Unipolar Induction. 183 



the current ; after 20 seconds, read again and reverse the 

 current ; after another 20 seconds, read again and throw off 

 the current ; after another 20 seconds, take a final reading. 

 This gives, by subtraction, three deflexions. The electro- 

 meter was not quite dead-beat, but reached the end of its 

 swing in just 20 seconds ; intervals of this length were 

 marked out by a torsion-pendulum actuating a sounder. The 

 galvanometer also was not quite dead-beat, but reached the 

 end of its swing in 15 seconds, so its extreme position was 

 read in each instance, giving three galvanometer deflexions 

 likewise. Sets of readings were taken in groups of four so 

 as to eliminate all effects that did not change sign both with 

 the current and with the direction of rotation. 



The apparent deflexion due to throwing the magnetic field 

 on was calculated by adding twice the middle deflexion, 

 reversed in sign, to the other two and dividing the sum by 6; 

 drift is thus eliminated. The result is a little too large 

 because of the under damping ; but the necessity for making a 

 correction was avoided by taking comparison readings in 

 exact imitation of the principal ones, using a known source 

 of potential. 



A current of 25 amp. was usually employed, and full speed 

 was about 2000 R.P.M, 



§ 4. Calculation of Charge on Inner Cylinder. 



It is easily shown that any point of the apparatus metalli- 

 cally connected to earth comes to a potential of Np elmg. 

 units, where p = rev. per sec. and 1ST = flux encircled by the 

 point in each revolution. Accordingly, the magnetic flux 

 through various sections of each cylinder and the shaft was 

 compared with that through the central section of the outer 

 cylinder by means of a ballistic galvanometer; a null method 

 was employed and great care was taken to eliminate stray 

 effects. It was found that the flux through any section was 

 proportional to the area of the section and to the sum of the 

 angles subtended by the mean ends (radius 4*93 cm.) of the 

 solenoid, with a maximum correction of 2 per cent., and this 

 fact was utilized in calculating additional values. 



The calculation now reduces to the solution of the fol- 

 lowing electrostatic problem : given the potentials over the 

 bounding surfaces of two spaces each having the form of a 

 right cylindrical shell, to find the distribution of electrification. 

 The work was done in steps so as to avoid the solution of 



