240 W. Haj'faiess — Magnitude of the Solar System. 



ascension which are furnished by the principal observatories in 

 vast numbers, and should give very accurate results on account 

 of their being made by methods which insure freedom from 

 constant errors. Nevertheless, the sun is not so well adapted 

 for precise observation as the stars, and Dr. Gill has recently 

 found that heliometer measurements upon asteroids which ap- 

 proach very near to the earth yield values of the parallactic 

 inequality superior to those obtained from right ascensions of 

 the sun. 



Our sixth gravitational relation is that which exists between 

 the moon's parallax and the constants of precession and nuta- 

 tion. Every particle of the earth is attracted both by the sun 

 and by the moon, but in consequence of the polar flattening 

 the resultant of these attractions passes a little to one side of 

 the earth's center of gravity. Thus a couple is set up, which, 

 by its action upon the rotating earth, causes the axis thereof to 

 describe a surface which may be called a fluted cone, with its 

 apex at the earth's center. A top spinning with its axis 

 inclined describes a similar cone, except that the flutings are 

 absent and the apex is at the point upon which the spinning 

 occurs. For convenience of computation we resolve this ac- 

 tion into two components, and we name that which produces 

 the cone the luni-solar precession, and that which produces 

 the flutings the nutation. In this phenomenon the part played 

 by the sun is comparatively small, and by eliminating it we 

 obtain a relation between the luni-solar precession, the nutation 

 and the moon's parallax which can be used to verify and cor- 

 rect the observed values of these quantities. 



In the preceding paragraph we have seen that the relation 

 between the quantities there considered depends largely upon 

 the flattening of the earth, and thus we are led to inquire how 

 and with what degree of accuracy that is determined. There 

 are five methods, viz: one geodetic, one gravitational, and 

 three astronomical. The geodetic method depends upon meas- 

 urements of the length of a degree on various parts of the 

 earth's surface, and with the data hitherto accumulated it has 

 proved quite unsatisfactory. The gravitational method con- 

 sists in determining the length of the seconds pendulum over 

 as great a range of latitude as possible, and deducing therefrom 

 the ratio of the earth's polar and equatorial semi-diameters by 

 means of Clairaut's theorem. The pendulum experiments 

 show that the earth's crust is less dense on mountain plateaux 

 than at the sea coast, and thus for the first time we are brought 

 into contact with geological considerations. The first astro- 

 nomical method consists in observing the moon's parallax from 

 various points on the earth's surface, and as these parallaxes 

 are nothing else than the angular semi-diameter of the earth at 



