Note 35.- capacity of a circular disk 433 



a time pT; but since the proportion of free molecules to combined ones is quite 

 unknown, the only definite result we can obtain from Kohlrausch's data is a 

 certain very small time T, such that if the electromotive force acted on the 

 molecules of the component during the time 7", it would impress on them a 

 velocity twice their actual average velocity. 



Since the time T is very small, it is more convenient to speak of the molecule 

 being brought to rest times in a second, and to calculate . 



NOTE 35, ART. 654. 

 On the Ratio of the Charge of a Globe to that of a Circle of the same Diameter. 



The true valuef of this ratio is Jir = 1-570796. . . ' : it had not been discovered 

 until much later . 



Cavendish has given several different values as the results of his experi- 

 ments. 



In the account of his experiments, which represents his most matured con- 

 clusions, he states this ratio is 1-57 (Art. 237). 



All the other values, however, either as stated by Cavendish or as dedncible 

 from his experiments, are lower than this. 



* [It is to be remembered that these remarks were published by Maxwell in 1879. 

 The hypothesis of free time T has been developed by J. J. Thomson, and later has 

 found application for the case of electrons, in a theory of electric conduction in metals 

 by Drnde and others.] 



t [According to Lord Kelvin, writing in 1869 (Papers on Electrostatics and 

 Magnetism, p. 179) the expression for the distribution of electricity on a circular 

 disk, involving this value of its electric capacity, was first given by Green near the 

 conclusion of his paper "On the Laws of the Equilibrium of Fluids analogous to 

 the Electric Fluid " (Cambridge Transactions), so late as 1832, and comparison made 

 with the experiments of Coulomb on a copper plate 10 inches in diameter. 



It is however the determination of capacity, a conception rendered possible by his 

 virtual introduction of the idea of potential, that is here original with Cavendish. 

 The law of density of the charge on a disk, here referred to, is an immediate inference 

 from Newton's theorem (Principia, Lib. I, Prop, xti, cor. 3) that a gravitating shell 

 bounded by similar ellipsoidal surfaces exerts no attraction throughout its interior. 

 Cf. Maxwell's Introduction, supra, pp. 10, 18. 



In a footnote Lord Kelvin records * an entry which I find written in pencil in 



an old memorandum book.' 



Plymouth, Mon. July 2. 1849. 



" Sir William Snow Harris has been showing me Cavendish's unpublished MSS-. 

 put in his hauis by Lend Burlington, and his work upon them : a most valuable mine 

 of results. I find already the capacity of a disc (circular; was determined experi- 

 mentally by Cavendish as 1/1-57 f that of a sphere of the same radios...." 



After due i niirmrai of surprise he proceeds " It is much to be desired that these 

 manuscripts of Cavendish gKnnlH be published complete; or, at all events, that their 

 safe keeping and accessibility should be secured to the world."] 



c. P. i. 28 



