2 STATEMENT AND EXPOSITION OF 



When VI and wi' are mere particles of matter Eqs. (1) are both reduced to 



It may be convenient to regard, once for all, a, m, and T, in so far as they appear, 

 as being special for the earth, while a', m', and 2" respectively represent like quan- 

 tities in the instance of any other planet. 



Now T and Shaving both been well ascertained, and being themselves constant, 



the same is true of their ratio, which involves also the constant value of (--) ; and 

 hence it follows that, to preserve Eq. (1)', we must have the value of (")" also con- 

 stant, and this, although the accepted value of a, the earth's mean distance from 

 the sun, which is the unit of measurement, may itself require correction in com- 

 parison with other standards. If it then be diminished, every other mean distance 

 a', as it is represented in Eq. (1)', will be found to be diminished in the same ratio; 

 and thus, while the numbers representing them remain unchanged, " all the dis- 

 tances have to be reckoned on a new scale. "^ 



Next, as respects the modifying factor "^ "' , in the second of Eqs. (1) As 



M -\- m 



it is moreover true, that M itself varies directly as a^ ; if aJ^ be diminished, M will 

 be diminished in the same ratio, and the like will be true of m! represented, as 

 usual, in terms of M as the measuring unit ; so that all such niasses will be repre- 

 sented by the same numbers as before, but all, as in the case of the distances, 

 " reckoned on a new scale," while the mass of the earth will, in this comparison, be 

 increased, as that will vary inversely as a^. 



Now the more recent determination of the solar parallax requiring that the 

 actual value of a should be diminished, it became requisite for the accurate deter- 

 mination of the values of the mean distances of such other planets as have ascer- 

 tained and appreciable masses, that those values, as already intimated, should be 

 rediscussed. 



This has been done with the aid of logarithms computed to ten decimal places 

 of figures ; and the results, to the seventh decimal place inclusive, are exhibited 

 in Table (A), in which withal, in their appropriate column, are also the values of 

 the masses made use of, with indications of the authorities to which they are 

 referable. 



The densities which besides are exhibited in Table (A), will be found to vary 

 more or less from those hitherto ordinarily accepted. This is due to the increase 

 in the relative mass of the earth, and also to the more accurate determination of 

 the masses of the planets. 



The arrangement of the series of planets begins with the most distant, as that 

 will be found to be the more convenient for the application of these data to the special 

 purposes of the whole investigation. 



' Sir J. Herschel's Outlines of Astronomy, lllh edition (357 c.) 



