68 NEWTON S PEINCIPIA. 



observations were the most accurate, three eminent obser 

 vers checking each other, and no one observation differing 

 from the computation much more than by the average of 

 the rest, while great differences occur in all the other cases, 

 and give rise to a suspicion of error. For in the comet of 

 1683, there was one day (Aug. 15) in which the latitude 

 differed between three and four times, and the longitude 

 three times more than the average ; and in the observations 

 of the comet of 1665 there are several errors in longitude 

 of twice, and one error of no less than five times, above 

 the average. These particular observations, and not the 

 theory, then, were probably at fault in those instances ; but 

 they affect the general average materially. 



The intimate connection between the purely geometrical 

 parts of the Principia, the Fifth and Sixth Sections of the 

 First Book, and the most sublime inquiries into the motions 

 of the heavenly bodies, those motions, too, which are the 

 most rapid, and performed in spaces the most prodigious, 

 may suffice to show the student how well worthy these 

 mathematical investigations are of being minutely followed. 

 Were they wholly unconnected with such important spe 

 culations in Physical Astronomy, and only to be regarded 

 as a branch of the Higher Geometry, they would deserve 

 the deepest attention, for their interesting development of 

 general relations between figures so well known as the 

 conic sections, for the marvellous felicity of the expedients 

 by which the solutions are obtained, and for the inimitable 

 elegance with which the reasoning is conducted. As a 

 mere matter of mathematical contemplation, beginning and 

 ending in the discovery of the relations which subsist be 

 tween different quantities and figures, they afford matter 

 of lasting interest to the geometrician. But it certainly 

 heightens that interest to reflect that the same skilful and 

 simple construction which enables us to describe a para- 



