LECTURES ON THE LUNAK THEORY. 



[LECT. 



Hence 



/JfrV/8 



~ 



and the accelerations of G are 



EM r" 



EM 



cos 



"I. ,-,,. 



...... J m GM - 



"I . 



...... J m ^ 



Now ?// is approximately : ; neglecting the square of this quantity, 

 we see that S moves about G in a pure ellipse. 



Consider now the accelerations of the Moon relative to the Earth ; 

 subtracting the accelerations of the Earth from those of the Moon, we 



find 



EG 



c , / SG SG\ ,, , 

 \SM* ~ SE 3 ) P arallel to 



let E + M = p., S = m' ; then these become 



a m'r \~ E-M r . 



^ + ^L 1 + E~+Mr' 3coS " 



m'rT E-Mr I 3 15 



1 . 

 + ...... J mME > 



\ 1 



s ft.J+ ...... J parallel to GS. 



In the accompanying spherical triangle, let G 

 be the centre of the sphere, SM' the ecliptic, and 

 M' the projection of M. 



Let l/u be the projection of ME on the plane 

 of the ecliptic ; 



6 the longitude of the Moon as seen from the Earth, 

 ff the longitude of the Sun as seen from G, 

 s the tangent of the Moon's latitude MM'. 



