THE ORBIT OF URANUS. 



127 



in the proper columns of the following table, under the head "Mean dates," 

 ]Mean cor. in R. A., and Mean cor. in Dec. These means are those given by the 

 observations as printed, without the application of the systematic corrections on 

 pages 120 and 121. In the columns "Corrected mean" these corrections are applied ; 

 this column would therefore exhibit no systematic differences between the results 

 of the diff'erent observatories, imless the observations of Uranus were affected by 

 errors different from those which affect the positions of the fundamental stars. A 

 careful comparison of the differences in various parts of the table shows that this 

 is unfortunately the case. A weight is next assigned to each individual result 

 depending on the number of observations, the general sufficiency of the data of 

 reduction, the mean discordance of the individual observations, and the quality of 

 the instruments. The critical reader will notice a lack of homogeneity among the 

 weights assigned, of which I shall speak presently. The mean of the separate 

 group-results is tlien taken with regard to these weights, and also the mean of the 

 mean dates, using for the latter the relative weights adopted for the several right 

 ascensions. Thus, we have a mean result derived from all the observations for 

 each month, or other groujvperiod, which is written under the horizontal lines. 



These corrections to right ascension and declination are next changed to correc- 

 tions of longitude and latitude, using for this purpose the following table, which 

 is computed from the formula? of Gauss : 



cos E = sin e cos a sec h = sin f cos 7 sec 8 



^ -, nin E cos b , , cos £" , t, 



A? = , — Aa -] f Ad 



cos o cos o 



Ah = — cos E cos ^ Aa -|- sin E AL 

 The differential coefficients in this table are expressed as a function of the right 

 ascension of Uranus only, which may be done because, owing to the small inclina- 

 tion and great distance of the planet, its geocentric position on the celestial sphere 

 is never more than about 2' from some point of the projection of its heliocentric 

 orbit. The coefficients of Aa are midtiplied by 15, that the right ascension may 

 be expressed in time. 



To Convert Errors of Right As<;k>j,siii\ and Dei -lination of Uranus into errors of 



LONUITUDE AND LATITUDE. 

 Wlien the Kight Ascension excee^ls 12', enter with R. A — 12'', anj change the signs of the quantities 



c)b 



/) 



"d 



on o<) 



R. A. 



10 

 20 

 30 

 40 

 50 



1 



10 

 20 

 30 

 40 

 50 



Lotraiithms of 



da 



1.1386 

 1.1387 

 1.1388 

 1.1389 

 1.1390 

 1.1391 



1.13fl2 

 1.1393 

 1.1394 

 1.1394 

 1.139.i 

 1.1395 



db 



da 



<5i 

 66 



6h 



66 



-0.7761 

 -0.7757 

 -0.7743 

 -0.7720 

 -0.7IJ87 

 -0.7ii43 



-0.7588 

 -0.7525 

 -0.7451 

 -0.7''(i5 

 -0.7-:70 

 -0.7162 



— 4 



— 14 



— 23 



— 33 



— 44 



— 55 



— 63 



— 74 



— 86 



— 95 

 —108 

 —118 



-1-9.6000 

 -1-9.59(16 

 4-9.5983 

 -1-9.5963 

 -j-9.5934 

 +9.5896 



+ 9.. '•.849 

 4-9 5794 

 4-9.5730 

 -|-9.56.i6 

 -1-9.5573 

 -1-9.5479 



- 4 



- 13 



- 20 



- 29 



- 38 



- 47 



- 55 



- 64 



- 74 



- 83 



- 94 

 -104 



9.9626 

 9.9626 

 9.9628 

 9.9632 

 9.9637 

 9.9645 



9.9653 

 9.9662 

 9 9673 

 9.96S5 

 9.9698 

 9.9711 



6b 



66 



— +0.92+ 



— -f 0.92+ 



