Intelligence and Miscellaneous Articles, 79 



Point Weights 



of immersion. in grams. Vibrations. 



110 2 6 



84 35 5 



76 4 4 



30 6-7 3 



The ratio of the numbers in the second and third columns will be 

 found to follow Melde's law. 



For qualitative or quantitative experiments upon beats or Lissa- 

 jous curves this method of loading the prong of a tuning-fork can 

 advantageously replace the bit of wax or the sliding weight, since 

 we have at our command a quick and precise method of adjustment. 

 — Silliman's American Journal, May 1874. 



ON CONSTANT ELECTRIC CURRENTS. BY M. HEINE, OF HALLE. 



Kirchhoff* has developed a simple expression for the electric 

 potential, with a constant current, in every point P of a circular 

 homogeneous plate into which the current enters at given points 

 Aj, A 2 , .... If each letter E represents a constant depending on 

 the strength of the current entering at the point A t , and if B t is 

 the conjugate point to A t , the electric potential of the circle in the 

 point P becomes 



Y=SE t log(PA t .PB l ), (a) 



when the summation is extended to all the points of inflow. Two 

 points A, B of the circle are called conjugate which lie on the same 

 right line MAB starting from the centre M, if the radius forms the 

 mean proportional between MA and MB. 



I have found the expression of the potential also for plates of 

 other shapes, and will here give it for the ellipse and the rectangle. 



Let the excentricity of the ellipse be 1 ; let the fourth power of 

 the difference of the semiaxes (of which the greater represents the 

 axis of the real, the smaller that of the imaginary) be put =q. 

 Let each point z of the ellipse be described by the elliptic function 



/2K . \ 



sn ( — arc sin z J, 



therefore the entire ellipse upon a circle with the radius —j= (as M. 



Schwarz has shown). If now a, p are the images of the inflow- 

 points A and an arbitrary point P of the ellipse, and if b denotes 



the point in the circle of radius — - conjugate to a, the electric po- 

 tential of the ellipse in the point P will be 



V = SE l log(pa t .^6 t ) (/3) 



If, lastly, we have a rectangle OXNY, whose base OX has the 

 length it and is the axis of the real, and its height OT equals 

 — log q and is the axis of the imaginary, we construct for each 

 point of inflow A the three reflected images B, C, D which arise 

 when A is assumed to be luminous, OX and OT reflecting (a?-4-y», 

 x —yi, —x—yi-) ~ v+yi)' If now each points be represented by 

 * Pogg. Ann. vol. lxiv. p. 497, vol. lxvii. p. 344. 



