492 Mr. H. Holt on a Method of Calculating 



v and v t are the true longitudes of the moon and sun measured 

 on the ecliptic supposed fixed. 



p = moon's true curtate radius, its mean value being unity. 



p l = earth's true radius vector. 



s = tangent of moon's true latitude. 



m t = mass of sun, the sum of the masses of earth and moon 

 being =1. 



3. The value of p t is so large in comparison with p, that 



the terms involving ^ and ^ may be rejected in the first three 



Pi. Pi 



approximations, in which case the equations (1), (2), (3) become 



^-§-^(l-|* 5 + ^ S 4 ) + ^,^+l m ,^cos2(,-, / )=0,(4) 

 S^l]+3 % 4 S in^-,)=0, (5) • 



jM + ^(^+T !S )+ ffl 4 =0 (6) 



Planes supposed coincident. — If the plane of the moon's orbit be 

 supposed to coincide with that of the ecliptic, s will =0; hence 

 the equation (6) will disappear, and equations (4), (5) will become 



dv 1 d 2 p 1 , p p .„. 



|[2^|] + 3^g S in2(,-, / )=0 (8) 



Earth's Orbit supposed circular. — If, in addition to the above 

 hypothesis, we assume that the earth moves in a circular orbit 



(in other words, if we reject the inequalities of v t and —3 and 



11 Pl 



suppose v t =n t t-{- e p and— 3 = —3, these denoting their mean values 



Pi a t 

 respectively), we shall have 



dv 2 d^p 1 m. m. . 



^-^-? + V 3P+i ^ p ^"^ ' ■ (9) 



iW¥\^%^^-^= Q ' ••■■•'.■ M 



v t in this case denoting the sun's mean longitude nf 4- e r 



m 

 Rejection of Inequalities ofv andp in the terms | — ~ p cos 2(v—v t ) 



a l 



