AND THE OTHER PLANETS OF THE SOLAR SYSTEM. 649 



which gives the value of £ at any place whose latitude is fx, on the day when the Sun's 



longitude is v, and at the time when his angular distance from the meridian is \^. 



The terms involving >^ will have for their period a day or a submultiple of a day; and, 



therefore, if we omit these daily inequalities, and restrict ourselves to the consideration of the 



mean value of £ and its annual and semi-annual inequalities, we shall have, substituting 



kS 



for V, and putting = ft, 



7r\r s 



£ = £ + ft | sin fx sin 7 sin v + Q + Q x cos 2u + &c. [, 



and, taking a year for the unit of time, we have 



v = 2irt, 

 and, therefore, 



£ = £ + ft \- sin iu sin 7 sin 2,-ict + Q + Q x cos 4nrt + &c> , 



and therefore, the above equation may be written, 



£ = £ + hQ + h . - sin ft. sin 7 cos I Zirt + hQ x cos iwt + &c. 



This expression for £ will coincide with that given above (p. 646), if we put 



B = I + hQ, 



A = ft .— sin /u sin 7, 



A' = hQ, 

 &c. = &c. 



7T 



m = 27T, e = -, 



2 



m = 4ir, 6=0, 



&c. &c. 



Hence the equation (7) becomes 



u - tf + ftQ) 



6,7T. . * r / ir at — .\ 



+ — -ft — sin u sin <ve - o v,r cos 27r£ v/tt — 



D 2 ' \ 2 a ) 



+ — ftQie-^COS Unt - -y/<hr - l\ 

 L)\ \ & / 



+ &C. 



18. This expression contains three unknown quantities a, b, and ft. Poisson* thus 

 determines their values. The third term, containing Q t , and the subsequent terms con- 



• p. 499. 



83—2 



