180 HISTORY OF PHYSICAL ASTRONOMY. 



required, may be judged of from what has already 

 been stated; that no one, with his methods, has 

 yet been able to add anything to his labours: few 

 have undertaken to illustrate what he has written, 

 and no great number have understood it through- 

 out. The extreme complication of the forces, and 

 of the conditions under which they act, makes the 

 subject by far the most thorny walk of mathematics. 

 It is necessary to resolve the action into many ele- 

 ments, such as can be separated ; to invent artifices 

 for dealing with each of these ; and then to recom- 

 pound the laws thus obtained into one common 

 conception. The moon's motion cannot be con- 

 ceived without comprehending a scheme more com- 

 plex than the Ptolemaic epicycles and eccentrics in 

 their worst form ; and the component parts of the 

 system are not, in this instance, mere geometrical 

 ideas, requiring only a distinct apprehension of 

 relations of space in order to hold them securely ; 

 they are the foundations of mechanical notions, and 

 require to be grasped so that we can apply to them 

 sound mechanical reasonings. Newton's successors, 

 in the next generation, abandoned the hope of imi- 

 tating him in this intense mental effort ; they gave 

 the subject over to the operation of algebraical rea- 

 soning, in which symbols think for us, without our 

 dwelling constantly upon their meaning, and obtain 

 for us the consequences which result from the rela- 

 tions of space and the laws of force, however com- 

 plicated be the conditions under which they are 



