392 



Dr. A. Macfarlane on the Disruptive 



Measurement of the Difference of Potential required to pass a 

 Spark through Air at the Atmospheric Pressure between 

 Parallel Metal Plates at different Distances, 

 Tins problem, as is well known, was investigated by Sir 

 William Thomson* for distances between -0025 and '15 cen- 

 timetre. I have been able to extend the investigation to a 

 distance of 1 centim. The plates used as electrodes were two 

 equal circular brass disks of 10 centims. diameter. Both were 

 rounded at the edge ; and the lower one had its face slightly 

 convex. The distance between the plates was measured by 

 applying a glass millimetre-scale to a mark on the upper part 

 of the rod. The shortest distance for which readings were taken 

 was '025 centim. , and the greatest about 1 centim.; within 

 that range the sparks were central and straight, while beyond 

 it they passed in a curved line between the edges of the disks. 

 Five series of observations were taken, and were found to 

 agree well with one another. One of them is plotted on dia- 

 gram 1, Plate XI. The curve drawn through the points of ob- 

 servation closely resembles a hyperbola. I drew the asymptote 

 which appeared to be indicated, found the equation of the cor- 

 responding hyperbola, and corrected that equation by a second 

 application of the graphic method. Thus in one case the cor- 

 rected equation is 



V = (66-69-3-7142s)v/(> 2 + -2s) 7 

 which gives 



V 2 = 889-52s + 4348-5s 2 -494-68s 3 + 3-7142s 4 , 

 where V denotes the difference of potential, and s the length 

 of the spark. For s less than 1 the third and fourth terms are 

 small; they are probably due to the finite nature of the plates. 

 By neglecting them we obtain a hyperbolic function for V 

 which agrees with the curve of observation at the beginning, 

 and is only slightly greater at the end. By this treatment of 

 the five series of observations I obtain the following results : — 



Series. 



Function for V. 



a. 



b. 



L 



II. 

 III. 

 IV. 



V. 





"1020 centim. 

 •1015 „ 

 •1018 „ 

 •1023 „ 

 •1051 „ 



6-800 C.G.S. units. 

 6-752 „ 

 6-852 „ 

 6-745 „ 

 7-163 „ 



66-69\A 2 + -2039 s 



66-51vV + -2030s 

 67-34n/s 2 + -2035* 



65-95a/6- 2 + -2046 s 



68-Ws 2 + '2102s 



Mean 





•1025 „ 



6-862 



V 



66-94 \/s 2 + -205 s 



* Papers on Electrostatics and Magnetism, p. 247. 



