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



Now let be the Moon's longitude at time t measured from the axis 

 of x, that is from the line of intersection of the variable and of the fixed 

 ecliptic. 



Also let nt and n't be the mean longitudes of the Moon and the 

 Sun, omitting, for the sake of brevity in writing, the constants which always 

 accompany nt and n't respectively. 



For the sake of simplicity, we will now neglect the eccentricities of 

 the two orbits as well as their mutual inclination. 



In this case we have, with abundant accuracy for our present purpose, 

 r = 0-9991 1,92 -0-00717,34 cos 2 (nt-n't)- 0-00002,00 cos 4 (nt-n't), 

 e = nt +0-01021,14 sin 2 (nt-n't) + 0'00004,24 sin 4 (nt-n't), 



where, as in my paper in the Monthly Notices, Vol. xxxvm. p. 46, the 

 angles are expressed in the circular measure, and the unit of distance is 

 the mean distance in an undisturbed orbit which would be described bv 



/ 



the Moon about the Earth in its actual periodic time. 

 Hence we have, as in the paper referred to 



j m ' 1-2 

 fL = n; and ^ -=-. 



Now choose the unit of time sucli that n n' 1 ; 

 therefore, since in the case of the Moon 



= 0-07480,13, 

 n 



we have n' = 0-08084,89, 



and 71=1-08084,89. 



From the values of r and above given, it is readily found that 

 y=rsm 6= -0'00868,79 sm(-nt + 2n't) 

 + 0-99909,31 smnt 

 + 0-00151,43 sin (3nt - 2n't) 

 + 0-00000,59 sin (5nt - n't), 



