246 



NOTES TO BOOK III. 



(G.) p. 230. I WILL insert here the explanation which 

 my German translator, the late distinguished astronomer 

 Littrow, has given of this point. The Rule of this In- 

 equality, the Evection, may be most simply expressed 

 thus. If a denote the excess of the Moon's Longitude 

 over the Sun's, and b the Anomaly of the moon reckoned 

 from her Perigee, the Evection is equal to l.8.sin (2a -b). 

 At New and Full Moon, a is or 180, and thus the 

 Evection is 1. 3 . sin b. At both quarters, or dicho- 

 tomies, a is 90 or 270, and consequently the Evection is 

 + 1. 3. sink The Moon's Elliptical Equation of the 

 center is at all points of her orbit equal to 6. 3 . sin b. 

 The Greek Astronomers before Ptolemy observed the 

 moon only at the time of eclipses ; and hence they neces- 

 sarily found for the sum of these two greatest inequalities 

 of the moon's motion the quantity 6. 3 . sin b l.3.sin>, 

 or 5. sin b : and as they took this for the moon's equation 

 of the center, which depends upon the excentricity of the 

 moon's orbit, we obtain from this too small equation of 

 the center, an excentricity also smaller than the truth. 

 Ptolemy, who first observed the moon in her quarters, 

 found for the sum of those Inequalities at those points the 

 quantity 6 . 3 . sin b + 1 . 3 . sin b, or 7 . 6 . sin b ; and 

 thus made the excentricity of the moon as much too 

 great at the quarters as the observers of eclipses had made 

 it too small. He hence concluded that the excentricity of 

 the Moon's orbit is variable, which is not the case. 





