Ago PHILOSOPHICAL TRANSACTIONS. [anNO 1788. 



fore be expected that these periods will come very near the truth; and indeed Dr. 

 H. for many months after used to calculate the places of the satellites by them, 

 and always found them in the situations where these computations gave reason to 

 expect to see them. The epochae, from which astronomers may calculate the 

 positions of these satellites, are Oct. I9, 1787; for the first 19^ 11'" 28"; and 

 for the 2d 17^ 22*" 40\ They were at those times 76° 43' north following the 

 planet; which is the place of the greatest elongation of the 2d satellite; where 

 consequently its real angular situation is the same as the apparent one. 



The next thing to be determined in the elements of these satellites, is their 

 distance from the planet; and as we know that, when the periodical times are 

 given, it is sufficient to have the distance of one satellite, in order to find that 

 of any other, he confined his attention to the discovery of the distance of the 

 2d. As soon as he attempted measures, it appeared that the orbit of this satel- 

 lite was seemingly elliptical; it became therefore necessary, in order to ascertain 

 its greatest elongation, to repeat these measures in all convenient situations; the 

 result of which was, that on the 18th of March, at 8^ 2"^ 50% he found the 

 satellite at the distance of 46". 46; this being the largest of all the measures he 

 had an opportunity of taking. Hence by computation it appears, that the satel- 

 lite's greatest visible elongation from its planet, at the mean distance of the 

 Georgium Sidus from the earth, will be 44'''.23. Admitting therefore at present, 

 that the satellite moves in a circular orbit about its planet, we cannot be much 

 out in taking the calculated quantity of 44'''.23 for the true measure of its distance. 

 And, having ascertained this point, we calculate, by the law of Kepler, and the 

 assigned period of the first satellite, that its distance from the planet must be 

 33^09. 



As we are now on the subject of such parts of the theory of planets as may 

 be determined by calculation, it will not be amiss to see how the quantity of 

 matter and density of our new planet will stand, when compared with the tables 

 that have been given of the same in the other planets; and in order to this, let 

 us admit the following data as a foundation for our computation, viz. The 

 parallax of the sun 8". 63. The parallax of the moon 57' 1 1''. 



Its sidereal revolution round the earth 27*^ 7^ 43"" 1 V.6. 



The mean distance of the Georgian planet from the sun 19.O8I8. 



The mean distance of its 2d satellite from the planet 44^^23. 



The periodical time of this satellite 13'^ 11^ 5"^ P.5. 



Hence we find that a spectator, removed to the mean distance of the Georgian 

 planet from the earth, would see the radius of the moon's orbit under an angle 

 of 27'^1866; and if 1, </, t, represent the quantity of matter in the earth, the 

 distance of the moon, and its periodical time; also m, d, t, be made to stand 

 for the same things in our new planet and its 2d satellite, we obtain, by known 



