246 Mr. T. Mizuno on the Function of 



or apertures. In fact, crossed cylindrical lenses, whether the 

 lenses are at right angles or are inclined obliquely, and also 

 spherical and cylindrical combinations, may be replaced by 

 their equivalent ellipsoidal or quadric lenses, or for an 

 ellipsoidal lens a pair of cylindrical lenses, or a spherical and 

 a cylindrical lens, may be substituted ; for the arrangement 

 or distribution of refracting substance is similar in such lenses 

 or combinations. And, moreover, the preceding geometrical 

 constructions afford a ready means for effecting the trans- 

 formation from any assigned type of the combinations named 

 to the type of any other. The method is applicable to 

 astigmatic lenses or combinations in which the curvatures are 

 not all of the same sign. 



XX. The Function of Self-Induction in Wehnelt's Interruptor. 

 BtjT. Mizuno*. 



WEHNELT t discovered a very interesting interruptor 

 and made a minute investigation on its properties. 

 Soon after this discovery, Simon J also carried out experi- 

 ments on the new interruptor and gave the theory of its 

 action. According to his theory, an electric current i sent 

 through the interruptor of the resistance w grows logarith- 

 mically, and finally attains such a value that the Joule's heat 

 expressed by the integral 



0-24 §i 2 wdt, (1) 



where 



i=*(i-<rH ( 2) 



w\ J v ' 



E being the impressed electromotive force, and L the 

 coefficient of sell-induction of the circuit, 

 is sufficient to call forth the vaporization of the electrolyte 

 in the neighbourhood of the active electrode. By this 

 vaporization the current is suddenly broken, but immediately 

 there takes place a cooling process in consequence of which 

 the vapour is condensed, the circuit being thereby re-estab- 

 lished, and the action of the interruptor continued. 



However, the condensation of the vapour is not the sole 

 requisite for maintaining the action of the interruptor. 



In fact, the self-induction of the circuit plays a very 

 important part at the instant of break in re-establishing the 

 once-broken circuit. This important fact was first found by 



* Communicated by the Author. 



f A. Welmelt, Wied. Ann. lxviii. p. 233 (1899). 



\ H.-T. -Simon, Wied. Ann. lxviii. p. 273 (1899;. 



