the Orbits of Comets. 43 



(-p) and (jj), which we have expressed, for the sake of 



greater simphcity, by the foregoing letters. 



If the number of observations is an odd one, we should 

 fix the epoch at the instant of the mean observation, which 

 will dispense with our caiculaling the parts independent of 

 z, in the two preceding formuliE ; for it is visible that these 

 ■parts are respectivelv equal to the longitude and to the la- 

 titude of the mean observation. 



In order to elucidate what has been said, by an example, 

 we shall select the second comet discovered by M. JSIecbain 

 in 17S1, and the orbit of which he calculated according to 

 this method : the observations which this learned astrono- 

 mer chose for this purpose, are referrf^d to the same hour of 

 the day, viz. 8^ £9' 44:'' mean time at Paris : the following 

 are the observations : 



Geocentric Lonsitude 

 of the Comet. 

 1781. Nov. 14 S07° i4' A3" = /3 

 30f->° 57' 32" = /3' 

 306° 5 J' 26" = |6" 

 3()t° 44' 53" = /3"' 

 306°4i'37" = jS"" 

 By taking for the epoch, the instant of the mean obser- 

 vation, i. e. the IQth of November, at S'' 2()' 44', we have 



?■ = — 5, '1! = — 2, i' — 0, t!' 

 which gives 



ip = — 5' 44",33 



f/3' = - 3' 3", 



J/3"= -2' 11", 



^;3'"= — 1' 5".53 



(J'/3 = 3^",266 ' 



6^/3'.= 10",4. 



5«/3"= I0".91'5 



Northern Latitude. 



53° 17' 9" = 7 

 44° J 7' 12"= y 

 SJ-j" J4'48"= 7" 

 33° 49' 1" = 7'" 

 29° 5^' 43" = Y'" 



3,i""=Q, 



oy =. — 3" 39' 59",0 

 Sy' = — 2°3r 12",0 

 Sy" = — 1°48'35",667 

 Sy"'= — IMG' 4r/'.() 



iy.= 



13'4-5",l' 

 8' 31 ",2*1; 

 5' 18",i'78 



S»/3 = 



2",733 I S'y — ~ 39",266d 



0",06S1 I py =— 21.", 12 :^6 



' i^^/3 =(/',25Mi I S^ = 1",37(J6 

 The formula (p) will therefore give for the geocentric 

 longitude of the comet, according to the small number z 

 of days reckoned from tlie epoch, 



306° 51' 26" — 133"',46.s; + lo'\5i.z\ 

 and the formula (r/) will give for the expression of its latitude, 



39" 14' 48"- 7855", 1 6. s; + 535", 4. z% 

 from which we extract 



a = 306^51' 26", 

 a = — 0,0432501, b = 0,345366, 



6 = 39° 14' 48", 

 h = — 2,213844, I = 17,54354. 



2d. We 



