NOTES TO BOOK III. 



(H.) p. 232. The Equation of the Center is the 

 difference between the place of the Planet in its elliptical 

 orbit, and that place which a Planet would have, which 

 revolved uniformly round the Sun as a center in a circular 

 orbit in the same time. An imaginary Planet moving in 

 the manner last described, is called the mean Planet, 

 while the actual Planet which moves in the ellipse is 

 called the true Planet. The Longitude of the mean 

 Planet at a given time is easily found, because its motion 

 is uniform. By adding to it the Equation of the Center, 

 we find the Longitude of the true Planet, and thus, its 

 place in its orbit. Littrow's Note. 



I may add that the word Equation, used in such cases, 

 denotes in general a quantity which must be added to or 

 subtracted from a mean quantity, to make it equal to the 

 true quantity : or rather, a quantity which must be added 

 to or subtracted from a variably increasing quantity, to 

 make it increase equably. 



(i.) p. 233. The alteration of the apparent diameter 

 of the moon is so great that it cannot escape us, even 

 with very moderate instruments. This apparent diameter 

 contains, when the moon is nearest the earth, 2010 

 seconds, when she is farthest off, 1762 seconds; that is, 

 248 seconds; or 4 minutes 8 seconds, less than in the 

 former case. [The two quantities are in the proportion of 

 8 to 7, nearly]. Littrow's Note. 



(j.) p. 235. Ptolemy determined the Radius and the 

 Periodic Time of his two circles for each Planet in the 

 following manner : For the inferior Planets, that is, 

 Mercury and Venus, he took the Radius of the Deferent 

 equal to the Radius of the Earth's orbit, and the Radius 

 of the Epicycle equal to that of the Planet's orbit. For 



