420 



MEMOIRS OF THE AMERICAN ACADEMY. 



Hygea 

 Themia 



Kuphrosyne 

 Doris 



Pales 



Enropa 



Mnemosyne 



Erato 



Cybele 



F r ( • i a 



Semele 



Sylvia 



Antiope 



634.3118 



636.7634 



633.8508 



647.1295 



655.6209 



650.0877 



632.6897 



640.8591 



560.8775 



569.0505 



652.9848 

 543.5800 



632.3591 



log a 



0.4984692 

 0.4973523 

 0.4988680 



0.4926769 

 0.4889025 

 0.4913564 

 0.4992106 

 0.4954901 



0.5340920 

 0.5299038 

 0.4900690 

 0.5431620 

 0.4993618 



O I It 



5 44 56.4 



6 42 52.9 



12 44 10.3 



4 23 42.9 



13 43 18.3 



5 49 14.3 



5 58 17.1 

 9 46 4.3 



6 54 36.4 



10 49 12.0 



11 49 36.5 

 4 39 22.6 



11 39 2.7 



IT 



I) 



234 58 40.6 



139 56 11.2 



93 27 51.5 



74 10 11.3 



32 3 13.1 

 101 45 37.6 



52 58 47.8 



33 55 38.0 



258 11 24.3 

 93 2 36.6 



28 25 39.1 

 337 8 6.1 

 293 49 3.5 



The expression of the inequalities, and the length of their periods which result 



from the substit 



f th 



values of the elements in the formulae 



14676.2 sin [Z — 2 U + 228 58 1.4] 

 14606.2 sin [Z — 2 Z' + 146 4 4.5] 



Hygea 

 Themis 



Euphrosyne 28996.5 sin [Z — 2 I! + 97 58 58.4] 



5086.7 sin [Z — 2 Z' + 85 41 49.4] 



Doris 

 Pales 

 Europa 



Erato 



Cybele 



Freia 



Semele 



Antiope 



11639.2 sin [X — 2 Z' + 33 36 12.6] 

 6584.4 sin [Z-2i'+ 111 29 19.2] 



9 1.9] 



Mnemosyne 12956.0 sin [Z — 2 Z' + 60 



13654.9 sin [Z — 2 Z' + 36 21 16.9] 



13145.4 sin [Z — 2 Z' + 251 13 31.6] 



32243.5 sin [Z — 2 L' + 98 15 25.5] 



10860.7 sin [Z — 2 Z' + 29 55 45.1] 



28567.8 sin [Z — 2 Z' + 288 44 31.6] 



97.96 years 

 91.72 « 



99.23 



« 



72.27- " 



61.57 « 



68.14 « 



102.58 " 



82.91 « 



94.49 



120.93 

 64.54 



103.57 



i. 



a 



« 



u 



These expressions 



can be regarded as 



values of 

 respect tc 



rough approximations only to the actual 



the 



qualities, since all terms of the third and higher orde 



th 



and 



and of 



with respect to the disturbing masses, have been neglected 



second and higher orders 

 Yet they are sufficiently 



show the order of magnitude of the Jupiter perturbations of the asteroids 



*. 



in question. 



The effect of these ine 

 the proportion roughly of 

 tion of the mass of Jupiter will depend on the observation of 



qualities at the time of opposition will be magnified in 



to a 



1 



Thus 



the case of Freia, the determina 



an arc of 12°. 7. 



