The motion of the stars 



89 



Using the second formula (72) we 

 obtain for o^' the following formula: 



TABLE IX. Mean peculiar velocities 

 of the stars. 



(81) 



In the following table I put together 

 the values of d-^a.^' calculated from this 

 formula. 



The value of ^^a,' is here expres- 

 sed in the unit used in table I (»class- 

 breadths»). For having its value in se- 

 conds of arc we have to multiply by 0".05. 

 This reduction is, however, not necessary 

 as another unit presents itself more na- 

 tm-ally. 



From the discussion of the moments 

 of the first order (determination af apex) 

 we know the product of and the ve- 

 locity — s — of the sun. Dividing ^^Og' 

 by Q'^s we may deduce the value of a^' 

 expressed in s as unit. These values of 

 Og' are given in the third column. If 

 the velocity of the sun is taken to 20 km 

 per second we obtain the values of a^' 

 — in kilometres — given in tlie fourth 

 column. Finally in the fifth column I 

 give the corresponding values of a^' cal- 

 culated from (79). 



The mean value of a' is 



(82) 



a^' = 0.7921 s + 0.0278 S 



= 15.84 Jem + 0.56 Jem. 



The corresponding value of g^' is 



(82*) a^' = 31.35 Jem ± 1.10 Jc7n. 



25. The mean errors in the coor- 

 dinates of the vertex have not been cal- 

 culated, because the mean errors in the 

 left members of (77), for each square, 

 are somewhat troublesome to compute. 

 We may infer, however, from the gra- 

 phical determination of the (true) vertex, 

 given in plate V, that the mean errors 



Lunds Universitets Årsskrift. N. P. Afd. 2. Bd 





12 



o/ : s 





' in km 



Oj' in km 



I 



+ 0.5419 



+ 0.5682 



+ 11.36 



+ 22.48 



2 



-|- 0.6464 



+ 0.6778 



+ 13.56 



+ 26.84 





+ 0.9403 





- 0.9859 



+ 19.72 



+ 39.03 



2 



-|- 0.5065 





- 0.5311 



H 



h 10.62 



+ 21.02 



bI 



A 



-)- 0.7213 



+ 0.7563 



+ 15.13 



' + 29.94 



B^ 



-j- 1.051 



+ 1.102 



+ 22.04 



+ 43.62 





-\- 0,6042 



+ 0.6335 



+ 12.67 



+ 25.07 



B, 



-|- 1.145 



-|- 1.201 



-f 24.02 



4- 47.54 



8 



-j- 1.014 



+ 1.063 



4-21.26 



+ 42.07 



-"Q 



-\- 0.5300 



+ 0.5557 



+ 11.11 



+ 21.99 



10 



-(- 0.5235 



+ 0.5489 



4- 10.98 



+ 21.73 



c. 



+ 0.9333 



+ 0.9786 





- 19.57 



+ 38.73 



c. 



^2 



+ 0 8095 



+ 0.8488 





- 16.98 



+ 33.60 



Os 



-j- 0.4826 



+ 0.5060 





- 10.12 



+ 20.03 



c. 



4 



-|- 0.6725 



+ 0.7055 





- 14.11 



+ 27.92 



5 



0.8497 



+ 0.8909 





- 17.82 



+ 35.27 



ö 



-|- 0.7000 



-j- 0.7340 





- 14.68 



4- 29.05 



C, 



7 



-|- 0.8011 



+ 0.8400 





- 16.80 



-f 33.25 



C. 



8 



-j- 0.8488 



+ 0.8900 





- 17.80 



4- 35.23 



C„ 



9 



-}- 0.7533 



+- 0.7899 





- 15.80 



4- 31. 27 



^10 



+(0.6949) 



+(0.7286) 





- 14.57 



-)- 28.83 



11 



-\- 0.9911 



+ 1.0392 





- 20.78 



-f 41.12 



^12 ^ 



-f- 0.8969 



+ 0.9404 





- 18.81 



4- 37.22 





+ 1.113 



+ 1.167 



+ 23.34 



+ 46.19 



D 



+ 0.9374 



+ 0.9829 



H 



h 19.66 



+ 88.91 





+ 0.7101 



+ 0.7446 



+ 14.89 



+ 29.47 



A 



4 



+ 0.6589 



-i- 0.6909 



4- 13.82 



+ 27.35 



A 



5 



+ 0.7605 



+ 0.7974 



-j- 15.95 



-1-31.56 



A 



0 



+ 1.111 



+ 1.165 



+ 28.30 



+ 46.11 



7 



4- 0.8037" 



+ 0.8427 



+ 16.85 



4- 33.35 



A 



+ 0 7310 



+ 0.7665 



+ 15.33 



-1- 30.34 



v 



-|- 0.591t! 



-\- 0.6203 



+ 12.41 



+ 24.56 



An 



* 10 



+ 0.7332 



+ 0.7688 



-f 15.38 



-j- 30.44 



A, 



+ 0.8905 



+ 0.9337 



+ 18.67 



-j- 36.95 



A, 



12 



+ 0.7420 



+ 0.7780 



H 



h 15.56 



-j- 30.79 





+ 0.7878 



H 



- 0.8260 



+ 16.52 



+ 32.69 



A 



+ 0.9313 



+ 0.9765 



+ 19.53 



-j- 38.65 



A 



■\- 0.6010 



+ 0.6302 



+ 12 60 



+ 24.94 



A 



+ 0.5037 



+ 0.5281 



+ 10.56 



4- 20.90 



A 



-f 0-5774 



+ 0.6054 



+ 12.11 



+ 23.97 





+ 0.4171 



+ 0.4373 



+ 8.75 



+ 17 32 



A 



+ 0.4967 



+ 0.5208 





h 10.42 



+ 20.62 



A 



-|- 0.6845 



+ 0.7177 



+ 14.35 



-j- 28.40 



A 



0 6120 



+ 0.6417 



+ 12.83 



+ 25.39 



Ao 



+ 0.8784 



+ 0.9210 



+ 18.42 



-I- 86.45 



A 



+ 0.6851 



+ 0.7184 



+ 14.87 



+ 28.44 



A 



+ 0.8866 



+ 0.9296 



4- 18.59 



+ 36.79 



12 



