VOL. LXXV.] PHILOSOPHICAL TRANSACTIONS. 651 



corroborating the above ; I have therefore 7" 4> 391™ 



also deduced its period from the best and - 4 53 f 



most distant observations, made when at 7 4 54* 



its least brightness ; they are thus : 7 d O h and 7 4 ^gi 



7 d 5 h . These results I reject, and retain the 7 4 32 



mean given by the first set, with which we may £ 4 4 ff_ 



proceed on to gain a much greater exactness. 7 4 26 



After making other comparisons, Mr. P. states Qn , mean , ength of 7 4 21 * 



the results for the periods as annexed : a single period. j 7 4 38 



As this approaches the most to the preceding result, it may be assumed as 

 nearest the truth, provided the changes be uniformly periodical. 



Fill. Astronomical Observations. By M. Francis de Zach, Professor of Ma- 

 thematics, &c. p. 137- 

 This paper contains an account of the observations on the eclipse of the 

 moon, made in the Observatory at Lyons, called au grand College ; also obser- 

 vations of the vernal equinox ; some observations on Jupiter's satellites, made at 

 Marseilles by M. Saint Jacques de Sylvabelle ; and lastly a new solution of a 

 problem that occurs in computing the orbits of comets. The lunar eclipse was a 

 total one on March 18, 1783. The beginning 7 h 53 m 39 s ap. time; total im- 

 mersion 8 h 50 m 55 s ; beginning of the emersion 10 h 32 m 2 s ; end of the eclipse 

 1 l h 32 m 18 s , whole duration 3 h 3g m s . After this follow some very few obser- 

 vations of Jupiter's satellites, of no use now ; and then, with regard to the pro- 

 blem on the orbits of comets, Mr. Z. says, it is known, that the indirect me- 

 thod to calculate the orbits of comets in a conic section, by means of 3 obser- 

 vations given, is rendered more easy and expeditious if there is a possibility of 

 drawing a graphical figure that represents nearly the orbit under consideration 

 by means of which the calculation is directed, and the required elements of the 

 comet's path may be rigorously determined. To draw the orbit of a comet that 

 moves in a parabola or ellipsis, the problem is reduced to find the position of the 

 axis and the perihelial distance; this position of the axis will be determined as 

 soon as the angle is known that the axis forms with another line whose position 

 is given ; this line may be an ordinate to a given point of the curve, or a tan- 

 gent, or a radius vector, &c. The latter is to be employed in preference, be- 

 cause the perihelial distance being a constant quantity, the angle of position 

 then becomes the true anomaly of the comet ; but as the data of this problem 

 are only geocentric longitudes and latitudes of the comet, deduced from the im- 

 mediate observations of right ascension and declination, the heliocentric longi- 

 tudes and latitudes must first be calculated ; but as those data are not sufficient, 

 what is not given must be arbitrarily supposed, viz. the shortened distances (dis- 



4 o 2 



