152 



ASTRONOMICAL OBSERVATIONS 





Comet. Earth. 





Berlin Mean Time. 



A A 





Longitude. 



Latitude. Longitude. Latitude. 



Log Radius Vector. 



Jan. 31, Sh 



15° 0' 50".0 



+ 65° 37' 49".6 



131° 3'29".6 



+ 0".3 



9.9936814 



Feb. 12, 



24 50 22 .3 



46 10 41 .5 



143 12 42 .4 



— .7 



9.9945791 



23, 



29 22 27 .8 



31 27 35 .5 



154 17 46 .9 



+ .5 



9.9956259 



March 3, 



32 2 14 .6 



22 28 .2 



163 19 40 .4 



— .1 



9.9966147 



12, 



34 14 5 .2 



14 26 39 .0 



172 19 2 .2 



— .4 



9.9976458 



24, 



36 45 4 .7 



6 27 27 .7 1 184 13 40 .3 



+ .7 



9.9991232 



The longitudes are referred to the mean equinox of January I, 1840. As- 

 suming Kysseus' approximate elements, the preceding places furnished me 

 twelve equations of condition, from which were deduced the following parabo- 

 lic elements, by the method of minimum squares : 



Perihelion passage, Berlin mean time, March 12. 981921. 

 Longitude of perihelion, .... 80° 20' 24".4 

 " ascending node, . . 236 48 39 .3 



Inclination of orbit, 59 14 2 .4 



Log. of perihelion distance, . . . 0.0870185. 



The errors of this orbit are as follow, the errors in longitude being multi- 

 plied by the cosine of the corresponding latitude: 







Longitude. 



Latitude. 



January 



31, 



-j- 4".4 



+ 2".6 



Februar 



^12, 



— 1 .4 



— 1 .9 





23, 



— 6 .1 



-f- 1 .5 



March 



3, 



— 2 .7 



— 1 .7 





12, 



+ .1 



— .7 





24, 



+ 5 .9 



+ 1 .1 



These errors certainly are not very great, yet they exceed what has already 

 been assigned as the limit of the probable error of the observations. It is, then, 

 probable that the orbit was not a parabola, especially as the errors follow an 

 obvious law, the extremes being positive, and the middle ones generally neo-a- 

 tive. It remains to vary the other element, namely, the eccentricity. This 

 was done by means of the following equations of condition, computed by the 

 formulae of Gauss and Bessel, in which the variations of the elements were 



d = 0.0002 

 t = 0.01 

 p = n = i = V 

 e = 0.001 



