FUNDAMENTAL PROBLEMS OF GEOLOGY. 229 



opposite classes of effects and to estimate the residual influence of all 

 probable collisions. It will be seen at once that this residual influ- 

 ence must be far less in magnitude than the sum of the forces of all 

 impacts, for the opposing classes neutralize one another, and hence 

 the resulting rotation is likely to be relatively low, though the total 

 force of impact be great. It is further evident that the result might 

 have varied considerably in the different planets, and this is in con- 

 cordance with the varying rotations actually presented by the several 

 planets. 



It is still further ob\'ious, on in.spection, that the greatest differ- 

 ences of velocity, and hence the greatest rotatory eflfects, must occur 

 in the extreme or limiting cases of collision that occur at the perihe- 

 lion and aphelion points of the nucleus' orbit ; for, where the orbits 

 have more nearly the same dimeu.sions and the crossings are at points 

 intermediate between these extremes, the differences of velocity are 

 less and the rotatory effects less, whatever their phases. 



By graphical inspection of all probable cases, it may be seen that 

 the possibilities of overtake favorable to forward rotation exceed 

 those favorable to retrograde rotation. This holds true on the as- 

 sumption of an equable distribution of planetesimals, w^hich maj- 

 fairl}' be assumed as an average fact, but not necessarily as always 

 the fact ; and hence the conclusion is not rigorous, and a backward 

 rotation is not impossible. From the nature of the case, a varying 

 rotation for the several planets is more probable than a nearly 

 uniform one. 



It is also obvious that the impacts on the right and left sides of a 

 growing nucleus, as well as those on the outer and inner sides, might 

 be unequal, and hence obliquity of rotation of varying kinds and 

 degrees might arise. As the solar system presents these variations, 

 the method of accretion here postulated seems to lend itself happily 

 to the requirements of the case. 



There is a supplementary factor arising from the order in zvhich 

 the contingency of collision arises. If a planetesimal is subject to two 

 equal contingencies of collision with the planetary nucleus of oppo- 

 site effect, it is obvious that the one which it first encounters has a 

 better chance of realization than the other ; for if the first is realized 

 the second loses its chance. Now, by inspection it ma}' be seen that, 

 in the shifting of the inner orbits, it will be possible for the plan- 

 etesimals to collide with the inner side of a nucleus earlier than with 

 the outer side, and hence forward rotation is favored. So, also, by 

 an examination of the orbits of the outer planetesimals a similar fact 



