of Electricity through Gases. 



185 



is 



polation when y is wanted for spheres which are near together 

 and for a value of c not directly given in the Table. If 

 the smallest distance between the spheres, that is the explo 

 sive distance, x is defined by the equation 



R=aV*/«. 



(5) 



If the normal force were to vary uniformly between the 

 spheres we should have ~R' = V/e, and x is the numerical factor 

 which has to be applied to B/ in order to obtain the true value 

 K. Column 5 shows that x varies with sufficient uniformity 

 to render interpolation easy. 



Table I. 



I. 



II. 



III. 



IV. 



V. 



c. 



Q- 



/(<?)• 



<££ m=y. 



X. 



21 



•7298 



•9331 



10-335 



10335 



2-2 



•6417 



•7099 



5-342 



1-0684 



23 



•5821 



•6157 



3-687 



1-1061 



2-4 



•5367 



•5641 



2-875 



1-1500 



2-5 



•5000 



•5329 



2398 



1-1990 



2-6 



•4693 



•5135 



2-089 



1-2534 



2-7 



•4431 



•5018 



1-876 



1-3132 



2-8 



•4202 



•4953 



1-723 



1-3784 



2-9 



•4000 



•4918 



1-607 



1-4463 



30 



•3820 



•4908 



1-517 



1-5170 



3-5 



•3139 



•5059 



1-273 



1-9095 



4-0 



•2680 



•5324 



1-169 



2-338 



5-0 



•2087 



•5870 



1-084 



3-252 



60 



•1716 



•6338 



1-050 



4-200 



7-0 



•1459 



•6723 



1-034 



5-172 



80 



•1270 



•7037 



1-024 



6144 



9-0 



•1125 



•7299 



1-018 



7-126 



100 



•1010 



•7519 



1-014 



8-112 



1000 



•0400 



•8892 



1-002 





When the explosive distance becomes less than the tenth 

 part of the radius of the spheres, the series given above can- 

 not be used with advantage. Plana * has written an elaborate 

 memoir on the distribution of electricity on two spheres which 

 are near together. Unfortunately he expresses everything in 

 terms of the total charge of the spheres, which itself is un- 

 known ; and his formulae are not, as far as I can see, useful 

 for our present purpose. Kirchhofff has given an equation 



* Memorie delta reale accademia delta scienze di Torino, tomo vii. 

 1845. 



f Collected Works, p. 96. 



