1902.] The Dissipation of Energy by Electric Currents. 



365 



In Table I the formula 3*95 



half cylinder, is used, in which B is the maximum average value of the 

 intensity of magnetic induction given by coil No. 4. It will be seen 

 that experiment gives a lower value for the total watts in the half 

 cylinder than the formula, and this is to be expected from the wave- 

 form. 



At 45 seconds periodic time and maximum average induction 

 density for No. 4 coil 5900, the ratio of the watts given by theory 

 and experiment is 3*15, which is much larger than the average. The 

 explanation is that the magnetic induction is crowded to the surface 

 of the cylinder, and as the wave-form for this portion is more nearly 

 rectangular, the result is to make the watts given by experiment rela- 

 latively smaller. At periodic time 90 seconds we see the same 

 influence at work when maximum average induction density given by 

 coil 4 is 6700. On the other hand, there is no great difference between 

 the results at 360 and 45 seconds periodic time with approximately 

 uniform distribution of the intensity of magnetic induction. 



field for the watts dissipated by induced currents per cubic centimetre 



of a cylinder to which an alternating magnetic force is applied whose 

 direction is parallel to the longitudinal axis of the cylinder. The 

 diameter of the cylinder is d centimetres, and the other symbols repre- 

 sent the same quantities as before. This formula for frequency 129 

 and p = 13 x 10~ 6 ohm is approximately verified by experiment. The 

 following results were obtained with a cylinder of mild steel 4 inches 

 (10*16 cm.) diameter,! and have been extended to the case of a 

 cylinder 0*1 cm. diameter on the assumption that similar electric and 

 magnetic events happen in cylinders of different diameters at times 

 varying inversely as the square of their diameters : — 



* See ' The Alternate Current Transformer,' yoI. 2, p. 487. 



f See Hopkinson and Wilson, ' Phil. Trans.,' A, vol. 186 (1895), pp. 93-121. 



2 C 2 



Alternating Magnetic Force. 



B 2 /" 2 ^ 2 



Fleming* gives the expression 0*616 ii 



in a uniform magnetic 



