NEWTON S PKINCIPIA. 311 



greater accuracy by means of an arithmetical calculus. 

 Moreover, observing that a remarkable comet had ap 

 peared four times at equal intervals of 575 years, he tried 

 to find an elliptic orbit whose greater axis should be 

 138-2957 times the radius of the earth s orbit, so that a 

 comet might revolve in it in 575 years. Taking this 

 ellipse as the orbit of the comet, the observations from the 

 beginning to the end were found to agree as perfectly 

 with the computed places of the comet as the motions of 

 the planets do with the theories from whence they are 

 calculated; and this agreement clearly shows that it was 

 one and the same comet that appeared all that time, and 

 also that the orbit of that comet has been rightly defined. 



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