REMARKS ON THE SMALL PLANETS. 207 



inequality readily explained ; for the difficulty of discoveries increas- 

 ing in proportion to remoteness from the sun, the planets known to 

 us will naturally be more thronged tog'ether the nearer they are to 

 that luminary. It is to be presumed, for the same reason, that the 

 real mean is higher than that stated ; for it is doubtful if existing 

 instruments would enable us to discover an asteroid whose perihelion 

 distance might be higher than three. 



The distances of the small planets from the earth vary between 

 widely extended limits, which may reach from one to five radii of the 

 earth's orbit. The nearest approach evidently takes place at the in- 

 stant of the star's opposition ; the distance being then about 0.8 for 

 Phocoea, Melpomene, Iris, and Flora, and rising to 1.8 for Mnemosyne 

 and 1.9 for Maximiliana. It is only at this point of time, for the 

 most part, that the discovery or even the observation of one of these 

 minute bodies becomes possible. Hence we must hasten to calcu- 

 late its elements, if Ave wish again to find it in the heavens, after an 

 absence of several months. When the calculation is founded on ob- 

 servations either imperfect or made at too short intervals, it sometimes 

 happens that the planet is lost.* Oftenest, however, succeeding 

 observations permit us to rectify the errors of a first result; thus it 

 was at first believed that Nysa would intersect the orbit of Mars, 

 while, in fact, it is always at least fifteen millions of leagues beyond 

 that planet. Nemausa promised still more. M. Valz had announced 

 Hhat it would pass at eight millions of leagues from the earth, and that 

 some day it might even approach within three millions of leagues. 

 Astronomers have been obliged to renounce this hope, and that to 

 their great regret; for the oppositions of this little orb would have 

 furnished them an excellent means of determining the distance of the 

 earth from the sun, a base so essential and yet so inaccurately known 

 for all the dimensions which we attribute to the solar system. 



TIMES OF THE SIDEREAL AND THE SYNODAL REVOLUTIONS OF THE ASTEROIDS. 



We know^ that by the third law of Kepler the sidereal revolution of 

 a planet depends on the length of half the greater axis of its orbit. 

 The number 2.645, which has been assigned, as above stated, for the 

 mean planet, corresponds to a mean heliocentric movement of 824". 8, 

 and to a sidereal revolution of 1,571 days, that is to say, of about 4^ 

 years. The shortest revolutions are those of Flora (1, 192.9 days) and 

 of Ariana (1,197.7 days ;) the longest are those of Euphrosyne (2,048 

 days) and of Maximiliana (2,343 days, or more than six years.) We 

 see that these numbers vary nearly as one to two. Of these planets 

 sometimes two and even three have the duration of their year almost 

 identical; thus between Metis (1,346.31 days) and Iris (1,346.46) 

 the difference is but o^ hours, and is but that of one day between 

 Asia (1,551 days) and Pseudo-Daphne, (1,552.) We may also remark 



■~" This occurred in the case of Daphne. In spite of assiduous and laborious research, 

 M. Goldschmidt has not been able to rediscover tliis planet ; but, while thus engaged, he 

 detected Pseudo- Daphne. This agaio having been lost in turn, he has but just suc- 

 ceeded in refinding it, (August 27, 1861.) after sounding the heavens for three montlis. 



