ON THE ABSOLUTE UNIT OF ELECTEICAL EESISTAXCE 151 



fact that, if Ohm's law be correct, the algebraical sum of the currents 

 at every point in the frame is zero, and hence the average magnetic 

 action on the needle zero. But although these currents can have 

 no direct action, they can still act by modifying the current in the 

 coil; for while the coil is nearing one of the supports the current 

 in the coil is less than the normal amount, and while it is leaving 

 it is greater; and although the total current in the coil is the normal 

 amount, yet it acts on the needle at a different angle. By changing 

 the direction of rotation, the effect is nearly but not quite eliminated. 

 The amount of the effect is evidently dependent upon the velocity 

 of rotation and increases with it in some unknown proportion, and 

 the residual effect is evidently in the direction of making the action 

 on the needle too small and thus of increasing R. If these currents 

 are the cause of the different values of R obtained with positive and 

 negative rotation, we should find that if we picked out those experi- 

 ments in which this difference was the greatest, they should give 

 a larger value of R than the others. Taking the mean of all the 

 results " in which this difference is greater than one per cent, we find 



for the Ohm 1.0033 earth ^ uadt , and when it is less than one per 



sec. 



cent, -9966 r - SC*r which is in accordance with the theory, the 

 sec. 



average velocities being ^ and *^ nearly. But the individual 

 observations have too great a probable error for an exact comparison. 



But whatever the cause of the effect we are considering, the follow- 

 ing method of correction must apply. The experiments show that R 

 is a function of the velocity of rotation, and hence, by Taylor's theorem, 

 the true resistance R must be 



R = R (1 -f- Aw + Bw 2 + &c.), 



and when R is the mean of results with positive and negative rotations, 

 R = R (1 -f Bw 2 + DW* + &c.). 



Supposing that all the terms can be omitted except the first two, and 

 using the above results for large and small velocities, we find .R 



_ . 9926 earth quad. But if we - ect the two resu i ts i n wn i c h the 

 sec. 



8 In the table published by the Committee the different columns do not agree, and 

 I have thought it probable that the last two numbers in the next to the last column 

 should read 1-0032 and 1-0065 instead of 1-0040 and -9981, and in my discussion I 

 have considered them to read thus. 



