Reseai-ches on the Distri'mtion of the Meau IVIotions of the Astevoiils. 



41 



7t, 







4j9.; 



s' 





 3s'- 



Numerical values of these limits for different cases of the second 

 order become as follows : — 



sis' i),xiœ -^xiœ ^/),xlO-^ (^^,^,^,^'xlO 



3/1 0-0275 -0-1 10 0-330 0-766 



5/3 0-222 -0-296 0-888 0-725 



48. The equation corresponding to (8) becomes 

 ^'^■=^^re' + (^a + s'ß){e'-e^)y 



dt 



8(V^-4îo,cos<?') I ^ '^ / f 



8(,s'a;— 4^2COS d') 



Putting ^'=;r and applying this equation to the case of the revolu- 

 tions very near to the contact, it may be seen that x increases in 

 the revolution of Type 2 and that it also increases in the revolu- 

 tion of Type 1 if 



^ « r^2 a J3s"^' 



Since the libration of Type 1 is impossible in the case of the second 

 order, the revolution of Type 1, if it does not change to the 

 revolution of Type 2, will remain unchanged. 



49. The equation corresponding to (10) becomes in this case 



8 -9 dll f —> / 9 — .\ tf , S,5\ ,- 9 -2\2 



-^P-i^'-jr = — s'ae-e{e- — e-) — s'ia + .^ je{e' — ey 



