VOL. LXXVIII.] PHILOSOPHICAL TRANSACTIONS. 4Q1 



principles, m = -^. And consequently the quantity of matter in the Georgian 



planet, is to that contained in the earth, as 177406 12 to 1. 



In order to calculate the density, Dr. H. compares the mean of the 4 bright 

 measures of the planet's diameter 3^^7975 to the mean of the 2 dark ones4'^295; 

 as they are given in his paper on the diameter and magnitude of the Georgium 

 Sidus, in vol. 73 of the Philos. Trans. Whence we obtain another mean dia- 

 meter 4'''.04 625; which is probably the most accurate of any yet ascertained. 

 Let us now suppose this measure to belong to the situations of the earth and of 

 the new planet as they were at 10 o'clock, Oct. 25, 1782; which is about the 

 middle of the several times when those measures from which this is deduced were 

 taken. Then by the tables we compute the distance of the two planets from the 

 sun and the angle of commutation ; whence, by trigonometry, we find the dis- 

 tance of our new planet from the earth for the supposed 25th of October; and 

 thence deduce its mean diameter, which is 3''.90554. This, when brought to 

 what it would appear if it were seen from the sun at the earth's mean distance, 

 gives l' 14''''.5246; which, compared with 17^26, the earth's mean diameter, is 

 as 4.31769 to 1. The Georgium Sidus therefore, in bulk, is80.49256 times as 

 large as the earth ; and consequently its density less than that of the latter in the 

 ratio of .220401 to 1 . Also the force of gravity, on this planet's surface, is such 

 as will cause a heavy body to fall through 1 5-f- feet in one second of time. 



It remains now only, in order to complete our general idea of the Georgian 

 planet, to investigate the situation of the orbits of its satellites. It has before 

 been remarked, that when Dr. H. came to examine the distance of the 2d, he 

 perceived immediately that its orbit appeared considerably elliptical. This induced 

 him to attempt as many measures as possible, that he might be enabled to come 

 at the proportion of the axes of the apparent ellipsis; and thence argue its situa- 

 tion. But here he met with difficulties that were indeed almost insurmountable. 

 The uncommon faintness of the satellites; the smallness of the angles to be 

 xneasured with micrometers which required light enough to see the wires; the 

 unwieldy size of the instrument, which, though very manageable, still demanded 

 assistant hands for its movements, and consequently took away a great share of 

 his own directing power, a thing so necessary in delicate observations; the high 

 magnifiers he was obliged to use, by way of rendering the spaces and angles to 

 be measured more conspicuous; in short, every circumstance seemed to conspire 

 to make the case a desperate one. Add to this, that no measure could possibly 

 succeed which had not the most beautiful sky in its favour; and we may easily 

 judge how scarce the opportunities of taking such measures must be in the vari- 

 able climate of this island. As far then as a small number of select measures 

 will permit, which, out of about 21 that were taken, amounts only to 5, he 

 enters on the subject of the position of the 2d satellite's orbit. 



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