Note io; disruptive discharge 375 



to f"" 1 ; r being the distance Op, and the exponent n very nearly such as would 



satisfy the simple equation 



(4 + 2) = 377, 



where 2/J is the angle at the summit of the cone. 



If 2jS exceeds TT, this summit is directed outwards, and when the excess is 

 not very considerable, n will be given as above: but 2/? still increasing, until 

 it becomes ZTT 2y, the angle 2y at the summit of the cone, which is now 

 directed outwards, being very small, n will be given by 



2 

 2n log - = i, 



and in case the conducting body is a sphere whose radius is b, on which P 

 represents the mean density of the electric fluid; p, the value of the density 

 near the apex 0, will be determined by the formula 



zPbn /r\"- 1 , 

 P = (a 4- b) y (a) 

 a being the length of the cone." 



Professor F. G. Mehler* of Elbing has investigated the distribution of 

 electricity on a cone under the influence of a charged point on the axis, and the 

 inverse problem of the distribution on a spindle formed by the revolution of 

 the segment of a circle about its chord. 



He finds that when the segment is a very small portion of the circle, so that 

 the conical points of the spindle are very acute, the surface-density at any 

 point is inversely proportional to the product of the distances of that point 

 from the two conical points. 



NOTE 10 [ART. 139]. 

 [Conditions for Disruptive Discharge^.] 



Sir W. ThomsonJ has determined in absolute measure the electromotive 

 force required to produce a spark in air between two electrodes in the form of 

 disks, one of which was plane, and the other slightly convex, placed at different 

 distances from each other. Mr Macfarlane has recently made a more extensive 

 series of experiments on the disruptive discharge of electricity. He finds that 

 in air at the ordinary pressure and temperature the electromotive force required 

 to produce a spark between disks, 10 cm. diameter, and from i to 0-025 cm - 

 apart, is expressed by the empirical equation 



V = 66-940 (s 2 + -205035)*, 

 where s is the distance between the disks. 



If we suppose that in the space between the disks the potential varies 



* Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function, und 

 ihre Anwendung in der Theorie der Electricitatsvertheilung. (Elbing, 1870.) 

 t [See for modern knowledge Sir J. J. Thomson, Conduction... in Gases.] 

 I Proc. R. S. 1860, or Papers on Electrostatics, chap. xix. 

 Trans. R. S. Edin. vol. xxvm, Part n (1878), p. 633. 



