1881.] Determination of the Ohm in Absolute Measure. 119 



I have applied (13) to estimate the correction for curvature in the 

 self-induction of each part of the double coil. For reasons which it 

 would take too long to explain, I arrived at the conclusion that the 

 value of the small term must be very nearly the same for a circular 

 section as for a square section of the same area, and the actual 

 section is nearly enough square to allow of the use of this principle. 

 The necessary addition to the originally calculated self-induction of 

 each part, in order to take account of curvature, comes out 119 '5 

 metres ; so that the final value of L for the double coil will on this 

 account be increased 239 metres. This is a small quantity, but a 

 much larger correction for curvature must be expected in the mutual 

 induction of the two parts. By a sufficiently approximate method I 

 find as the correction to twice the mutual induction 3,469 metres, 

 giving altogether for twice the mutual induction 149,289 metres. 

 This added to 302,159 (=301,920 + 239) metres gives as the final 

 calculated value of L for the double coil, 



L= 451,448 metres. 



This result is confirmed by calculation of the mutual induction by 

 means of a table, founded on elliptic functions. In this way, and with 

 a suitable formula for quadrature, we find, 



2M=149,394 metres, 



agreeing nearly enough with the value found by Maxwell's method, viz., 

 149,289 metres.* When all the evidence is taken into consideration, 

 there can remain, I suppose, little doubt that the value 451,000 is 

 substantially correct, and that the reductions of the Committee are 

 affected by a serious under- estimate. 



Professor Rowland, in ignorance apparently of Maxwell's previous 

 calculation, has shown that if in the original experiments we assume an 

 unknown cause of error proportional to the square of the speed, and 

 eliminate it, we shall arrive at a value of the ohm differing very 

 appreciably from that adopted by the Committee. In this way he 

 finds that — 



1 ohm=-9926 eartl1 q» adran l, 

 second 



Rowland is himself disposed to attribute the error to currents induced 

 in the frame. Our experiments prove these currents had not much 

 effect, though they may explain the difference between the value of 

 L which best satisfies our experiments (where the currents could 

 not exist), i.e., 451,000, and the higher value 457,000 calculated by 



* The arithmetical calculations were made from the data given by the Committee 

 (Reprint, p. 115), a = -158194, 2b' = '03851, b = '01841 (not '1841), c= "01608, all in 

 metres. w = 313. The whole number of turns (313) was supposed to be equally 

 divided between the two parts. 



VOL. XXXII. K 



