The motion of tlie stars 



97 



If r = 0, h. e. if the line of symmetry 

 is parallel to one of the axes, the solution 

 given in § 30 fails, the equation for t be- 

 ing no longer valid. We must then take 

 recourse to the solution of Peakson. The 

 correlation surfaces of table I are, however, 

 too little precise — contain too few indivi- 

 duals — for allowing to determine the mo- 

 ments of the fifth order. Such squares must, 

 for the present, be left out of consideration. 



32. Applying the methods of § 30 I 

 have for every one of the 48 squares per- 

 formed the computations necessary for dis- 

 secting each correlation surface into two 

 sphœrical star-streams. The result has been, 

 throughout, a negative one. In every case, 

 or in nearly every case (some squares have 

 been excluded), the calculation has given 

 imaginary values of one of the dispersions 

 or a^. It is, accordingly, not possi- 

 ble to explain the observed deviations of 

 the correlation surface for the linear velo- 

 cities from the normal form through the 

 hypothesis of two star-streams. 



For checking this result I have turned, 

 for every square, the system of coordinates 

 through an angle cp, so that the new system 

 of coordinates has the axis of x pointing 

 to the vertex (system K^. If there are two 

 star-streams the frequency curve of the new 

 a;-coordinates ought to be composed of two 

 normal components, whereas the frequency 

 curve of the new ^/-coordinates ought to be 

 a normal curve. Neither of these conclusions 

 is, however, fulfilled. 



I give in table X the value of the 

 skewness and of the excess for each square 

 in the system K^. 



Here Ü' denotes the new x-coordinate 

 (positive in a direction against the vertex), 

 V the new ^/-coordinate. The upon an 

 average negative values of Su> with minima, 



Luuds Univ:s Årsskrift. N. F. Afd. 2. Bd 8. 



TABLE X. Skewness and excess 

 in System iQ. 







" yi 



E 



F, . 



J2j y t 



A 



n ßii 



y fl ina 

 —\- U.4VÖ 



A 109 





A 



n 7*>r; 

 \J.iZO 



_L n 1fi7 



A nQ7 







+ 0.290 



+ 0.653 



— 0.291 



-f 0.154 



J3 

 ^2 



n 10Q 



— yj.i^o 



-L 0 ßQA 

 U.Dtf» 



A lAQ 



A (\0'\ 



R 



"s 



yj.ooo 



J-. 0 qqi 



\J.OOJl 





{\ onq 



y J . auo 





X.UWo 



— ■ W.iälO 





A 900 





A QQQ 



\J.oOj 



A 009 



A nift 



\J.\J-±X) 



A 91 0 



R 



A OQïi 



0 470 



A Q09 



A OQQ 



R 



A OQK 



A 119 



A OP.A 



A 911 



R 

 ^8 



—1— 0 ftRO 



A onp. 



\J.OiO 



A 9ft1 



A 904 



R 



-1- 0 



U.OOU 



1 A OQA 



0 1Q1 





R 



— i— 0 noft 



1 QIA 



A QAQ 



\J.O\JO 







— 0.425 



-t- 0.581 



— 0.191 



— 0.303 



n 

 ^2 



U.UiSB 



-\- 1.584 



— 0.333 



1 A TAa 

 — f- U.iUo 



Cs 



— 0.262 



— 0.043 



— 0.292 



~ 0.524 



n 



^4. 



1 . A on^t 







A RQ9 



C! 



0 



A AOA 



0 999 



A KIQ 





A ACiA. 



1 ni7 



A 91 J. 



A Q7f; 







_4_ A 907 



A aoa 



A Afip; 





A QOQ 



A Qcn 



A oaa 



A AI Q 



n 



"^9 



-U () ail 



A R7fj 



A OSI 



A i7r; 



yj.x 1 0 



n 



A f\QO 



V. J.OÖ 



. A 9Qft 



A 901 





-4- 0 9^4. 



—1— 0 070 



A 97 J. 



A AF.ii 



0 



'-'12 



A AQQ 



\Jt\JuO 





A Qdft 



yj.oto 



A Qfti 





— 0.284 



-f- 0.416 



— 0.274 



— 0.214 



7") 



-|— U.UliS 



_L A f;,iq 



— p u.o4y 



A QOQ 



Q1 A 



— U.oiO 





— 0.270 



-|- 0.726 



— 0.102 



+ 0.066 



n 



^4 





— C\ 9A9 



0 in9 



\J.X\Ja 



A OJ.Q 



n 





1 497 



A 990 







0 797 



A KAQ 



VJ, J.ÖO 



A 1Q9 



D 



A (too 



A Q09 



— 0 119 





n 



^8 



A aoA 



1 oqq 



— y/.vD^ 



_I_ A 007 



n 



0.427 



1.689 



0.185 



_|_ 0.476 



D 



-J— 0 rt79 





A Af\Q 



A 10Q 



T) 



A OHQ 



4- 0 07Pi 



A ïiin 



yj.oxv 



A AQ-t 



yj.'tox 





A 007 



1 A OQ! 



A 9Q1 







— 0.372 



-I- 0.219 



— 0.302 



— 0.443 





— U 0 99f\ 

 \J.aa\J 



_L_ A A07 



0 ÎÏ10 



r \ A AO 



Es 



-f 0.062 



— 0.266 



— 0.272 



— 0.260 



4 



-f- 0.242 



— 0.028 



— 0.083 



— 0.190 



E, 



— 0.702 



— 0.642 



-|- 0.038 



— 0.216 



E, 



— 0.178 



-f- 0.310 



— 0.269 



— 3.375 



E, 



— 0.464 



— 0.049 



— 0.256 



— 0.216 



E, 



— 1.222 



— 0.168 



-f 0.165 



— 0.250 



E, 



— 0.686 



-f 0.442 



— 0.234 



— 0.183 



Ero 



— 0.337 



-f 0.037 



— 0.268 



— 0.301 



Ft 



— 0.410 



— 0.702 



— 0.245 



— 0.060 



E, 



— 0.276 



— 0.365 



— 0.241 



— 0.266 



13 



