EEMAEKS ON THE SMALL PLANETS. 213 



proximations are computed at one hundred and eight; sometimes two 

 orbits continue very near one another through a great part of their 

 circuit; thus, for a space of 192 degrees, the orbits of Euterpe and Mas- 

 salia are never separated more than a tenth part of the half of the 

 greater axis of the earth's orbit. The approximations being once indi- 

 cated by the graphic method, we can determine them more exactly 

 b}' means of calculation, and it is eas}" afterwards to investigate the 

 period at which two planets must pass at the same time by the nearest 

 points of their respective orbits. M. Littrow has thus found that the 

 42 planets he has studied would, in the decennial period, 1858 to 

 1867, undergo eighteen ])hysical conjunctions^ to which he has invited 

 the attention of astronomers. It is readily conceived that the num- 

 ber of these conjunctions increases by a law much more rapid than 

 the number of new planets in such sort that, if we should recommence 

 the calculation for the TO planets now known, we should doubtless 

 find many other approximations of the same kind; but this Avould 

 require long and tedious application, without leading to definitive re- 

 sults as long as there shall remain asteroids to be discovered. There 

 are cases, however, where the investigation of physical conjunctions 

 only requires a graphic construction extremely simple; such is the 

 case where the two orbits to be considered have very nearly the 

 same line of nodes and the same inclination to the ecliptic. We may 

 particularly specify the orbits of Fides and Maia; their elements 

 present less difference than often exists between the elements of one 

 and the same planet, as given by different calculators. This is shown 

 by a comparison of the two following tables : 



Fides. Maia. 



Longitude of the ascending node 8° 12' 8" 12' 



Inclination 3° 7' 3° 5' 



Semi-great axis 2,642 2,654 



Eccen'tricity 0, 174 0, 155 



Longitude of perihelion • 65'-^ 7' 43° 54' 



If we disregard the mutual inclination of the two orbits, which is 

 but of two minutes, we may trace these two orbits on the same plane, 

 and we thus find two points of intersection, one of which almost 

 coincides with the perihelion of Maia. The distance between the 

 two curves rises at no point beyond the twentieth part of the radius 

 of the terrestrial orbit. At the present time the mean longitudes of 

 the two planets differ about forty degrees, but this difference con- 

 stantly diminishes, though slowly. When it shall have disappeared, 

 the two planets, notwithstanding their inconsiderable mass, and by 

 reason of their continual nearness, Avill exert upon one another an 

 action, perhaps, sufficiently strong to unite them in one single body, 

 or cause them to revolve, as the components of a double star,, around 

 their common centre of gravity. 



