of Electrical Discharges. 259 



nitric acid, the magnets weighed after each immersion in the 

 acid, and their magnetic moments determined. The results of 

 this process with one pair of magnets are plotted in fig. 2, in 

 which the ordi nates are magnetic moments and the abscissas are 

 weights in units of fifty milligrams. The curves therefore 

 represent magnetic moments decreasing with weights. It will 

 be observed that the moment of A decreases from the first 

 continuously, while that of B first rises to a maximum and 

 then falls according to the law exhibited by A. These curves 

 afford a complete explanation of the anomalous deportment of 

 the magnets upon exchanging them in the coils. B has a thin 

 external shell magnetized in a sense opposite to that of the 

 underlying portions. When B takes A's place, this external 

 magnetism is reversed by the first subsequent discharge and 

 made similar to the underlying portions ; while A, being placed 

 under B's former conditions, suffers a reversal on the exterior, 

 thus losing in resultant magnetic moment, or " evident mag- 

 netism." When the magnets are examined after a single dis- 

 charge of the Leyden jar they give rise to exactly similar 

 curves, except that the reversed portion of curve B is some- 

 what longer. 



An examination of the conditions under which an oscilla- 

 tory discharge takes place, and particularly of the formula for 

 the period of an oscillation, will throw light on the reversed 

 curve of B. The first mathematical discussion of electrical 

 oscillations was by Sir William Thomson in 1853,* and was 

 founded on the "equation of energy." Kirchhofff subse- 

 quently arrived at similar equations by introducing into the 

 expression for the electromotive force a coefficient of self-in- 

 duction. Later writers, Chrystal,J Mascart and Joubert,§ have 

 followed the method of Kirchhoff. These investigations show 



/IL . 

 that the discharge will be oscillatory when R<Cy 77, in which 



R is the resistance of the discharger, L the coefficient of self- 

 induction, and C the capacity of the principal conductor. The 



period of an oscillation is — where n~y — — . When R 



n xj\j 4JL 3 



is very small, the period of an oscillation is proportional to 



^LC. In all my experiments the greatest value of R, not 



including the air resistance of the spark, was 0*58 ohm. We 



may, therefore, for our purposes consider the period of an 



oscillation jointly proportional to the square root of the ca- 



* Mathematical and Physical Papers, vol. i, p. 540. 



fGesammelte Abhandlungen, "Zur Theorie der Entladung einer Leydener 

 Flasche," p. 168. 



± Encyclopaedia Britannica, vol. viii, p. 81. 



§ Electricity and Magnetism, vol. i. p. 512, English edition. 



