150 



ASTRONOMICAL OBSERVATIONS 



Hudson observations in right ascension accord with each other quite as well 

 as the European observations; the declinations seem entitled to very little 

 weight. 



The results are shown in the following table. 





Corrections of Ephemeris. Comet's Places by Ephemeris. 



Corrected Places freed from Aberration. 1 



Berlin Mean 

 Time. 





I 



A. R. 



Dec. 



A.K. 



Dec. 



A.K. 



Dec. 



Jan, 31, S"* 



4- 14".7 



— 8".l 



326°24'50".6 



+ 61°25'23".5 



326° 25' 5".3 



+ 61°25'15".4 



Feb. 12, 



— 12 .7 



— 1 .1 



358 8 37 .6 



51 2 51 .8 



358 8 24 .9 



51 2 50 .7 



23, 



— 17 .3 



+ 7 .8 



13 19 53 .3 



40 11 24 .7 



13 19 36 .0 



40 11 32 .5 



Mar. 3, 



— 28 .0 



+ 17 .6 



21 1 45 .4 



32 39 1 .4 



21 1 17 .4 



32 39 19 .0 



12, 



— 32 .6 



+ 22 .4 



26 35 13 .5 



26 27 52 .4 



26 34 40 .9 



26 28 14 .8 



24, 



— 40 .2 



+ 25 .0 



32 10 37 .8 



19 51 50 .7 



32 9 57 .6 



19 52 15 .7 



It is important to know the probable error of the preceding results. If we 

 regard the corrections in each group as observed values of the same quantity, we 



obtain the probable error of the mean by the formula £ = . / ^ ^^ ^^-. 



V n [n — 1) 



These errors are exhibited below, those in right ascension being each 

 multiplied by the cosine of the corresponding declination. The last co- 

 lumn represents the probable error of the entire observation, being equal to 

 \J A. R. error^ + Dec. errorl 



January 31, 

 February 12, 



23, 

 March 3, 



12, 



24, 



A.K. 



1".5 

 1 .1 

 1 .1 

 .9 

 1 .3 

 1 .7 



Dec. 



Total Error 



2".3 



2".7 



2.3 



2 .5 



I .3 



1 .7 



.8 



1 .2 



.7 



1 .5 



.8 



1 .9 



The supposition that the correction of the Ephemeris remains constant 

 throughout the entire period embraced by one group is incorrect, and we 

 should obtain a more satisfactory result if we knew the proper correction of the 

 Ephemeris for the date of each observation. As, however, the above correc- 

 tions follow no obvious law, it is impossible to obtain, very satisfactorily, the 

 correction for each date by interpolation. I have therefore contented myself 

 with the above numbers, and conclude that if an orbit can be found, whose 

 errors are confined within these limits, nothing more can reasonably be de- 

 manded. The preceding right ascensions and declinations were converted into 

 longitudes and latitudes by employing the apparent obliquity of the ecliptic, 



