52 Sven Wicksell 



and the direction cosines are 



a n = 0.0000 a 12 = -f 0.4978 a 12 = — 0.8673 



a 21 = — 0.9658 a 22 = — 0.2244 a 23 == — 0.1289 



a 31 = — 0.2588 a g2 = -f 0.8327 cx 33 = -f 0.4807. 



Space doesn't permit a reproduction of the numerical equations of transformation. 

 Of course they are of a character to give the characteristics sought explicitely and 

 linearity expressed in terms of the characteristics (of the same order) in the equa- 

 toreal system. It will suffice to know that the transformations have heen thor- 

 ougly and painfully checked. 



We obtain for the moments of the second order the expressions 



V N %'oo — 3 8629 1 — & t 2 JV^j 0 = 0.5710 q' — 0.4362 



V jV 020 = 2 0975 9.' — G - 4871 V ^101 = °- 1266 9 — 0 - 2258 



V N ''V02 = 12002 ( I — 0 1520 V ^ 0 1 1 = 0 ' 2252 4 — 0 - 2314 



and using the notations of the preceding chapter: 



Characteristics of the third order referred to 

 the Galactic System. 





*8 



H ijk 



ttW 



H ijk 



»1* ß a'oo 



4 0.6201 



— 1.1441 



+ 0.0485 



V ß's'i 0 



+ 0.7865 



— 1.1464 



+ 0.1370 



V B?, o 



+ 0.2577 



— 0.7280 



+ 0.1854 



V ß o' 3 o 



+ 0.4075 



— 0.5166 



+ 0.0720 



V ßo'„ , 



+ 0.1023 



— 0.3358 



+ 0.0723 



V Bol 8 



4- 0.2065 



— 0.5225 



+ 0.0450 



V ß'oos 



+ 0.2342 



— 0.2248 



4- 0.0180 





— 0.1002 



— 0.4201 



+ 0.0384 



V ß'='o , 



-f 0.2817 



— 0.5345 



4" 0.0681 





+ 0.1394 



— 0.2258 



+ 0.2221 



