﻿286 Lord Rayleigh on the Minimum Current 



the Fourier series representative of the actual current were 

 effective- On this account the quantities in the third column 

 should probably be increased, for the presence of overtones 

 could hardly fail to favour audibility. 



Although a considerable margin must be allowed for vary- 

 ing pitch, varying acuteness of audition, and varying con- 

 struction of the instruments, it is scarcely possible to suppose 

 that all the results above mentioned can be correct, even in 

 the roughest sense. The question is of considerable interest 

 in connexion with the theory of the telephone. For it 

 appears that a priori calculations of the possible efficiency of 

 the instrument are difficult to reconcile with numbers such as 

 those of Tait and of Preece, at least without attributing to 

 the ear a degree of sensitiveness to aerial vibration far sur- 

 passing even the marvellous estimates that have hitherto been 

 given * . 



Under these circumstances it appeared to be desirable to 

 undertake fresh observations, in which regard should be paid 

 to various sources of error that may have escaped attention 

 in the earlier days of telephony. The importance of de- 

 fining the resistance of the instruments and of employing 

 pure tones of various pitch need not be insisted upon. 



As regards resistance, a low-resistance telephone, although 

 suitable in certain cases, must not be expected to show the 

 same sensitiveness to current as an instrument of higher resist- 

 ance. If we suppose that the total space available for the 

 windings is given, and that the proportion of it occupied by 

 the copper is also given, a simple relation obtains between 

 the resistance and the minimum current. For if 7 be the 

 current, n be the number of convolutions, and r the resistance, 

 we have, as in the theory of galvanometers, 727 = const., 

 n -2 r — const., so that y s /r= const., or the minimum current 

 is inversely as the square root of the resistance. 



The telephones employed in the experiments about to be 

 narrated were two, of which one (T x ) is a very efficient in- 

 strument of 70-ohms resistance. The other (T 2 ), of less 

 finished workmanship, was rewound in the laboratory with 

 comparatively thick wire. The interior diameter of the 

 windings is 9 millim., and the exterior diameter is 26 millim. 

 The wudth of the groove, or the axial dimension of the coil, is 

 8 millim., the number of windings is 160, and the resistance is 

 *8 ohm. Since the dimensions of the coils are about the 



* Proc. Hoy. Soct vol. xxvi. p. 248 (1877). Also Wien, YVied. Ann. 

 vol. xxxvi. p. 834 (1889). 



