The general Characteristics of the frequencyfunction of stellar movements 85 



TABLE III. 



Equations of transformation for the coefficients of the third order. 





«1 



a. 





«4 





rt 6 





^8 



ö 9 



a io 



" U 



°V2 



a i3 



A i 



4- i.oooo 



O.oooo 





0.0000 





0.0000 











— 0.2415 



4- 0.112 



+ 0.0010 



A i 



— I.0000 



0.0000 





0.0000 





0.0000 











4- 0.1003 



4- 0.017 



0 0000 



B, 



+ 0.0295 



— 0.8604 





— 0.0908 





4 0.2795 











— 0.9455 



4" 0,886 



4- 0.0554 



B 2 



+ 0.5295 



— 0.2030 





— 0.3847 





4- 0.2795 











— 0.3297 



4- 0.283 



4- 0.0228 



B s 



4- 1.0000 



0.0000 





0.0000 





0.0000 











— 0.0002 



4- 0.053 



4- 0.0007 



B 4 



+ 0.5295 



+ 0.2030 





4" 0.3847 





4- 0.2795 











4- 0.0532 



— 0.358 



4- 0.0198 



B s 



4" 0.0295 



4- 0.8604 





4" 0.09Ü8 





4- 0.2795 











4- 0.7733 



— 1.543 



4- 0.1627 



B a 



— 0.0295 



4" 0.8604 





4" 0.0908 





— 0.2795 











4- 0.1142 



— 0.946 



4- 0.0589 



B 1 



— 0.5295 



+ 0.2030 





+ 0.3847 





— 0.2795 











4- 1.5635 



— 1.284 



4- 0.0687 



Ö. 



— 1.0000 



0.0000 





OOODO 





0.0000 











— 0.5115 



■4-O.I22 



— 0 0010 



R 

























1 () 229 



q 0203 



B 10 



— 0.0295 



— 0.8604 





— 0.0908 





— 0.2795 











— 0.1910 



4- Omi 



— 0.0475 



Ot 



+ 0.0173 



— 0.9011 





— 0.0647 





4- 0.2415 











4- 0.8357 



4- 1-375 



— 0.0687 



o 2 



4- 0.3535 



— 0.3535 





— 0.3535 





4- 0.3535 











— 0.3948 



4- 1.133 



— 0.0794 



c. 



4- 0.9011 



— 0.0173 





— 0.2415 





4- 0.0647 











+ 0.0448 



4- 0.356 



— 0.0198 



o 4 



4- 0.9011 



+ 0.0173 





4- 0.2415 





4- 0.0647 











— 0.2165 



— 0.155 



4- 0.0020 



c 5 



+ 0.3535 



4- 0.3535 





4" 0.3535 





4- 0 3535 











+ 0.6308 



— 0.787 



4- 0.0709 



C e 



+ 0.0173 



4- 0.9011 





4- 0.0647 





4- 0.2415 











4- 0.3972 





4- 0.0981 



C, 



— 0.0173 



4- 0.9011 





+ 0.0647 





— 0.2415 











4- 0.4242 



— 1.140 



4- 0.0819 



c s 



— 0.3535 



4- 0.3535 





4- 0.3535 





— 0 3535 











4- 0.8599 



— 1.646 



4- 0.0967 



c» 



— 0.9011 



4- 0 0173 





4- 0.2415 





— 0.0647 











— 0.0513 



— 0.169 



4- 0.0020 



c 10 



— 0.9011 



— 0.0173 





— 0.2415 





— 0.0647 











— 0.2710 



+ 0.172 



— 0.0106 





— 0.3535 



— 0.3535 





— 0.3535 





— 0.3535 











— 0 4205 



4- 0.785 



— 0.0401 





— 0.0173 



— 0.9011 





— 0.0647 





— 0.2415 











— 0.9130 



4- 1.772 



— 0.1837 





-\ 



— h 





— ^4 



— &5 



- K 



— ^ 



6 8 





-bio 



&11 



&» 



