294 Mr. E. P. Adams on the Electromagnetic 



time-integration of the curve be 



MSq. 



y A ? 



and the mean value of the force at the upper needle 



Then the effect on the needle-system will be the same as 

 if constant forces of these magnitudes acted upon it. The 

 same result could be obtained by imagining two coils of 

 wire passing through the centres of the two sets of spheres, 

 through which a current was sent in opposite directions of 

 such magnitude that the same amount of electricity passed at 

 any point per second as in the case of the charged spheres. 

 The force at the lower needle due to the calibrating-coil is 



2wlh 



(/i a + « a )4 



= 2ttIC, 



li being the radius of the coil, and x its distance from the 

 plane of the needles. 



The force at the upper needle due to the calibrating-coil is 



2-l[ 1 -(f/P 2 (co^)-^( 7 ;) 4 p 4 (cos6)+ . . . .J-fcrlD, 



r being the distance of the centre of the coil to the upper 

 needle, and 6 the angle between the axis of the coil and r. 



Let M be the moment of the lower needle, and H the 

 earth's horizontal magnetic force at its centre ; M' and H' 

 the corresponding values for the upper needle. Let 6 be the 

 angular deflexion of the needle-system produced by the 

 current in the calibrating-coil, and cf> the angular deflexion 

 produced by the moving charged spheres. 



Equating the couple acting on the needle-system due to 

 the earth's field to the couple acting on the needle-system due 

 to the current in the calibrating-coil, and putting "M/M'=J, 

 we have 



HM-H'M' 2ttI(C-D) 

 M ~ tantf ' 



Similarly, equating the couple acting on the needle-system 

 due to the earth's field to the couple acting on the needle- 

 system due to the revolving charged spheres, we have 



HM-H'M' 27rNy(A-B) 

 M "~ Vtan<£ ' 



