112 G. F. Becker — Certain Astronomical 



u = Z t 2na cos A. 

 At the equator this becomes 



" = 2 Th E W - 



E J (z) being in this case the quadrant of an ellipse the numerical 

 eccentricity of which is sin e. The quantity h is a function of 

 the sum of the masses of the sun and earth, say m, the major 

 semiaxis of the earth's orbit, A, and the eccentricity, e, in fact 



/r = Am (1 - e 2 ). 



Now the major axis of a planet's orbit has until lately been 

 assumed to be absolutely constant. In 1879, Mr. D. Eginitis 

 showed that a surmise of Tisserand's was correct, and that the 

 major axis is subject to a secular inequality of the third order 

 with respect to the masses.* For most purposes, however, this 

 minute change is negligible as well as the increment of mass 

 due to the accumulation of meteoric matter. Hence e may be 

 regarded as the only variable in the value of h. If the 

 obliquity were zero and the eccentricity were zero, so that the 

 orbit would be a circle of radius A, its plane also coin- 

 ciding with that of the equator, E x (z) would reduce to re/2, and 

 the solar energy received between equinoxes at the equator 

 would be 



Ha 



u = 



y Am 



Now the unit in which radiant energy is measured is arbitrary ; 

 this last value is a convenient unit and I have adopted it. 



For computation it is desirable to reduce the elliptic integral 

 of the third class to integrals of the first and second classes. 

 This is possible by a well known theorem which applied to 

 n\x) and n i {[x) gives 



IT (k) = n(u, Bi „ e, I ) = F'(x) + ^ | F'M E («, =^*t) 



_E' W f(„,^)} 



E and F denoting integrals of amplitude less than re/2, and 

 IT ( M ) = n( M , cos A, fj = F» + ^ | F'Ou) E (/,, e) 



- Ann. Observ. Paris. Mem. vol. xix, 1889, paper H. 



