in the case of permanent currents. If a permanent 

 current of strength i produces a deflection a?, we may put w=pi, in which 



t 2 

 case it is easy to see that p = q - ^ . In accordance with the usage fre- 



quently adopted in other cases, we may call q the dynamical and p the 

 statical coefficient of sensitiveness. 



