392 W. Harkness—The Solar Parallax. 
The relations eee small changes in p, 0, a, and V, are 
given by the equat 
dp = — 00177 dé — 0:0295 dV (32) 
dp = — 0°432 da— 00295 dV (33) 
where @ is in seconds of mean time, @ in seconds of are, and V 
in thousands of kilometers. To determine p with a probable 
error not exceeding + 0/01, the probable errors of the other 
quantities must not exceed the following values, namely: 
6, + 0*40, and V, + 240 kilometers; or a, + 0’ 016, and ve 
+ 240 kilometers. “Whatever may be said respecting V, it is 
quite certain that our present knowledge of @ and a does not 
approach this degree of accuracy. The probable error of p 
seems to be at least + 0-05. 
The photo-tachymetric method is embarrassed by serious 
theoretical difficulties. 1st. As we are ignorant of the optical 
constitution of inter- planetary space, we have no sure means of 
passing from the velocity of light at the earth’s surface to its 
velocity in space. . There is no rigorous proof that the 
constant of aberration gives the exact ratio of the velocity of 
light to the earth’s orbital velocity. 8d. The velocity of light 
is the velocity of transmission of a single wave, while Fizeau’s 
and Foucault’s methods determine the velocity of transmission 
of a group of waves. Lord Rayleigh bas shown that these 
two things are not necessarily the same. If the ordinary theory 
of aberration is accepted the velocity of light to which it refers 
is the velocity of a single wave, while the velocity determined 
from the eclipses of Jupiter's satellites is that of a group of 
waves. (Nature, 1881, vol. xxiv, pp. 382 and 460.) 
Breneeing the theory of aberration the reader may consult, 
e Chimie et de Physique, 1818, t. ix, p. 57; Oeuvres 
completes d’Augustin Fresnel, t. ii, p. 627 ; ‘Stokes, in L. E. 
Phil. Mag. 1845, vol. xxvii, p. 9; 184 6, vol. xxviii, p 
: 1846, vol. Xxx, p. 6: Klinkerfues, in ANn, 1866, bd. Ixvi, 
s. "437 1868, bd. Ixx, s. 239 ; 1870, bd. lxxvi, s. 33; Sohncke, 
ANn, 1867, bd. Ixix, s 209 : Ho ek, ANn, 1867, bd. Ixx, s. 
193 ; "Veltmann, ANn, 1870, bd. Ixxv, . 145; Airy, Greenwich 
Observations, 1871, p. cxix ; Proceed. Roy. Soc. 187 73, vol. xxi, 
p, 121: Villarceau, Conn. de Temps, 1878, Additions ; Michel- 
son, this Journal, 1881, vol. xxii, p. 120. 
Conclusion. 
For convenience of reference the limiting values of the solar 
parallax, found by the various methods described in the fore- 
going pages, are presented here. It should be remarked, how 
ever, that 1 in selecting these values the results of all diusscesiona 
