494 Lord Rayleigh. on the Self-induction and 



With these values the effects 8L, 8R of the core of 3 # 3 

 millim. diameter may be calculated ; but no very good agree- 

 ment with observation is to be expected, since the conditions 

 of infinite length, isotropy, &c. were but inadequately satisfied. 

 Inserting in (16) m = 205/ 28*6, a = \L65, /*=99'5, we get 



SL = 1650, SR=10 6 x 9-436. 



These are expressed in absolute measure, and reckoned per 

 unit length of core.. To obtain numbers comparable with 

 the experimental readings, we must multiply by 24*1 (the 

 length of the core), and reduce SL by division by 1553, and 

 8U by division by 10 9 x '0492. The result is 



(SL)=25°-6, (8R)=4-6; 



which agree moderately well with the observed values, viz. 



(8L) = 24i°, (SB) = 3-8, 



If the material composing the core were non-conducting, 

 P=l, and 



SL =4mV 2 aV--l). 



The ratio of the actual effect to that which would be got 

 from the same aggregate section of a bundle of wires, infinitely 

 thin and insulated from one another, is thus 



SL _ /eP- 

 8L j*-l > 



of which the numerical value in the present example is '303. 

 The corresponding ratio of observed effects for the solid wire 

 (softened), and for the bundle of 35 wires of the same aggre- 

 gate section was 



28i/84 = -339. 



The general result of these experiments is to support the 

 conclusion arrived at by Oberbeck that the action of iron 

 cores, submitting to periodic magnetizing forces of feeble 

 intensity, can be calculated from the usual simple theory, 

 provided we do not leave out of account the induced internal 

 currents which often play a very important part. Oberbeck's 

 observations were made with the electrodynamometer, and 

 with rather low frequencies of vibration — about one tenth of 

 that used in most of the observations here recorded. 



We have seen in several examples that the self-induction 

 of a combination of conductors, being a function of the pitch, 

 admits of an indefinite series of values ; and the question 

 suggests itself to which (if any) of these corresponds the 