&1« 





0.0000 



0.0000 





4- 0.9848 



— 0.1736 



0.0000 



0.0000 







0.0000 



4- 0.5175 



— 0.495 



4- 0.0100 



A 



0.0000 



0.0000 





— 0.9843 



— 0.1736 



0.0000 



0.0000 







0 0000 



4- 0.1030 



+ 0.335 



— 0.0009 



B t 



+ 0.1929 



4" 0.5940 





— 0.3751 



— 0.0674 



4- 0.4808 



— 0.6386 







4- 0.2075 



4" 0.5650 



— 0.843 



4- 0.1369 



B, 



4- 0.8175 



4- 0.5940 





— 0.0210 



— 0.4620 



— 0.4012 



— 0.2439 







4- 0.3357 



4- 0.6545 



- 0.715 



4- 0.0969 



B s 



0.0000 



4- 0.0000 





4- 0.7083 



— 0.7059 



0.0000 



0.0000 







0.0000 



4- 0.2540 



— 0 305 



+ 0.0126 



#4 



— 0.8175 



4- 0.5940 





— 0.0210 



— 0.4620 



4- 0.4012 



— 0.2439 







— 0.3357 



— 0.0675 



~ 0.782 



4- 0.0812 



B h 



— 0.1929 



4- 0.5940 





— 0.3751 



— 0.0674 



-- 0.4808 



— 0.6386 







— 0.2075 



4- 0.1635 



— 0.723 



4- 0.3139 



B» 



— 0.1929 



— 0.5940 





4- 0.3751 



— 0.0674 



— 0.4808 



— 0.6386 







4- 0.2075 



— 0.2585 



4- 0.136 



4- 0.0612 



B-t 



— 0.8175 



— 0.0940 





4- 0.0210 



— 0.4620 



4- 0.4012 



— 0.2439 







4- 0.3357 



— 2.1745 



4- 1.586 



— 0.0626 



B s 



0.0000 



0.0000 





— 0.7083 



— 0.7059 



0.0000 



0.0000 







0.0000 



— 0.2450 



4- 0.234 



— 0.0048 



B a 



4- 0.8175 



— 0.5940 





+ 0.0210 



— 0.4620 



— 0.4012 



— 0.2439 







— 0.3357 



— 0.8935 



4- 0.302 



+ 0.0023 



B w 



4- 0.1929 



— 0.5940 





4- 0.3751 



— 0.0674 



4- 0.4808 



— 0.6386 







— 0.2075 



4- 0.4515 



4- 0.262 



4- 0.0333 



c x 



4- 0.0486 



4- 0.1812 





— 0.1165 



— 0.0649 



+ 0.1929 



— 0.9034 







+ 0.2421 



4- 1.6205 



— 1.614 



4- 0.1839 



c, 



4- 0.2652 



4- 0.2652 





— 0.0884 



— 0.4842 



— 0.0884 



— 0.4842 







4- 0.4842 



4- 0.2010 



— 0.856 



4- 0.2364 



c, 



4- 0.1812 



4- 0.0486 





4- 0.1929 



— 0.9034 



— 0.1165 



— 0.0649 







4- 0.2421 



4- 0.3480 



— 0.463 



4- 0.0857 



c< 



— 0.1812 



4- 0.0486 





4- 0.1929 



— 0.9034 



+ 0.1165 



— 0.0649 







— 0.2421 



4- 0.3590 



— 0.394 



+ 0.0216 



c. 



— 0.2652 



4- 0.2652 





— 0.0884 



— 0.4842 



4- 0.0884 



— 0.4842 







— 0.4842 



4- 0.4335 



— 0.963 



4- 0.2936 



Ce 



— 0.0486 



4- 0 1812 





— 0.1165 



— 0.0649 



— 0.1929 



— 0.9034 







— 0 2421 



4- 2.1330 



— 1.102 



4- 0 2218 



c 7 



— 0.0486 



— 0.1812 





4- 0.1165 



— 0.0649 



— 0.1929 



— 0.9034 







4- 0.2421 



4- 0.3315 



4- 0.018 



4- 0.1258 



c g 



— 0.2652 



— 0.2652 





4- 0.0884 



— 0.4842 



4- 0.0884 



— 0.4842 







4 - 0.4842 



4- 0.8020 



— 1.207 



4- 0.2004 



c 9 



— 0.1812 



— 0.0486 





— 0.1929 



— 0.9034 



4- 0.1165 



— 0.0649 







4- 0.2421 



4- 0.7370 



— 0.104 



4- 0.0100 





4- 0.1812 



— 0.0486 





— 0.1929 



— 0 9034 



— 0.1165 



— 0.0649 







— 0.2421 



4- 0.5400 



- 0.154 



4- 0.0101 





4- 0.2652 



— 0.2652 





4- 0.0884 



— 0.4842 



— 0.0884 



— 0.4842 







— 0.4842 



4- 0 4020 



— 0.533 



4- 0.0920 



c 12 



+ 0.0486 



— 0.1812 





+ 0.1165 



— 0.0649 



+ 0.1929 



— 0.9034 







— 0.2421 



— 0.4445 



— 0.149 



4- 0.0875 



