130 OUTLINES OF NATURAL PHILOSOPHY. 



to the sine of double the angular distance of the 

 moon from the sun, minus her mean anomaly. 



a. If c be the mean longitude of the moon, and 

 that of the sun ; the mean anomaly of the moon 

 being $, this inequality is 



(1 21'5".5) X sin(2(0) #). 



b. This inequality is called the Evection : it was dis- 

 covered by PTOLEMY, and is, after the equation of 

 the centre, the first of the lunar irregularities that 

 was observed, 



c. The argument of it, or 2 ( d )^-#, increases 

 at the rate of 11 18' 59", or ll.3166^er day; 



so that its period is _ r, ^r^> or31d.8119; that is, 



1 1 t 



in the space of 31 days J9 hours 28 minutes near- 

 ly, the evection runs through all its changes, and 

 is beginning to renew them in the same order. 



At the new and full moon, or at the Syzygies> 

 when d is either nothing or 180, the ar- 

 gument is Xy which gives the evection negative, 

 if X be less than 180, and positive, if it be greater, 

 contrary to what happens to the equation of the 

 centre, which is therefore diminished in both cases. 

 At the quadratures, the equation to the centre is 

 increased by the evection. The evection appears, 

 therefore, as an inequality in the equation of the 

 centre, by which it increases when the moon is in 



the 



