204 LORD RA.YLEIGH. 



In the above discussion the capacity q of the secondary will probably 

 be thought to play an unexpectedly important part, and the question 

 may be raised whetlier it is really this capacity which limits the spark- 

 length in actual coils. It is not difficult to prove by experiment that 

 capacities of the order above estimated, applied to the secondary termi- 

 nais, do in fact reduce the spark-length, though not, so far as I have 

 seen, to the extent denianded by the law of q~~ } - . But we must remember 

 that this law lias been obtained on the assumptions, not to be fulfilled 

 in practice, of absolute suddenness of break and of entire absence of 

 eddy-currents in the iron. If under thèse conditions secondary capacity 

 were also absent, it would seeni that there could be no limit to the 

 maximum potential developed. The experiments of Prof. J. J. Thomson ] ) 

 may be considérée! to show that eA 7 en in extrême cases, such as the pré- 

 sent, the iron, as a magnetic body, would not fail to respond. 



As regards the eddy-currents, it may be well to consider a little fur- 

 ther upon what their importance dépends. If there were no secondary 

 circuit, the magnétisai of each wire of the iron core would be continued 

 at the moment after break, supposed infinitely sudden, by a superficial 

 eddy-current. A secondary circuit, closely intertwined with the primary, 

 would transfer thèse eddy-currents to itself, and so continue for the 

 first moment the magnetism of the core. But a little later, as the mag- 

 netism diminished, eddy-currents would tend to be formed, and their 

 importance for our purpose dépends upon their duration. If this be 

 short, compared with the time-constants of the secondary circuit, their 

 influence may be neglected. Otherwise the electromotive force of the 

 falling magnetism lags, and acts to less advantage. The time-constant, 

 viz., the time in which the current falls in the ratio e : 1, for the prin- 

 cipal eddy-current in a cylinder of radius R is given by 



(2-404) 2 ' 



where C represents the conductivity and the permeability. 



If cl be the thickness of a thin sheet baving the same time-constant 

 as the wire of radius i£, it is easily shown in the same way that 



d:lî = 7r: 2-404. 



x ) „Recent Researches," p. 323. 



2 ) Brit. Ass. Rep. p. 446, 1882; Scientific Papers, II, p. 128. 



