28 



KNUT LUNDMARK, GLOBULAR CLUSTERS AND SPIRAL NEBULiE. 



20,000 K — 3,215 X + 5,957 Z + 2,676 7 = + 7,364 

 — 3,215 +10,281 —1,024 +1,231 = — 4,126 

 + 5,957 — 1,024 +7,069 —0,373 = + 1,231 

 + 2,676 + 1,231 —0,373 +2,656 =+1,051 



The elimination equations: 



1,0000 K — 0,1608 X + 0,2979 Z + 0,1338 7 = + 0,3682 



1.0000 X + 0,0067 Z + 0,1701 Y = — 0,3013 



1 ,0000 Z — 0,2189 Y = — 0,1854 



1,0000 Y = + 0,1993 



X = - 0,336, 



Vo = 



— 0,415 ± 0,311 



7= + 0,199, 



A = 



-31° ±47° 



Z 0,142 



D = 



+ 21° ± 44° 



Z = + 0,330 







E = ± 0,406 . 







And, supposing K = 



we obtain: 



1,0000 X — 0,0996 Z + 0,1197 Y = — 0,4013 



1,0000 Z — 0,0359 7= + 0,1177 



1,0000 7= + 0,6296 



X = — 0,463, V = — 0,794 ± 0,354 



7= +0,030, 4 = -55° ±21° 

 Z= + 0,140, Z> = — 10° ± 18° 



E = ± 0,469 



from which follow the residuals: 



-v 



K = + 330 



v 



X = 

 v 



-V 



X=+ 330 



v 



K = 



v 



- 300 km 



- 370 km 



- 774 km 



- 500 km 



+ 156 km 



+ 94 km 



+ 316 



+ 326 



+ 138 



- 940 



- 448 



- 507 



+ 300 



+ 309 



+ 119 



-1000 



- 459 



- 605 



+ 278 



+ 332 



+ 181 



-1140 



- 487 



- 812 



- 200 



- 68 



- 90 



- 200 



+ 252 



+ 138 



-1020 



- 823 



- 979 



- 100 



+ 438 



+ 240 



- 500 



- 90 



- 23 







+ 387 



+ 239 



- 100 



+ 233 



+ 288 



- 600 



- 337 



- 556 



- 400 



+ 336 



+ 293 



- 158 



+ 234 



- 367 



- 825 



- 154 



- 165 



- 275 



+ 237 



- 210 



