Measurement of Small Capacities and Inductances. 503 



Table III. — Measurement of Capacity of Wires of various 

 diameters suspended vertically in a large room. 



! 

 Diameter of 





Mean Value 



Calculated 



Difference in per 



Length of 



of Capacity 



value by 



cent, between the 



inches. 



wire in feet. 



in M.M.Fds. 



the formula 



observed and 





observed. 



above. 



calculated values. 



•0047 



11-44 



18-79 



17-62 



6-6 



•0075 



12-23 



21-36 



19-59 



9-0 



•0127 



1229 



22-56 



20-73 



8-8 



•0182 



1221 



2376 



21-38 



11-1 



•0278 



1204 



24-24 



2206 



9-9 



•0485 



12-33 



26-51 



23-97 



10-6 



•1381 



12-02 



32-36 



27-00 



19-8 



The above formula has been deduced on the assumption 

 that the form of a very long thin wire may be considered as a 

 limiting case of a prolate ellipsoid of revolution. It can be 

 shown that the electrical capacity (C) of an ellipsoid of 

 semiaxes a, b, and c in infinite space is given by the ex- 

 pression * : 



i = ir du 



C 2 Jo \fja 2 + ii){b 2 + u)(c 2 + u) 

 If we put b = c in the above formula, it can be shown that 



C = 



2 s/cfi-b 



!0ge 



v« 



a- sja 2 -^ 



Hence the above expression gives us the capacity of the 

 ellipsoid of revolution. 



If the ellipsoid is very elongated so that b is very small 

 compared with a, then if e is the eccentricity of the principal 

 elliptical section, e is nearly equal to unity, and l + e is 

 nearly equal to 2. 



Hence (1 + e)(l — e) = 2(1 - e) nearly 



and a(l — e 2 ) = 2a(l — e) nearly. 



Accordingly, since v a 2 — b :i = ae, we can say that 



a — n/ a' 2 — lr — b 2 /2a nea rl\\ 



and 



a 4- s/ a? — b 2 



- :> = 2 loge 2a/b. 



\/a^l 



* See Article Electricity by Prof. Chrystal, 9th Edition of the 

 Encyclopaedia Britannica, vol, viii. p. 30. 



