the Distances between the Planets and Sun. 463 



cumstance that, to obtain an approximation to the observed 

 distance of any planet comprised in the outer group, we must 

 employ the theoretical distances of the three planets last prece- 

 ding ; while to obtain a similar approximation in the inner group, 

 we require the theoretical distances of the two last preceding 

 planets only. 



It would seem, then, that the law regulating the distances 

 between the planets in the two groups changes in passing from 

 the one group to the other; so that, to discover its nature, it 

 would appear desirable to take the asteroids as the starting-point, 

 and examine the relations of distance between the inner and outer 

 planets separately. Thus we obtain the following results. 

 Beginning at Mercury, we have for the comparative distances 

 of the inner group of planets from that planet these numbers : 

 Venus, 3-36; Earth, 5*13; Mars, 11-37; Juno,22'83. Again, 

 beginning at Juno, we have for the comparative distances of the 

 outer group of planets from that planet — Jupiter, 25*33 ; Saturn, 

 68-69; Uranus, 165-12; Neptune, 273-67. 



At first sight these numbers are not promising. Except that 

 the distance between Juno and Jupiter is not far different from 

 the total distance between Juno and Mercury, there appears 

 nothing like a law of progression in either series. However, we 

 must consider that if the distances between the planets are 

 governed by any law of symmetry, it is highly improbable that 

 this law should be directly observable. If, as many concurrent 

 arguments indicate, the solar system has arisen out of the gra- 

 dual consolidation of a mass of material formerly diffused over 

 the whole area now occupied by the orbits of the planets, what- 

 ever symmetry exists between their respective distances must 

 belong to the distribution of the original centres of aggregation 

 whereby the planets have been produced, and concern the primi- 

 tive, not the present position of these bodies. So that a theory 

 which exhibits this symmetry must be one which can account 

 for the present places of the planets by means of the probable 

 changes in their original arrangement due to the consolidation 

 of the constitutive mass. Now these changes may be expected 

 to occur in the following order : — 



1. Since the consolidation depends upon the attraction exer- 

 cised by the central mass upon its outer portions, the first act 

 must be to draw these parts nearer to the centre. 



2. The differences of pressure produced by the effort of the 

 outer particles to approach the centre would give rise to a rota- 

 tion of the whole mass, and thus throw its equatorial portion 

 further from the centre. 



3. When the consolidation became considerable, a great 

 amount of heat would be developed from the collisions of the 



