144 Astronomical and Nautical Collections. 



Sin A= li^L^; whence a'= fi°.17'.34", ^"'=9°.12'.19". 

 r 



For the elongations from the earth, we have 



Sin I- g ^'"(^-'') . hences'=19°.47'.47",and£"=:15^-2.5'.16": 

 r cos X 



consequently the heliocentric longitudes of the comet arc 0'= 



0.'2°.29'.5", and C'"— 0'.5°.54'.3". By means of the expression 



cot w— . "^ -7; ;7- —cot (C"'— C), we find w = 



tang h sm (C — O^ 



7°.ir.45"; whence the longitude of the descending node, since 



the latitudes are south, will be C'-w-0^2°.29'.5"-7°.ll'.45" 



r=ll».2.5°.18'.7". The inclination is found, from the equation 



tangz=-^-r^^ — ^,=: 41°.21'.30''. In the next place, we have 



sm u 



cos ?<':=:cos x' cos o), and cos m"'= cos x'" cos (C" — C-\-a), 



consequently m'- 9°.32'.54', u" — 14°.0'.40", and v!" — u- x 



=4°.27'.46'. Hence we find (p, taking the third observation, 



because it is nearer to the sun, by means of the formula tang 



r" 1 



1 <» — cot i V — V . -^, ; which gives J (p= 67°.56'.12", 



"■ r sin \ X 



and the true anomaly of the comet in the third observation 

 1 3.5°.52'.24 ". If we add to <p the distance of the comet from 

 the y , or ?{"', = 14°.0'.40", we obtain the distance of the peri- 

 helium from the descending node = 149°.53'.4"; consequently, 

 the longitude of the perihelium is 49.25°.ir.H". The distance 

 or at the perihelium is r" cos - j ^ — . 1 1782 : whence we find 

 the time from the third observation to the perihelium, =: 

 24d.20h.22m. ; and the time of the perihelium October 7, 

 10h.22m. 



[A''ote. — It must here be remarked that it has been usual 

 with all astronomers, since the time of Halley, to apply the 

 term Longitude of the Perihelium to the sum of two angles 

 lying contiguous to each other in different planes; one the 

 longitude of the node, reckoned on the ecliptic, the other the 

 distance of the perihelium from the node, measured on the 

 plane of the orbit. To reduce the longitude of the perihelium 

 to the ecliptic, in the common sense of the term, would be of no 

 practical advantage. Tr. From a letter of the Author.] 



