To determine masses for the satellites of the two outer planets, we have to be more empirical even than we have yet been. A little trouble will show that the whole mass of all the satellites and rings of Saturn put together is about 1/7820th of the mass of the planet, and we shall avail ourselves of this proportion to assign masses for the satellites of the remaining planets, the numbers and names of which are the only data we have been able to find. Considering then, that Uranus has only four satellites and no rings, we think if we give them 1/15,000th of the mass of their primary, it will be a very fair allowance; and with the same empiricism we have adopted for the solitary satellite of Neptune 1/40,000th of the mass of its primary.
However rude and crude these approximations may be, we have the satisfaction of thinking that the masses obtained by their means, can have no appreciable effect upon the operations into which they are to be introduced, whilst they enable us to deal with a complete system or machine. But for these we have another Table No. II. to present, a _résumé_ of the foregoing one, for greater facility of reference.
TABLE II.--VOLUMES OF THE VARIOUS MEMBERS OF THE SOLAR SYSTEM AT THE DENSITY OF WATER. ---------+------------+-------------------+-----------------------+ | | Volume in | Total Volume in | Name. |Designation.| Cubic Miles at | Cubic Miles at | | | Density of Water. | Density of Water. | ---------+------------+-------------------+-----------------------+ Sun | | |482,169,000,000,000,000| | | |-----------------------| Mercury | Planet | | 92,735,000,000| Venus | " | | 1,131,960,000,000| Earth | " | 1,471,169,000,000| | Moon | Satellite | 18,141,236,000| 1,489,310,236,000| | |-------------------| | Mars | Planet | | 160,728,460,000| ---- | Asteroids |One fourth of Earth| 367,792,000,000| Jupiter | Planet |479,292,741,000,000| | " |4 Satellites| 76,180,317,000| 479,368,921,317,000| | |-------------------| | Saturn | Planet |154,351,000,000,000| | " |8 Satellites| 19,539,774,315| | " | 3 Rings | 195,000,000| 154,370,734,774,315| | |-------------------| | Uranus | Planet | 25,874,664,000,000| | " |4 Satellites| 1,724,977,600| 25,876,388,977,600| | |-------------------| | Neptune | Planet | 29,107,237,000,000| | " |1 Satellite | 727,680,925| 29,107,964,680,925| ---------+------------+-------------------+-----------------------+ Total of Planets, Satellites and Rings | 691,966,535,445,840| ------------------------------------------+-----------------------+ Dividing 482,169,000,000,000,000 by 691,966,535,445,840 makes the mass ofthe whole of the members to be 1/696·86th part of the mass of the sun, instead of 1/700th as generally stated by astronomers.