246 FT. JIarhiess — Magnitude of the Solar System. 



obtained from transits of Yenus, oppositions of Mars and oppo- 

 sitions of certain asteriods ; the lunar parallax, found both 

 directly, and from measurements of the force of gravity at the 

 earth's surface ; the constants of precession, nutation and aber- 

 ration, obtained from observations of the stars ; the parallactic 

 inequality of the moon ; the lunar inequality of the earth, usu- 

 ally obtained from observations of the sun, but recently found 

 from heliometer observations of certain asteriods : the mass of 

 the earth, found from the solar parallax, and also from the 

 periodic and secular perturbations of Yenus and Mars ; the 

 mass of the moon, found from the lunar inequality of the earth, 

 and also from the ratio of the solar and lunar components of 

 the ocean tides ; the masses of all the planets, obtained from 

 observations of their satellites whenever possible, and when no 

 satellites exist, then from observations of their mutual pertur- 

 bations both periodic and secular ; the velocity of light, 

 obtained from experiments with revolving mirrors and toothed 

 wheels, together with laboratory determinations of the index 

 of refraction of atmospheric air ; the light equation, obtained 

 from observations of the eclipses of Jupiter's satellites ; the 

 figure of the earth, obtained from geodetic triangulations, 

 measurements of the length of the seconds pendulum in vari- 

 ous latitudes, and observations of certain perturbations of the 

 moon ; the mean density of the earth, obtained from measure- 

 ments of the attractions of mountains, from pendulum experi- 

 ments in mines, and from experiments on the attraction of 

 known masses of matter made either with torsion balances or 

 with the most delicate chemical balances ; the surface density 

 of the earth, obtained from geological examinations of the sur- 

 face strata ; and lastly, the law of distribution of density in the 

 interior of the earth, which in the present state of geological 

 knowledge we can do little more than guess at. 



Here then we have a large group of astronomical, geodetic, 

 geological and physical quantities which must all be considered 

 in finding the solar parallax, and which are all so entangled 

 with each other that no one of them can be varied without 

 affecting all the rest. It is therefore impossible to make an accu- 

 rate determination of any one of them apart from the remain- 

 der of the group, and thus we are driven to the conclusion that 

 they must all be determined simultaneously. Such has not 

 been the practice of astronomers in the past, but it is the 

 method to which they must inevitably resort in the future. 

 A cursory glance at an analogous problem occurring in geodesy 

 may be instructive. When a country is covered with a net of 

 triangles it is always found that the observed angles are sub- 

 ject to a certain amount of error, and a century ago it was the 

 habit to correct the angles in each triangle without much regard 



