ASTEROID SUPPLEMENT. 



Adopting the following values of n, the corresponding values of a are found to 

 be for 



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Ceres, 



Pallas, 



Juno, 



Vesta, 



Astrrea, 



n = 281110.5 

 n = 281174.6 

 ii = 297282.4 

 n = 357318.7 

 n = 313428.6 



log a ■. 

 log a : 

 log a -■■ 

 log a : 

 log a : 



= 0.4424798 

 = 0.4424138 

 = 0.4262850 

 = 0.3730274 

 = 0.4109720 



a = 2.770000 

 a = 2.769579 

 a = 2.668609 

 a = 2.360627 

 a = 2.576155 



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Hebe, 

 Iris, 



Floi-a, 

 Metis, 

 Hygeia, 



n = 342978.4 

 ii = 351620.0 

 n = 396782.4 

 n = 351546.5 

 ii = 231877.3 



log a ■ 

 log a 

 log a 

 log a 

 log a 



= 0.3848866 

 = 0.3776818 

 = 0.3426962 

 = 0.3777426 

 = 0.4982256 



a = 2.425977 

 a = 2.386063 

 a = 2.201386 

 a = 2.386397 

 a = 3.149385 



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Parthenope, 



Clio, 



Egeria, 



Irene, 



Eunomia, 



n = 337564.7 

 n = 363291.7 

 11 = 313296.1 

 n = 311778.8 

 n = 301543.6 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.3894930 

 = 0.3682274 

 = 0.4110944 

 = 0.4125000 

 == 0.4221644 



a = 2.451845 

 a = 2.334680 

 a = 2.576881 

 a = 2.585235 

 a = 2.643409 



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Psyche, 



Thetis, 



Melpomene, 



Fortuna, 



Massalia, 



n = 259387.5 

 n = 333324.5 

 ii = 372571.0 

 n = 346696.3 

 n = 346935.0 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.4657652 

 = 0.3931530 

 = 0.3609250 

 = 0.3817650 

 = 0.3815646 



a = 2.922572 

 a = 2 472595 

 a = 2.295752 

 a = 2.408602 

 a = 2.407490 



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Lutetia, 



Calliope, 



Thalia, 



Themis, 



Phoccea, 



ii = 341251.3 

 n = 260561.4 

 ii = 304601.2 

 n = 230157.6 

 n = 348415.7 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.3863482 

 = 0.4644578 

 = 0.4192406 

 = 0.5003810 

 = 0.3803328 



a = 2.434155 

 a = 2.913788 

 a = 2.625672 

 a = 3.165053 

 a = 2.400672 



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Proserpine, 



Euterpe, 



Bellona, 



Amphitrite, 



Urania, 



n = 299449.4 

 i n = 360561.4 

 n = 279486.4 

 ii = 317485.8 

 ii = 356829.1 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.4241822 

 = 3770784 

 = 0.4441574 

 = 0.4072482 

 = 0.3734242 



a = 2.655720 

 a = 2.382750 

 a = 2.780721 

 a = 2.554160 

 a = 2.362785 



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Euphrosyne, 



Pomona, 



Polymnia, 



Circe, 



Leucothea, 



n = 227218.7 

 n = 312038 9 

 n = 353282.6 

 n = 294022 

 n = 252728.1 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.5041018 

 = 0.4122586 

 = 0.3763164 

 = 0.4294780 

 = 0.4732954 



a = 3.192286 

 a = 2.583799 

 a = 2.378573 

 a = 2.688302 

 a = 2.973688 



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i 



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Atalanta, 



Fides, 



Leda, 



Lastitia, 



Harmonia, 



n = 284199.7 

 11 = 301801.1 

 n = 285726.3 

 n = 281889.5 

 11 = 379644.5 



log a 

 log a 

 log a 

 log a 

 log a 



= 0.4393088 

 = 0.4219174 

 = 0.4377644 

 = 0.4416786 

 = 0.3554798 



a = 2.749849 

 a = 2.641906 



a = 2.740088 

 a = 2.764895 

 a = 2.267148 



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Daphne, 

 Isis, 



n = 353182.1 

 n = 340776.8 



log a 

 log a 



= 0.3763988 

 = 0.3867512 



a = 2.379024 

 a — 2.436415 



Hence, since 



i? 2 = 



a 2 



1— a 2 ' 







or, if a = sin B, 















/? 2 = 



tan 2 <5, 







we have for 













