526 
Proceedings of the Eoyal Society of Edinburgh. [Sess. 
5. The equations of condition were then formed by using MartlTs 
formulae on page 518. The following, derived from the 1892 observations 
of Prof. Barnard, will serve as an example of these — 
Position-Angle. 
Date. 
Sin du. Sin dN. Sin dl. 
2e sin Q. 
2e cos Q. 
s sin dp. 
1892 Nov. 13. 
- 9-55 
54)0 + 
7*05 
+ 8*23 
- 4*84 
= 
+ 0*08 
18. 
-11-7 
4*51 
3-01 
+ 11*3 
+ 2*94 
= 
-0*14 
20. 
-15-9 +9-11 + 
5*77 
- 4*32 
- 15-3 
= 
-0*07 
Dec. 9. 
- 10'4 
6*72 + 
0*549 
- 10-4 
+ 0*426 
= 
-0*11 
16. 
-10-6 +0-27 +1D9 
- 4-48 
+ 9*60 
= 
+ 0*02 
1893 Jan. 8. 
- 9-48 
4-62 + 
9-10 
- 7*17 
+ 6*21 
= 
+ 0*37 
13. 
-1D6 
4*91 
2*62 
-11*3 
+ 2*47 
= 
+ 0*18 
20. 
- 9-59 
3*25 +10-3 
- 6*29 
+ 7-24 
= 
+ 0*10 
Distance. 
Date. 
Sin du. Sin dN. 
Sin dl. 
2e sin Q. 
2e cos Q. 
da/a. 
ds. 
1892 Nov. 13. 
+ 0-014 -0*016 
+ 0*005 
- 4*29 
- 7*27 
+ 16‘9 
= 
- 0*25 
18. 
+ 7-03 -9-26 
- 1*72 
- 5*08 
-8*41 , 
+ 13*7 
= 
+ 0*01 
20. 
-4-78 -0-711 
- 12*2 
-6*22 
-2*21 
+ 10*2 
= 
+ 0*37 
Dec. 9. 
+ 5-37 -6-25 
+ 0*171 
+ 5*69 
+ 7*54 
+ 15*5 
= 
+ 0*03 
16. 
-5-97 +4-71 
- 4*38 
+ 4*30 
+ 8*62 
+ 15*1 
= 
-0*07 
1893 Jan. 8. 
-1-74 +1-63 
- 0*776 
+ 4*17 
+ 7-46 
+ 16*7 
= 
- 0*27 
13. 
+ 7-17 -9-21 
+ 1*44 
+ 5*55 
+ 8*19 
+ 13-6 
- 
+ 0*05 
20. 
-3-25 +2-87 
- 1*72 
+ 4*02 
+ 7*78 
+ 16*3 
-0*17 
6. Next the normal equations were 
formed for each series : — 
NORMAL EQUATIONS. 
Lick Observatory — Prof. Barnard. 1893*0. 
Sin du. Sin dN. 
Sin dl. 
2e sin Q. 
2e cos Q. 
da [a. 
Sin du +1220 - 39 
-321 
+ 291 
- 46 
+ 56 
= 
- 1*86 
Sin dN 
+ 483 
- 54 
+ 41 
- 155 
- 211 
= 
-4*91 
Sin dl 
+ 607 
- 95 
+ 106 
- 232 
+ 1*05 
2e sin Q 
+ 759 
+ 168 
+ 158 
= 
-7*82 
2e cos Q 
+ 899 
+ 349 
= 
+ 1*50 
daja 
+ 1776 
— 
-7*51 
Lick Observatory — Prof. Barnard. 1894*0. 
Sin du. Sin dN. 
Sin dl. 
2e sin Q. 
2e cos Q. 
da/ a. 
Sin du +1360 +173 
-444 
-536 
- 140 
+ 78 
= 
-2*23 
Sin dN 
+ 495 
-145 
- 120 
+ 194 
- 207 
— 
+ 1*32 
Sin 6.1 
+ 613 
+ 90 
- 71 
- 158 
— 
+ 0-08 
2e sin Q 
+ 916 
+ 178 
- 178 
— 
-8*45 
2e cos Q 
+ 1037 
- 316 
= 
+ 1*31 
daja 
+ 2360 
= 
+ 0*09 
