228 Intelligence and Miscellaneous Articles. 



entirely covered with numerous Hall's electrodes, each connected 

 with the one opposite. Let E be the electromotive force of the 

 battery which urges the primary current, J its intensity, r— 1 1 nbd 

 the resistance which it finds in the plate, w the remaining resistance, 

 i the entire intensity of the Hall current, p = b | kU its resistance in 

 the plate, w the remaining resistance, then : 



E — al = w J, cb=wi, E — — — — I = ivj = wbfoi, 



K 



— v + hu b = yi=Mv, KW\l=(l+f)u+hv, hu=(l + cl>)v; 



in which f=w \ r, <£= w \ p. The resistance is therefore increased in 



the ratio : 1, since 



1 + fi 



Sitzungsberichte der Jcaiserlic7ien AJcademie in Wien, April 8, 1886. 



ON THE GOLD-LEAF ELECTROSCOPE. BY FR. KOLACEK. 



In the following way we get at a relation between the angle of 

 divergence <f> and the difference of potential P between the leaves 

 and the envelope (base-plate metal-case). Let be the capacity 

 of the electroscope, considered as a condenser, which depends on <■/> ; 

 E = PC the quantity of electricity on the inner coating ; Z, g the 

 length and weight of one of the leaves, which are assumed to be 

 quite equal ; E 2 /2C the electrostatic, and 2l/2g(l — cos (p/2) the 

 ordinary energy of mechanical origin corresponding to a rise of 

 the centre of gravity of the leaves. If the electroscope has been 

 left to itself and insulated, the variation of the entire energy 

 E 2 /2C-f g.l(l— cos 0/2) equal to zero of a virtual deflection d(f> is 

 imparted to the leaves. If we consider that C, but not E, is affected 

 by the variation, the following equation results between $ and P: — 



sinj 



J clC ' 



Eor an infinitely small <p, (dCfd(p)(}>=0 is to be considered constant, 

 and the deflection in this case indicates magnitudes, which are pro- 

 portional to the square of the above difference of potential. For a 

 greater (p an expansion in series must be made. The formula with 

 two constants a$ + &0 2 =P 2 may be experimentally confirmed to a 

 divergence of about 18°. 



The leaves, 8 centim. in length, were projected in fifteenfold 



