1891.] Application to Periodic Electric Currents. 215 



can be reduced to zero by taking cti small enough. But of course 

 (37) ceases to be applicable unless fej be small relatively to a^ In 

 correspondence with (40), 



e> = % 01, e 2 = i fc 2 (41) ; 



As an example of (37), suppose 



Then (37) = nearly. 



640 



Also approximately 



If 6 2 represent the stiffness of a condenser, / 2 must be a positive 

 inductance, and its magnitude, relatively to /i, would probably con- 

 stitute a difficulty. 



As an example, with a^ equal to zero, take 



td\ = -jJjj &2 fl 2 == 0. 



en (37) = (40) = ^ b ? nearly, 



and 



* 



2 & 2> /I = I *2> /2 = To 



o far as the general theory is concerned, it is a matter of indif- 

 ference whether the indicating instrument be in the branch e, or in 

 /. The latter corresponds to the connections in De Sauty's method 

 of testing condensers by means of the galvanometer. In practice, 

 more space would probably be available for the coils of a transmitting 

 instrument than of the receiving instrument, at least, if the latter be 

 a telephone ; and this would tell in favour of choosing that branch for 

 the transmitter which should have the larger time constant (L/R). 



To get an idea of the relative capacities, resistances, and induct- 

 ances involved, we must assume a particular pitch. A frequency 

 suitable for telephonic experiments is 1000 per second, for which 

 p = 2000 TT. Thus, if the value of a 2 for a condenser of capacity C, 

 and for an inductance L, and that of a x for a resistance B, are all 

 numerically equal, 



BR = 2OOOn-L = 

 1 R be 1 ohm, equal to 10 9 C.G.S., the corresponding capacity is 

 l'6xlO~ 13 C.G.S., equal to 160 microfarads, and the corresponding 

 OL. XLIX. Q 



2000 TrC' 





