42 STATEMENT AND EXPOSITION OF 



for some distance within ; so that the planets of greatest mass would not be the 

 outermost, but the masses of the successive planets will be greater and greater, so 

 long as the density increases in a gi'eater ratio than that in which the volume 

 diminishes; aided, withal, by the whole-planet arrangement, which supervenes in 

 the Saturn and Jupiter arrangement, and, in the instance of Saturn, (42), by the 

 half-planet acquired. 



And this arrangement of the masses we actually find, with some variation in 

 the instance of Uranus/ 



(68) Closely analogous to this arrangement of the masses in the great planetary 

 system is that which we find in the System of Saturn ; viz. Japetus outside, for 

 one of the larger satellites, followed by Titan, the Jupiter of the system, with 

 smaller satellites after it (Hyperion he/ore it, in the place analogous to that of 

 Uranus), and other satellites, larger than Hyperion, farther inward. 



(59) Then too, in the System of Ju])iter, the relative masses of the satellites 



are — 



Satellite IV 42659 



" ni 88497 



"11 23235 



1 17328 



so that the mass of Satellite IV. approaches to being more than double that of 

 either Satellite II. or Satellite I. ; while the mass of Satellite III. is more than the 

 double of tJiat again; the great masses outside of the others; and yet, as in the 

 other systems, the greatest of all not the outermost. 



Arrangements of the Asteroid-mass. 



(60) The neutral points for the Asteroid-mass, towards Jupiter on the one side 

 and Mars on the other, have, (49), been already stated. But when we come to 

 apply the formula for the ring-like mass; viz. that which has, (55), been especially 

 in question, we do not succeed. We thus have a negative indication that the 

 Asteroid-mass, as a whole, did not have a ring-like form. 



But if we suppose a lialf-planet arrangement of the mass, we shall have 



Distance of exterior half-planet . . . . . 3.34083 



« " interior " 2.47748 



And then the sum of their squares . . . . 17.29905 + 



1 sum 8.64953- 



Square of mean distance (A), in Table (B) in (14), . 8.28067; 



again approximating to the requirements of the formula. 

 The neutral point, or point of equal attraction, between Jupiter and 

 the exterior half-planet will be ....... 3.35790 



That between the two half-planets, ... ... 2.94068 



Between the interior half-planet and Jfors, ..... 2.14438 



' May be in a measure accounted for and explained by the special influences to which, (43), that 

 planet appears to have been subjected. 



