150 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1786, 



Computed Places of the Comet , on supposition that it shall return to its 

 Perihelium January 1, 1789> "^ noon. 



Times. 



1788. 

 April 23, 7 

 June 4, 1 



Distance 

 from O , 



July 

 Aug. 



Sept. 



Oct. 



Nov. 



Dec. 



14, 5 



2,46" 



20,43 



7, 3 



24, 



10,26 



26,64 



9>34 



23,39 



7,21 



23,32 



24,35 



1789. 

 Jan. 1, 



4. 



3. 5 



3. 



2.75 



2. 5 



2.25 



2. 



1.75 



1.50 



1.25 



1. 



0.75 



0.50 



0.49 



0.45 



Distance 

 from the 

 earth. 



4.52 

 3.54 

 2.57 

 2.15 



1.79 

 1.51 

 1.29 

 J. 13 

 1. 01 

 0.88 

 0.76 

 0.62 

 0.50 

 0.51 



0.59 



Heliocentric 

 longitude. 



Heliocentric 

 latitude. 



The last observation made by Hevelius on the comet in 1661, was when its 

 distance from the earth was O.986, and from the sun 1.37, with what he calls a 

 very long and good telescope ; at which time it appeared faint and small with it, 

 though still sufficiently visible. Let us suppose this to have been a telescope of 

 Q-feet focal length, with an aperture of 1 .Qo inch ; then, because the diameter of 

 the aperture of a telescope sufficient to render the comet equally visible should be 

 as the product of its distances from the sun and earth, and the product of the 

 numbers above-mentioned O.986 and 1.37 is 1.35, we shall have the following 

 analogy to find the aperture of a refracting telescope sufficient to show the comet 

 as it appeared to Hevelius : as 1.35 : 1.65 inch :: 9:11 inches, so is the product 

 of distances from the sun and earth to the diameter of the aperture required in 

 inches. 



XXV. A new Method of finding Fluents by Continuation. By the Rev. S. Fince, 



J.M., F.R.S. p. 432. 



The utility of finding fluents by continuation was manifest to Sir Isaac Newton, 

 who first proposed it ; and since his time some of the most eminent mathemati- 

 cians have employed much of their attention on it. The method which I have 

 investigated and exemplified in this paper I ofl^er as being entirely new ; and at 

 the same time it not only exhibits, at once, the general law up to the required 

 fluent, but also appears, from some of the instances here given, to be more ex- 



