28 



Walter Gyllenberg 



TABLE VIII. 



Direction cosines of the apex 



(7. = 270° o=+30°) in relation 

 to the system K a . 



Square 

 1 



c» 



C 23 



C 3 3 



Ai 



0. 



4- 0.9396 



4- 0.3121 



Ai 



0. 



— 0.7660 



4- 0.6427 



Bi 



— 0.8237 



4- 0.5426 



4- 0.1653 



B, 



— 0.5090 



-)- 0.8492 



— 0.1404 



B, 



0. 



4- 0.9664 



— 0 2571 



b\ 



+ 0.5090 



+ 0.8492 



— 0.1404 



ß ä 



-j- 0.S237 



4- 0 5426 



+ 0.1653 



B,. 



-\- 0 8237 



-f- 0.1634 





B, 



-j- 0.5090 



— 0 1432 



+ 0.8488 



B* 



0. 



— 0.2604 



4- 0.9655 



ß. 



— 0.5090 



— 0 1432 



4~ 0.8488 



Bio 



— 0.8237 



4- 0.1634 



4- 0.5431 



C, 



— 0.83G5 



4- 0.54)2 



— 0.0920 



c 2 



— 0.6123 



+ 0.6373 



— 0.4680 



C, 



— 0.2241 



4- 0.6933 



— 0.6850 



c 4 



+ 0.2241 



+ 0.6933 



— 0.6850 



c 6 



-}- 0.6123 



4- 0 6373 



— 0.4680 



C 6 



-j- 0.8365 



+ 0.5402 



- 0 0920 



c 7 



-f 0.8365 



4- 0.4282 



4- 0.3420 



C s 



-j- 0.6123 





4" 0.7180 



c, 



-j- 0.2241 



+ 0.2751 



4- 0'9350 





— 0.2241 



4- 0.2751 



4- 0.9350 





— 0.6123 



4- 0.3311 



4- 0.7180 



c 12 



— 0.8365 



+ 0.4282 



4- 0.3420 



Di 



— 0.8365 



4- 0.4282 



— 0.3420 



D 2 



— 0.6123 



4- 0 .3311 



— 0.7180 



D 8 



— 0.2241 



4- 0.2751 



— 0.9350 



D 4 



4- 0.2241 



+ 0.2751 



— 0.9350 



D- 



-|- 0.6123 



+ 0.3311 



— 0.7180 



Df 



-j- 0.8365 



4" 0.4282 



— 0.3420 



D-, 



-f 0.8365 



+ 0.5402 



+ 0.0920 



d] 



+ 0.6123 



4- 0.6373 



4- 0.4680 



D, 



_j_ Q 2241 





_j_ 0.6850 



D 10 



— 0.2241 



+ 0.6933 



+ 0.6850 



Du 



— 0.6123 



4- 0.6373 



4- 0.4G80 



D„ 



— 0.8365 



-j- 0.5102 



4- 0.0920 



£1 



— 0.8237 



+ 0.1634 



— 0.5431 



E 2 



— 0.5090 



— 0.1432 



— 0.8488 



£ s 



0. 



— 0.2604 



— 0.9655 



£4 



4- 0.5090 



— 0.1432 



— 0.8488 



E 6 



+ 0.8237 



4- 0.1634 



— 0.5431 



ß 0 



4- 0.8237 



4- 0.5426 



— 0.1653 



£7 



+ 0.5090 



+ 0.8492 



4- 0.1404 



£h 



0. 



4- 0.9664 



4- 0.2571 



ß 8 



— 0.5090 



+ 0.8492 



4- 0.1404 



ß M 



— 0.8237 



4- 0.5426 



— 0.1653 



F, 



0. 



— 0.7660 



— 0.6427 



F» 



0. 



4- 0.9396 



— 0.3421 



Now for each square and for each spectral 

 class and magnitude the values of ï s 2 were cal- 

 culated. In the usual way we may now compute the 

 mean deviation. The stars in the different squares 

 however being small, I have not for this purpose 

 used the observed mean, but computed the de- 

 viation about a theoretical mean £ 0 — that is the 

 value of s obtained for every square and spectral 

 class as the component of the solar motion and 

 defined in the following way: 



£ 0 — S cos. the angle (apex — square). 



Here the sun's relative velocity, S, is to be taken 

 from the table IV. As for the position of the 

 apex, this was assumed to be a = 270°, 8= + 30", 

 the same for all types, because a variation in the 

 position of the apex will in a much smaller degree 

 influence the value C 0 than a variation in the 

 relative velocity of the sun. 



The cosines of the angles between the apex 

 and the centres of the squares may be taken from 

 the table VIII, where the direction cosines of this 

 assumed apex in relation to the system K 3 are 

 tabulated. 



The following designations are used: 



c 13 = cos (apex — X), 

 c 23 = cos (apex — Y), 

 c 33 = cos (apex — Z). 



25. The quantities, in the following denoted 

 as dispersions, are all calculated from the formula 



( 1 8) wo 2 = Is 2 — nl\ - 2C o £*, 



which formula for Ç 0 = z 0 = : n is transformed 

 into the general expression for the dispersion 

 about the mean. 



The table IX below contains the values of 

 a obtained in the manner described. 



A short glance at the table shows that the 

 mean velocity within the different spectral groups 

 is very varying without any conspicuous regularity. 



