PREFACE. XI 



and Alchemy, Chronology, History, and Theology. Many of 

 the Mathematical papers contain Newton's preparations for the 

 Principia, and notes which spring out of questions that were 

 started by his correspondents. It must be recollected that 

 Newton practically gave up his mathematical studies after 1696, 

 even the superintendence of the second edition of the Principia 

 being given to Cotes, and thus that after this date there is little 

 of value in these subjects ; and as most of what is contained in 

 them, especially all that relates to the revision of the Principia, 

 has been published, there is little to be found beyond what has 

 already appeared. 



The case is different, however, with respect to the papers 

 referring to three subjects, viz. 1st, the Lunar Theory, 2nd, the 

 Theory of Atmospheric Refraction, and 3rd, the Determination 

 of the Form of the Solid of Least Resistance. 



It is expressly stated by Newton himself that the Lunar 

 Theory as given in his Principia is a mere specimen or fragment 

 of the subject, intended to show how some of the more prominent 

 lunar inequalities could be traced to the disturbing action of 

 the Sun, and how their amounts could be calculated approxi- 

 mately by theory. 



The only part which is developed with any fulness of detail 

 is that relating to the inequality called the variation, and also 

 that which treats of the motion of the node and the change of 

 inclination of the orbit to the ecliptic. 



In a short scholium given in the first edition of the Principia, 

 Newton mentions that by similar computations he has found 

 the motion of the moon's apogee, and he states some of the 

 numerical results which he has obtained, but he does not give 

 the calculations themselves, as he considers them too complicated 

 and not sufficiently accurate. 



In the second edition this short scholium is replaced by a 

 long one, in which Newton states many of the principal results 

 of the Lunar Theory, partly as found from theory alone and partly 

 as deduced by combining his theory with observation ; but he 

 confines himself to results alone, and does not give the method 

 by which these results have been obtained. Unfortunately also, 

 the statement given in the first edition, as to the result which 



