Oscillations in tJie Discharge of a Let/den-jar. 97 



that the magnetic force acting on the needle is proportional 

 to the length o£ the arc traversed by the discharge. 



The circuit was rectangular in shape and measured 145 by 

 125 cms. The wires forming it were of copper '035 cm. in 

 radius, and the self- inductance of such a circuit calculated by 

 the formula 



L = 4^Hog e -, 



where 1= length of wires, b = distance between them, and a 

 is their radius, was found to be about 10 4 C.G.S. units. The 

 capacity of the leyden-jar employed was 2500 E.S. units ; 

 therefore assuming R = 0, we get time of oscillation 



T = 27rVLC 

 = :j-7T6i approximately; 



T_ 1 



* ' 2 10 6 * 



If yj, 7 2 be the maximum currents for first and second half- 

 oscillations respectively, then since the current at any time 7 

 is given by 



o„ -», . t . 



7= - ,e 2L sin t — ; 



_ R T 



then y x =joCv e 2L ' * , 



where jo = 1/VLO, 



_r_ :£f 

 and y 2 =pCv e ^l'4; 



_ R_ T 



.*. the damping 70/71 = 6 2L '*. 



The observations were made in the following way: — The 

 needle was magnetized to saturation in a solenoid which had 

 a fixed iron core extending through part of its length. 

 Against this core the needle was pressed so that it was 

 thoroughly magnetized, and could be replaced in exactly the 

 same position every time it was to be remagnetized. The 

 needle w T as then placed in position at the centre of the circle, 

 and the deflexion compensated by a neighbouring magnet. 

 If the arm of the circle was at C (fig. 1), when a discharge 

 passed no effect was produced on the needle; but if any part 

 of the arc was included there was a deflexion due to the 

 partial demagnetization of the needle. The deflexion was 

 noted, the needle removed, completely demagnetized, and 



Phil. Mag. S. 6. Vol. 2. No. 7. July 1901. H 



