130 On the Elements of the Solar System. 



duties assigned to them, are the best warrant for the accuracy of 

 their conclusions, which the case admits. 



The semi-diameter of the sun, at the earth's mean distance, being 

 settled at 16' 0'.9, as determined by Beesel, from nearly 1700 tran- 

 sits, and its equatorial horizontal parallax at 8".5776, as deduced by 

 Professor Encke, the volume of the sun, compared with that of the 

 earth, and the distances of all the planets from the sun, with their 

 corresponding rates of motion, must be somewhat greater than th-ey 

 are usually represented. The diameters of the planets, at the mean 

 distance of the earth from the sun, being assumed as in our table, 

 it follows that their mass-values and volumes will be relatively af- 

 fected in the proportion of their differences. The volume of Mer- 

 cury, for example, will be comparatively less, while that of Saturn is 

 considerably greater, than they were wont to be considered. 



Taking the expression of these elements, as adopted by a tribunal 

 the most competent of the age, to which the subject could be refer- 

 red, I have made them the basis of the following computations. The 

 unit of lineal measure employed in these calculations, of course is 

 the equatorial diameter of the earth, estimated at 7924 English miles, 

 according to Baily and Laplace. 



The earth's mean distance from the sun in miles, then, will be 

 8". 5776 : 206264'\S:: »y« ! 95,273,868.S67748554. Having 

 found this element, I proceeded next to construct logarithms to a 

 great number of places, corresponding to the sidereal revolutions of 

 the planets, and by means of these, determined their respective dis- 

 tances, retaining as many figures in the result, as seemed at all desi- 

 rable. These results were verified in every instance, by independent 

 modes of calculation, and the process by each was repeated, until 

 the terminal figures of the decimals corresponded. 



Logarithms to twelve places are appended for the convenience of 

 testing the accuracy of the results, and to save the labor of construc- 

 tion when they may be wanted for other purposes. 



N. B. — The diameters of the Asteroids not being given in the 

 Report above mentioned, were derived from Biot's Traite Elemen- 

 taire (PJlstronomie Physique. 



New Britain, (Berlin,) Con., January, 1834. 



