214 



CELESTIAL MECHANICS. I. V. 21. 



opposite side of the centre] : then if the plane of x^^, and y^,^ 

 be that of the equator, we shall have z^^, parallel to the 

 earth's axis, pointing to the north pole [, and inclining 

 towards the sign 2b, towards which y is positive]; the 

 obliquity of the ecliptic will then be [ + ] 0, and i^ will be 

 the longitude of the axis x with respect to the vernal 

 equinox, which is the intersection of the two planes on the 

 side of 4-x; the distance of x^^^ and i/,^^ from the same line 



will be (p and o-\-^ respectively, these angles varying with 



/w 



the rotation of the earth. 



Now if x^y y^y and z^, be an intermediate system of 

 orthogonal coordinates, x^ being the line of the vernal 

 equinox, y^ the projection of the earth's axis on the plane 

 of the ecliptic, and z, coinciding with the axis of the 



ecliptic z ; the ordi- 

 nates a:, 3/, x^, and y^ 

 being in the same 

 plane, we have 

 xzzx^ cos il'+y, sin 4^; 

 y=y, cos4<— x^sin^l.; 



In the next place, let a:,,, y^^ and z^^ be another system 

 of coordinates, of which x^^ is parallel to the line of the 

 vernal equinox, and z^^ to the earth's axis, y^^ being conse- 

 quently in the plane of the 

 equator : we have then y^^ and 

 z^, in the plan© passing through 

 y^ and z^, while x, and x^, coin- 

 cide: consequently 



y/=y/y cos 6 +z,, sin fl; 

 z,=z,,cos 6— y^^sin 9. 



