96 NEWTON S PRINCIPIA. 



corollary made any particular application to the moon s 

 motion, adds, &quot; the apsis of the moon has a velocity twice 

 as great nearly &quot; (apsis lunas est duplo velocior circiter), 

 (Cor. 2. to Prop. xlv. B. i.);* and though in the propo 

 sition in which he applies his theory to find the disturbing 

 force of the sun, (xxv. B. iii.) he finds it to be to the cen 

 tripetal force as 1 to 178J nearly (or double what he 

 had argued upon in the former proposition), he is so far 

 from deducing from thence any inference that the apsides 

 by the theory move 3 in each revolution, that he makes 

 no application at all of the proposition to finding their 

 motion. But in the celebrated scholium where he sums 

 up all the disturbances, he treats of this motion, and he 

 expressly shows that it only comes out to be anything 

 like the true motion of 3 by an assumption contrary to 

 the theory ; that is, by taking not the true equation to the 

 sun s mean motion, but the equation on the hypothesis of 

 its following the inverse triplicate ratio. The words above 

 quoted from the general proposition upon the apsides in 

 the first book, are quite sufficient to protect Newton s 

 memory from any such aspersion as that now under con 

 sideration. 



It may further be remarked, that Bailly s general 

 criticism on Newton s whole investigation of the moon s 

 motion is singularly unfortunate. He represents him 

 as having only given a rough sketch of the subject, 

 leaving others to fill up. He says, that this is the 

 part of Newton s work most involved in obscurity; that, 

 concealing the route he pursued, he plainly has not 

 taken the problem in its full extent, but only shown ge 

 nerally, and by a few examples, that those irregularities 

 could be deduced from the theory; though he renders 



* It is remarkable that these words are not in the first edition of the 

 Priucipia. 



