82 Prof. Encke on the Construction of the 



agreeably to which the numbers expressing the intensity of 

 their light have been calculated for the positions of these 

 planets in this year. The unity of these numbers is the light 

 which each of these planets would have, at the time of an 

 opposition at which both the planet and the earth would be 

 at their respective mean distances from the sun ; or, if we call 

 the semiaxis major of the orbit a, and denote by r and A the 

 distances of the planet from the sun and earth at any opposi- 

 tion, the intensity of the light of the planet at that moment 



o*(a !)' 

 = ~T~ 



The numbers hence resulting for these planets are ; for 

 10-43 19-88 



Vesta, 



Juno, 



Pallas, 



24-31 



Ceres 



23-90 



r* A* 



where the present elements are used. The intensities of light 

 hence resulting, at the different oppositions, are as follows : 



This manner of estimating the light of a planet seems to be 

 more convenient, because the small planets are principally ob- 

 served during their oppositions, and the numbers show at 

 once whether they are nearer or more distant. Prof. Bessel 

 has been very attentive to the appearance of Ceres and Pallas 

 at the times of their opposition in 1830. Ceres had the 7th 

 or 8th, Pallas the 8th or 9th magnitude ; consequently, when 

 their light is = 1, neither of them will much differ from the 

 8th magnitude ; and the comparison of the light of Pallas at 

 the opposition of 1831, when it will be only one-third of the 

 former, will afford a measure of the actual decrease of the light, 

 as compared with the numbers by which the intensity of light 

 is expressed. 



M. Wolfers has for this year also executed a great part 

 of the calculations, namely, the ephemeris of the sun, four 

 months of the moon's geocentric positions, the calculations for 

 Jupiter's satellites, and the superior older planets. To M. 

 Herter I am again indebted for the positions of the moon 

 during four months. M. Lauritz-Ravn undertook Mercury 



and 



