1881.] Determination of the Ohm in Absolute Measure. 117 



a formula which exhibits the time-constant of the coil P in terms of 

 the period of the galvanometer needle. Further to deduce the value 

 of L in absolute measure from the formula requires a knowledge of 

 resistances in absolute measure. 



In carrying out the experiment the principal difficulty arose from 

 want of permanence of the resistance balance, due to changes of 

 temperature in the copper coil. The error from this source was, 

 however, diminished by protecting the coil with flannel, and was in 

 great measure eliminated in the reductions. The result was L= 455,000 

 metres. This is on the supposition that the ohm is correct. If, as we 

 consider more probable, the ohm is one per cent, too small, the result 

 would be L= 450,000. 



Without attributing too great importance to this determination, 

 there were now three independent arguments pointing to the higher 

 value of L : first, from the experiments of the Committee ; secondly, and 

 more distinctly, from our experiments ; and thirdly, from the special 

 determination ; and I entertained little doubt that a direct calculation 

 from the dimensions of the coil would lead to a similar conclusion. 



This direct calculation proved no very easy matter. Mr. W. D. 

 Niven (whom I was fortunately able to interest in the question) and 

 myself had no difficulty in verifying independently the formulae given 

 in "Maxwell's Electricity and Magnetism," §§ 692, 705, from which 

 the self-induction of a simple coil of rectangular section can be found, 

 on the supposition that the dimensions of the sections are very small 

 in comparison with the radius. In the notation of the paper on the 

 electro-magnetic field, if r be the diagonal of the section, and the 

 angle between it and the plane of the coil, 



L=4rf a j~l og(? — + T V- cot 29-±7T cosec 20 



— ^cot 2 0log e cos6> — £ tan 2 6> log, sin 6>J . . . (10). 



In the paper itself, probably by a misprint, cos 20 appears, instead 

 of cosec 20, in (10). The expression is, as it evidently ought to be, 

 unchanged when \tv—0 is written for 0. By an ingenious process, 

 explained in the paper, the formula? is applied to calculate the self- 

 induction of a double coil.* 



The whole self-induction of the double coil is found by adding 

 together twice the self-induction of each part and twice the mutual 

 induction of the two parts. The self-induction of each part is found (to 



* The following misprints may be noticed : — 



Page 509, fine U, for B read C. 



„ 13, for L(AC) read M(AC). 

 for L(B) read L(C). 

 Attention must be directed to the peculiar meaning attached to depth. 



