REMARKS ON THE SMALL PLANETS. 215 



asteroids discovered withiu fifteen years. For instance, M. Gold- 

 sclimidt observed that on the 26th January, 1S58, Pales was invisible 

 through a telescope which showed stars of the twelfth magnitude, 

 while on the 2d of February following, this same planet equalled in 

 brightness neighboring stars of the eleventh magnitude. 



We have just seen that the attempts of Schroeter, Herschel, La- 

 ment, and Maedler to arrive at a direct measurement of the diameters 

 of Pallas, Ceres, or Vesta, have yielded results but little accordant. 

 With regard to the other asteroids such measurements have not 

 been even attempted; but the approximative value of the real dimen- 

 sions of each of them has been obtained from indirect considerations. 

 In fact, the magnitude under which a star shining by a reflected light 

 is to be classed, depends evidently on the distance of that sto,r from tlie. 

 sun, on its distance from the earth, on its real diameter, and on the re- 

 Jlective poiver (albedo) of its surface. . Four of these quantities being 

 "given, wx can iind the fifth. For the ancient planets, the albedo alone 

 is unknown; for the magnitude of each of them is easily expressed in 

 numbers by taking for bases the photometric measurements of MM. 

 Steinheil and Seidel. We thus find that the albedo is nearly the same in 

 Saturn, Jupiter,Yenus, and Mercury; a little inferior in Mars, on account 

 of the red color of that star. As the asteroids, moreover, have in gene- 

 ral the white tint of the four first planets, we see that it is allowable to 

 suppose, also, that they have the same reflective poWter. Hence the 

 real diameter of these small bodies will alone remain unknown. 



This being granted, it results, from the investigations of M. Seidel, 

 that the magnitude of a star increases by one unit when its distance 

 from the earth increases in the ratio of I to 1.6. From this M. Arge- 

 lander has deduced a very simple formula. 



Let: 



6=1.6; 



a, the semi-axis major of the orbit of a planet; 



r, the mean distance of that planet from the sun; 



A, the mean distance of that planet from the earth; 



M. the magnitude of the star for r = a and A = a — 1; 



TO, the magnitude of the star for r ■=. r^, and A = AoJ 



d, the real diameter expressed in leagues of 4 kilometers. 



We shall have : 



log. dz=i 2,7913 — m log. 6+ log. r„ + log. A^, 



= 2,7913— M log. b -f log. a -j- log. (a— 1.) 



