328 Messrs. Trowbridge and Sabine on 



along the guides which kept the stylus on the blackened 

 cylinder. 



Calling L the coefficient of self-induction, we have 



^=2,o g g + l* 



in which I is the length of conductors contained between two 

 parallel planes ; b the distance apart of the conductors ; a the 

 radius of wires. 



In our case the effect of the ends was found to be inappre- 

 ciable. The induction due to the ends can be calculated by 

 the repeated employment of the formulse for geometric mean 

 distance f for two lines whose directions intersect at right 

 angles. 



Lord Kayleigh has given the following formula for induct- 

 ance under rapid oscillations : — 



L '=< A Vg) ; 



in which A is a constant, depending on form of circuit ; jjl is 



27T 



permeability ; R is resistance ; p = -~ where t is time of 



oscillation ; I is length to and fro of inductance-circuit. 

 The final value of 1/ for our case is 17 = 39697. 

 The radius of the wire employed was a=*0501 centim. 

 The length was measured in three sections : — 



No. 1, length 1197*0 cm., distance between wires b x = 31'55 cm. 

 No. 2, „ 281-0 „ „ „ 6 2 =16'lcm. 



No. 3, „ 103-0 „ „ „ 6 3 =ll-3cm. 



The ohmic resistance of the wires was *742 x 10 9 for direct 

 current, and 1*54 x 10 9 for alternating currents of period t — 

 •0000031. 



The difficulty in the process of photographing the spark 

 consisted in discharging the air condenser through the induc- 

 tion-circuit at the instant the revolving mirror was in a 

 position to reflect the image of the spark to the photographic 

 plate. The terminal connected with the revolving mirror, 

 which allowed the electrical discharge to pass when the mirror 

 was in the desired position, had to be adjusted with extreme 

 care. The speed of the image at the photographic plate was 

 about 1 mile per second. 



The photographs were measured by means of a dividing- 

 engine. At first an objective of low power was used on the 

 microscope of the dividing-engine. It was found, however, 



* Maxwell, § 685, vol. ii. t Ibid. § 692, vol. ii. 



