Effect of Electrical Convection. 1^7 



conditions. Hence the total deflexion due to one surface of 

 the disk is 



4ttNK f R 2 



D,= ^^l arWdr. 



v 



Jk v 



Since there are four surfaces the entire effect due to them all 

 can be written 



where M is the mean value of M' for the four surfaces. 

 Considering D the observed deflexion, we have 



167rNKf** „. 

 v=. — y\ — I <rrM.ar. 



The value of v thus determined is a test for the accuracy of 

 the assumption that a convection current is magnetically 

 equivalent to a conduction current. 



The surface-density of the disks is uniform except on the 

 edge and at the centre opposite the opening in the tinfoil 

 condensing-plates. The uniform surface-density over the 

 main body of the disk is 



J _ V 



a 2tt(B-£) 



where V is the potential of the disk, the condensing-plates 

 being earthed, B the distance between the couoensing-plafces, 

 and J3 the thickness of the disk. 



The excess on the edge of each side is (Maxwell, Elec. & 

 Mag. § 19(3) 



q = 2ttR 1 <7 - log* \ 2cos Jti) 



R,B V, f 9 tti3\ 



The effect of this excess can be calculated by considering 

 it as concentrated in a circle of slightly smaller radius R f than 

 that of the disk. The lack of uniformity opposite the internal 

 edge of the condensing-plates may be allowed for by taking 

 for R x a value somewhat less than the radius of the opening 

 in the tinfoil, and considering the surface-density uniform. 

 This last correction is less than one per cent., since the 

 velocity of this portion of the disk is very small and its effect 

 on the coil also very slight. We then have 



4VNK Jf^ RB. / tt/3n 



•- pwpy J J Rj rM (h ' + "tT 10 ^ \ 2 cos 2b) m ; 



