NEWTON S PRINCIPIA. 307 



motions are subject. Comets are found to move more 

 than ordinarily slow or swift according to the position of 

 the earth. They have, in fact, an annual parallax. There 

 fore they belong to the region of the planets. This result 

 Newton confirms by some considerations on the brightness 

 of their heads. He proves that they shine by reflected 

 light, and then comparing their light with that of the 

 planets, he shows how much those persons are mistaken 

 who remove the comets almost as far as the fixed stars. 



If the comets move in the region of the planets, they 

 must be subject to the attractions of the sun and the 

 other planets. Neglecting for a first approximation these 

 latter attractions compared with that of the sun, we know 

 that the comet, being attracted towards the sun by a force 

 which varies inversely as the square of the distance, 

 must move in a conic section with the sun in one focus, 

 and describe round it areas proportional to the times. 

 This conic section may be either an ellipse, hyperbola, or 

 parabola. In the former case the squares of their periodic 

 times are as the cubes of their mean distances. This will 

 furnish us with a complete test of the truth of our argu 

 ments. By observations made on the latitude and lon 

 gitude of a comet, we can calculate its orbit with an 

 accuracy depending on the degree of approximation to 

 which we have earned the solution. We can then deter 

 mine the distance and position of a comet at any moment. 

 If these results agree with observation, there can be no 

 doubt that our theory is correct. The difficulty of the 

 problem is unfortunately as great as its importance. The 

 comets move in such elongated ellipses, that, as a first 

 approximation at least, we may consider their orbits as 

 parabolas. But Newton speaks of the problem, even when 

 thus simplified, as &quot; Problema hocce longe difficillimum&quot; 



(2.) Newton proposed two ways of determining the 



x 2 



