486 ' PHILOSOPHICAL TRANSACTIONS. [aNNO 1779- 



tance from the perihelion 0.6743815, its log. 9.8289057; 6, the semi-axis of the 

 orbit described by the comet 3.1478606, its log. O.498OI55. Hence the log. of 

 the semi-parameter is 0.0807300, and the log. of the excentricity 9.8952927, 

 and therefore the periodic time 5.585 years. 



From these elements, Mr. L. computes a great number of the comet's places 

 by theory, and compares them with the actual observations that had been made; 

 and he finds them commonly to agree within less than 1 minute, both in longi- 

 tude and latitude. He next makes a small variation in the elements, and thence 

 computes some of the comet's places by theory; thus, supposing the periodic time 

 to be 5.6 years, the log. of the orbit's semi-parameter 0.0808000, the log. of the 

 perihelion distance 9.8288794, time of the perihelion 13.5400 of August, lon- 

 gitude of the node 4^ 12° 9', inclination of the orbit 1° 33' 40", elongation from 

 the node 44° 7' 5g"; then several of the comet's places being calculated from 

 these, they are found to agree nearly as well with the observations as the former. 



Mr. L. next tries, by supposing the periodic time to be much greater, and 

 thence deducing the other elements from 2 of the observations, whether by com- 

 putation the other places will agree with observation. And first, supposing the 

 periodic time to be 6 years, and the log. of the semi-parameter O.O81700O; then 

 the other elements will be, viz. log of the perihelion distance 9.8273218, time 

 in the perihelion 13.2850 of August, longitude of the node 4' 12° 6', inclina- 

 tion of the orbit l" 34' 30", elongation of the perihelion from the node 44° 9' 

 56', and hence he computes 5 of the comet's places, to compare them with the 

 observations, which differ but little. Next assuming the log. of the semi-para- 

 meter 0.08 18500, with the same periodic time 6 years, and thence computing 

 the rest of the elements from 2 of the observations, and the other places from 

 these; then the results from these 2 suppositions differ more than the former 

 from the actual observations. 



Again, making other suppositions with 7, &c. years for the periodic times, 

 &c., the results are found, on trial, to come out still more irregular, and different 

 from the observed places of the comet. In this way, trying several other num- 

 bers, some greater and some less than the former, and calculating from them, 

 he finds still other deviations, more or less, from the actual observations. Hence 

 he concludes that the list of elements first mentioned, are the most proper ones, 

 as best agreeing with observation. After which the astronomer royal makes the 

 following remark. 



In a pamphlet of 18 pages in 4to., published at Upsal in 1776, Mr. Eric 

 Prosperin, astronomer to the king of Sweden, has shown by his calculations, 

 that the observations of near 4 months made on this comet by M. Messier could 

 not be represented by a parabolic orl)it; and thence founds a strong conjecture, 

 and on the circumstances of the different parabolas which he found necessary to 



