48 Sven Wicksell 



Writing generally (for i 4- j -f- k = 3) 



V B iß - = 38 g' 3 + fl» - g' 2 ) + AJ (2 - 3g' + g' 3 ) 

 we obtain as solutions the following table. 



Characteristics of the third order referred to the Equatoreal System. 





K 



Hk 



K 



xjk 



K 



V B' 





— 0.0425 



— 0.0511 



+ 0.00042 



V B' 



120 



+ 0.2459 



— 0.1570 



+ 0.01845 



V B' 



102 



+ 0.0598 



+ 0.0049 



+ 0.01781 



V B' 



030 



— 0.7711 



+ 1.3911 



— 0.09693 



V B' 



210 



— 0.1033 



+ 0.5714 



— 0 .00124 



»!« B' 





— 0.1018 



+ 0.6061 



— C .17810 



V B' 



003 



+ 0.3852 



— 0.4757 



+ 0.03083 



V B' 





+ 0.8806 



— 0.3370 



+ 0.02888 



V B' 



021 



+ 0.3102 



— 0.5831 



+ 0.20650 







— 0.3449 



+ 0.1531 



— 0.03695 



20. Finally the normal equations for the characteristics of the fourth order 

 will be of 4 kinds. We have 



3 equations of the form 

 V B\. M \ 4- V B"^ K + V B"n, \ = K Q" + K 2' 3 (1 - «' 8 ) + 

 + K «'(2 - 2' - 2s' 3 + q' b ) + h 7 g' 2 + Ä 8 (6 - 12g' + 3g' a + 4g' 3 - g'«), 

 as given by the table 



given i: 



'»1 



h 



K 



K 



'*5 



K 



», 



K 



5.1872 

 — 0.1910 

 + 0.4208 



— 0.1910 

 + 5.3017 

 -f- 0.3659 



4- 0.4208 

 4- 0.3659 

 4- 2.6662 



— 4.6122 



— 1.3703 



— 1 .6690 



4- 2.1772 

 4- 0.1140 

 + 1.5274 



— 0.9482 



— 0.2482 



— 0.2971 



4" 1.5501 

 — 0.0091 

 4- 0.6524 



4- 0.0623 



4- o.oioi 



+ 0.0266 



3 equations of the form 



V B" l03 \ + v B" 301 h + v B "i2i h = h q 6 + h g'V - ?' s ) + 



+ k, q'(2 - g' - 2g' 2 + ? ' 5 ) + fr 7 g' 2 + *„(6 - 12,/ + 3g' 2 + 4g' 3 - g' 6 ) 

 i the table, 





K 



K 





h 



K 



ft, 



K 



+ 6.1838 

 4- 0.9637 

 + 0.3234 



4- 0.9637 

 4- 7.8612 

 4- 0.2101 



+ 0.3234 

 4- 0 2104 

 4" 2.5169 



— 5.4631 



— 2.2731 



— 2.2637 



+ 0.2298 



- 0.1651 



— 0.4414 



— 0.1220 

 4- 0.5974 

 + 0.1218 



4" 0.5826 

 — 0.7957 

 4" 0.5936 



— 0.0073 



— 0.0357 



— 0.0326 



