On the observations of Comets. 95 



the comet of 1695, is known only by observations made at 

 sea by a French missionary : several others also are known 

 only by few and imperfect observations ; and it is not im- 

 probable, that in the antarctic expeditions now preparing, 

 there may be discovered a comet, altogether invisible from 

 any observatory. It is therefore, highly desirable for the ad- 

 vancement of astronomy, that all lovers of science should 

 make all possible observations whenever a comet appears. 

 The want of proper instruments, is indeed a great im- 

 pediment; but even without a telescope, the positions of 

 a comet might be ascertained with sufficient accuracy by 

 measuring with a circle of reflection, or a sextant, its 

 distances from two other heavenly bodies whose positions 

 are exactly known. This method of which Hevelius and 

 Halley made use in the formation of their catalogues of 

 stars, might for its simplicity, be used at sea, where as- 

 tronomical instruments could be used only with difficulty. 

 These considerations have induced me to present to the pub- 

 lic, the following essay, on the manner of ascertaining the 

 positions of comets from the distances observed. 

 Fig. 1. 



Let p (fig. 1 ,) be the pole of the earth, c 

 the place of a comet, and a and b two fix- 

 ed stars. Pc will be the comet's polar dis- 

 ance, and the angle cpa the difference be- 

 tween its right ascension and the right as- 

 cension of the star a. Measure the distan- 

 ces ca and cb from the comet to each star, 

 and mark tije time. The distances may be taken simultane- 

 ously when there are two observers ; but when there is only 

 one, the distances from one star must be reduced to the time 

 at which the distances from the other star were taken. A 

 circle of reflection would be the best instrument for these 

 observations ; but even with a sextant, the distances may be 

 had with great accuracy, by taking the mean between several. 

 ^*g- 2- The distances will be affected by the 



refraction. They may be reduced to true 

 distances by any of the known methods, 

 or by the following, which is sufficiently 

 simple and correct. 



Let z be the zenith, c and a the true pla- 

 ces of the comet and star, d and a' their 

 apparent places. Making c'z=N, a'z== 

 N', and c'a'=D we have 



