294 H. A. Rowland et al. — Ratio of the Electromagnetic 



E 



-£)' 



F =: -0013 for first ball of condenser and -0008 for other, as in- 

 vestigated below. 



I = correction for torsion of fibre = as it is eliminated. 



e = constant of electrometer = 17 -221. 



G= " " ballistic galvanometer = 19087. 



p = radius of large circle = 42-105 cm. 



n = number of coils on circle = 1. 



c =■ constant of electroclynamoineter = '006454. 



K-= moment of inertia of coil of electrodynamometer = 826*6. 



b = distance of plane of large circle from needle = 1*2 7. 



= capacity of condenser = 50*069 or 29*556.' 



D= distance of mirror from scale = 170*18 cm. 



w = weight in pan of balance. 



t = time of vibration of suspended coil. 



T= " " " of needle of balistic galvanometer. 



fi zzz deflection of needle on scale when constant current is passed. 



a = reading of head of electrodynamometer when constant 

 current is passed. 



6 =. swing caused by discharge of condenser. 



d = distance of plates of electrometer. 



N= number of discharges from condenser. 



A = logarithmic decrement of needle. 



A=z correction due to discharges not taking place in au instant. 



The principal correction, requiring investigation is A. Let 

 the position and velocity of the needle be represented by 



x = a sin bt and v = ajb cos bt, where b = ~. 



At equal periods of time t n 2t n 3^, etc., let new impulses be 

 given to the needle so that the velocity is increased by v at 

 each of these times. The equations which will represent the 

 position and velocity of the needle at any time are, then, 



between and t t x = a n s\r\bt v = a b cosbt 



" t t and 2t t x = a' sinb(t+t') v = a'b cosb(t+t') 

 " 2t t and 3t / x ■- a" sinb(t+t") v = a"b cosb(t-{-t") 



At the times 0, t n 2t t etc. we must have 



x = v = ajb 



a sin bt=a! sin b{t l + 1') v a + ajb cos bt^a'b cos b(t t + 1') 



a 1 smb(2t i -\-t') = a" smb(2t l -j-t") v n a'b cos b(2t l -\-t") 



etc. =a"bcosb(2t l -\-t") 



etc. 



Whence we have the following series of equations to deter- 

 mine a', a", etc., and t ; , t" etc. 



a' 9 b>=a n 2 b*4-vj+2» n a n b cos bt, ; sin bU,-\-t')=^ sin bt 



