﻿348 Prof. P. Lowell on the Asteroids. 



If A is plus 



- cos (6>- 7 ) = 2 sin 2 i (<9- 7 )-l, 

 if minus 



cos (0-7) = 2cos 2 i(0-y)-l. 



14. Following are the tables for the gap n = 3u r . 

 Table III. 



1 













dw 





















dt 



















de 















e. 



-&— TST . 



Ml — 111. 



0. 



dt 



secular. 



periodic. 



Va. 



\/Acosi(0-y). 





650 



117° 13' 



18° 54' 



21-1 



10° 46' 















474 



316 55 



292 56 



19 3 



8 27 









8"-2 







556 



224 45 



88 11 



184 



5 47 















248 



311 5 



234 59 



165 



3 41 















17 



136 27 



250 15 



16 2 



7 40 









9 5 







.335 



162 47 



275 57 



15-3 



10 22 





•23* 



— '75* 



10 -5 







329 



266 12 



204 14 



14-7 



1 36 















495 



208 44 



13 40 



127 



8 28 







-•32 



4 -1 







132 



85 48 



139 48 



63 



19 21 



-•10 





-•08 



20 -6 



15"'8 



L 



1/3 



Period 



of 



Jupiter. 

















* Only important terms included. 



Table IV. 













d-w 





1/3 



e. 



Period 



_ , 



n x — In. 



<p. 



dt 



Va. 



periodic. 



of 



Jupiter. 









619 



148° 2" 



349° 36' 



108 



4° 18' 



+ "-41* 



4"-2 



518 



314 20 



309 40 



11-6 



12 42 



4- -51 



5 -5 



46 



143 32 



341 34 



12-9 



9 38 





4 -7 



292 



305 15 



317 54 



16-7 



1 41 







421 



6 48 



21 13 



18-4 



17 1 





10 '6 



660 



287 54 



251 10 



194 



5 53 



- -15 



7 -9 



355 



182 46 





20-1 



6 13 







472 



273 28 





21-7 



5 38 







89 















* Only the important terms in this column considered. 



From the table we see that but one asteroid (132) fulfils the 

 criterion for libration. It will also be noticed that it falls 

 on the sunward side of the gap, as is also the case with the 



