OP ARTS AND SCIEN'CES. 



121 



Soft iron 

 Piano steel 

 Nickel . . 

 German silver 



15.0 X 109 



20.7 X 10^ 



30.G X 109 



23.0 X 109 



The ratio of the strengths of successive discharges during the oscil- 



rT 



lation is given by the function e^^, where r is the ohmic resistance, 

 T the time of a double oscillation, and L the self-induction. The 

 ratio of one discharge to the nth one after it is e'^2/;. If we as- 

 sume — and it is a large assumption, but one which perhaps the result 

 will in some measure justify — that the ratio of the strength of the first 

 to the strength of the last visible discharge is more or less a constant, 



T 

 we may make use of the above data. Denote ^^ by A, and call 



the unknown resistance of tlie short connecting lead wires and of the 

 spark X. Then will r =. R' -\- x, and ?i will be the number of com- 

 plete oscillations visible. 



Take cases (1) and (2), large copper and large German silver 

 wires : — 



n^ {R\ + X)^ «2 (i?'2 + x) ; 



9.5 (0.66 + x) =z 3 (9.2 + x) ; 



X ■= 3.4 ohms. 



Taking cases (1) and (4) similarly, 



«i (E\ + x)=n, (R', -f x) ; 

 9.5 (0.66 + x) = 5 (3.5 -f- x) ; 



X = 2.6 ohms. 



Experiments with other copper wires having 7?' equal to 3.4 and 

 1.27 gave and 8 for the values of n respectively, or 



X = 2.4 ohms. 



The resistance (R') of the lead wires forming part of x was 0,8 

 ohm, leaving as a possible value for tiie resistance of the spark 

 about 2 ohms. 



If, taking this value of x, we calculate the value of R' necessary to 

 damp out the oscilhition in one complete double discharge iu the case 

 of the large iron wire, we shall have 



9.5 (0.66 X 3) =. 1 (R' + 3); 



R' = 30 ohms. 



