﻿296 Lord Rayleigh on a Quantitative 



Unfortunately such an estimate is a matter of extreme diffi- 

 culty, partly on account of imperfection in our knowledge of 

 the magnetic properties of iron, and partly from mathematical 

 difficulties arising from the particular forms employed in 

 actual construction ; and indeed the problem does not appear 

 to have been attacked hitherto. In view, however, of the 

 doubts that have been expressed as to theory, and of the 

 highly discrepant estimates of actual sensitiveness which have 

 been put forward, it appears desirable to make the attempt. 

 It will be understood that at present the question is as to the 

 order of magnitude only, and that the result will not be with- 

 out value should it prove to be 10 or even 100 times in error. 

 One of the elements required to be known, the number (n) 

 of convolutions, cannot be directly observed in the case of a 

 finished instrument ; but it may be inferred with sufficient 

 accuracy for the present purpose from the dimensions and 

 the resistance of the coil. Denote the axial dimension by £ , 

 the inner and outer radii by rj L and r} 2) the section of the wire 

 by a and its total length by l } so that la is the total volume 

 of copper. The area of section of the coil by an axial plane 

 is ^(V2 — Vi)) an d of this the area na is occupied hj copper. 

 If we suppose the latter to be half the former, we shall not be 

 far from the mark. Thus 



w<r= if (%— «/i) (1) 



On the same assumption, 



fr-WW-ifl (2) 



Accordingly, if R be the whole resistance of the coil, and r 

 the specific resistance of copper, 



R= 4 = Wfe+^) 



o- f(%-*h) 



As applicable to actual telephones we may take £ =1 centim., 

 772 = 377! ; and then K = 47rm 2 . In G.G.S. measure r = 1600, 

 and thus 



n2== 47rxl600 (4) 



If the resistance be 100 ohms, 



R=10 n , and n=2230. 



When the resistance varies, other circumstances remaining 

 the same, 



n oc y'R. 



We have now to connect the periodic force upon the tele- 



