Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/264

electrostatic units of electricity, it will be interesting to compare some recent determinations of this ratio. These we give in the following table. Since the determinations are affected by any error in the standard of resistance, we have corrected the results, first, on the supposition that the B. A. ohm = .987 true ohms (Lord Rayleigh's result), and secondly, on the supposition that the B. A. ohm = .989 true ohms, which is essentially assuming that the legal ohm represents the true value.

Ratio of Electromagnetic and Electrostatic units of Electricity in millions of meters and seconds.

	Date. ⁠	As Published. ⁠	B. A. ohm = .987 ⁠	B. A. ohm = .989.
Ayrton & Perry,[1]	1878	298.0	296.1	296.4
Hockin,[2]	1879	298.8	296.9	297.2
Shida,[3]	1880	299.5	295.6	296.2
Exner,[4]	1882	301.1 (?)	291.7 (?)	292.3 (?)
J. J. Thomson,[5]	1883	296.3	296.3	296.9
Klemenčič,[6]	1884	301.88 (?)	301.88 (?)	302-48 (?)

These numbers are to be compared with the velocity of light in air, in millions of meters per second, for which Professor Newcomb gives 299.778. Of the electrical determinations, that of J. J. Thomson appears by far the most worthy of confidence. That of Klemenčič—the only one as great as the velocity of light—was obtained by the use of a condenser with glass,—a method which would presumably give too great a ratio. Exner's value is obtained from the mean of three determinations, one of which differed from the others by about three per cent. If we reject this discordant determination, the mean of the other two would give when corrected for resistance 294.4 and 295.0. If we set aside the determinations of Exner and Klemenčič, the remaining four, which represent three different methods, are very accordant, the mean being nearly identical with the result of J. J. Thomson, and about one per cent, less than the velocity of light.

Professor Michelson's experiments on the velocity of light in carbon disulphide afford an interesting illustration of the difference between the velocity of waves and the velocity of groups of waves—a subject which is treated at length in an appendix to the second volume of Lord Rayleigh's Theory of Sound. If we write ${\text{V}}$ for the velocity of waves, ${\text{U}}$ for that of a group of waves, ${\text{L}}$ for the wave-length, and ${\text{T}}$ for the period of vibration,

${\text{V}}={\frac {\text{L}}{\text{T}}},$⁠${\text{U}}={\frac {d({\text{T}}^{-1})}{d({\text{L}}^{-1})}}\cdot$

For purposes of numerical calculation, it will be convenient to transform these formulæ by the use of $\lambda$ for the wave-length in

1. Phil. Mag., (5), vol. vii, p. 277
2. Report Brit. Assoc., 1879, p. 285.
3. Phil. Mag., (5), vol. x, p. 431
4. Sitzungsberichte Wien. Akad., vol. lxxxvi, p. 106.
5. Phil. Trans., vol. clxxiv, p. 707
6. Sitzungsberichte Wien. Akad., vol. lxxxix, p. 298.