248 NOTE ON THE INEQUALITY IN THE MOON'S LATITUDE [29 





and therefore 8ft = -- . cos (0 - C), 



which is the inequality in latitude due to the motion of the ecliptic, 

 expressed in the circular measure. 



This value of S/8 agrees exactly with that found in my article inserted 

 in Godfray's Lunar Theory, since c cos i in this formula has the same signi- 



fication as :: in Godfray, viz. the mean angular velocity of the Moon's node. 

 o 



The steps, however, by which this result is arrived at, are slightly 

 different in the two investigations. In the earlier one, the variation of 



cos i was neglected, and S\jj was taken ---- . , whereas in the present 



COS I 



investigation the variation of cosi is taken into account, and Si/ is taken 

 = cos i SN, on the assumption that MM' is perpendicular to NM. 



It should be remarked that in both forms of this investigation, the 

 neglect to take account of any variation of the Moon's radius vector and 

 orbital longitude, due to the motion of the ecliptic, may produce errors in 

 the coefficient of the inequality in latitude which are of the order of the 



small quantity - sin' 2 i, so that the investigation is incompetent to decide 

 o 



such a question, for instance, as whether . or is the more correct 



c cos i c 



value of this coefficient. 



The coefficient above found, expressed in seconds, is 



0) 



c cos i sin 1" ' 

 In order to evaluate this quantity numerically, we observe that 



c cos^ 



is the ratio of two angular velocities : viz. the velocity of rotation of the 

 plane of the ecliptic, and the mean angular velocity of the Moon's node ; 

 and in comparing these it is indifferent what unit of time is employed. 

 According to the data adopted before, taking 1 year as the unit of time, 



sinl", or p = 0'479. 



