NEWTON S PRINCIPIA. 67 



First, as regards the comet of 1680, or Halley s comet. 



In comparing four observations with the geometrical com 

 putation, Sir Isaac Newton found an error of 5 3&quot; on 

 an average in the latitude, and about V in the longitude. 

 But Halley, having afterwards made the computations 

 with greater accuracy by arithmetical operations, found 

 the average error, on sixteen observations, in the latitude 

 only about 52&quot;, and in the longitude 1 28&quot;. The average 

 error found on a comparison of the theory with twenty- 

 one observations made abroad, was found by Halley only 

 to be 50&quot; in the latitude, and 57&quot; in the longitude.* 



Secondly, as regards other comets. 



In the computations of the comet 1665, the error was, 

 on an average of eighteen observations, 8&quot; in the latitude, 

 and in the longitude V 25&quot;. In the latitude the errors 

 by excess nearly balance those by defect, the one being to 

 the other as 40 to 49. In the longitude, supposing the 

 observation of December 7 accurately stated (which, from 

 the error amounting to 7 33&quot;, seems very doubtful), the 

 errors by excess are sixteen times more considerable than 

 those by defect. In the comets of 1682 and 1683, on 

 comparing the observations of Flamstead with the theory, 

 the error was 1 31&quot; in latitude, and 45&quot; in longitude, for 

 eleven observations of the former comet, and for seventeen 

 of the latter comet, I 10&quot; in latitude, and 1 29&quot; in lon 

 gitude. But the comet of 1723 came nearer its computed 

 place ; the average error of latitude on fifteen observations 

 of Bradley, compared with the same number by Halley 

 himself, and Pound (his uncle), was only 21&quot;^ in the la 

 titude, and somewhat under 25&quot; in the longitude. It is to 

 be remarked that this is apparently the case in which the 



* This omits the observation made 26th December, as there is mani 

 festly an error in the figures of that observation. 



F 2 



