324 ADDRESS ON PRESENTING THE GOLD MEDAL OF THE [43 



the shortest distance between the two orbits is less than x^-th part of 

 the Earth's mean distance from the Sun ; so that, as M. D' Arrest remarks, 

 the time of their actual intersection cannot be very distant from the present. 



One of the most curious circumstances connected with this group is, 

 that there are several cases in which the mean distances are nearly identical 

 with each other. Thus the mean distances of Ceres and Pallas are so 

 nearly equal that their order of magnitude is sometimes changed by per- 

 turbation. The same remark applies to Iris and Metis, and also to the 

 three planets, Astrcea, Egeria, and Irene. 



It should be noticed that this identity of mean distance would not 

 be at all explained by supposing the planets in which it occurs to have 

 been originally one. 



There are also some remarkable cases in which the mean motions are 

 nearly commensurable. Thus the mean motions of Juno and Vesta are very 

 nearly in the ratio of 5 to 6, while those of Juno and Flora are as 3 to 4, 

 and consequently those of Vesta and Flora as 9 to 10*. 



The extreme smallness of the apparent diameters of these bodies makes 

 it very difficult to determine their real diameters by direct measurement. 

 According to Sir W. Herschel's observations, the diameters of Ceres and 

 Pallas would not be far from 140 English miles, while Schroter's obser- 

 vations would make them much larger. Stampfer has attempted to determine 

 their diameter by means of their apparent brightness, supposing the reflective 

 power of their surfaces to be the same as that which obtains in the case 

 of Jupiter, Saturn, Uranus, and Neptune. This supposition is obviously 

 rather precarious, especially as the reflective power of Mars is found to 

 be much less than that of the other planets ; but Stampfer's result agrees 

 very closely with the above-mentioned determination of Sir W. Herschel. 

 Several of the more recently-discovered planets appear to be much smaller 

 than these; and it is not improbable that there are many more which, by 

 their excessive minuteness, elude our telescopes altogether. In this point of 

 view, these asteroids would seem to form a connecting link between the 

 larger planets and the aerolites, the cosmical nature of which appears to be 

 pretty well established. 



* The mean daily sidereal motion of Juiio is 814"-24; that of Vesta, 977"-20; and that 

 of Flora, 1086"-08. Also f x 814-24 = 977-08, and f x 814-24 = 1085-65. 



