THE ORIGIN OF THE EARTH. 75 



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 concord- 

 ance with the varying rotations actually presented by the several 

 planets. 



It is still further obvious, on inspection, that the greatest differences 

 of velocity, and hence the greatest rotatory effects, must occur in the 

 extreme or limiting cases of collision that occur at the perihelion and 

 aphelion points of the nucleus' orbit ; for, where the orbits have more 

 nearly the same dimensions and the crossings are at points intermediate 

 between these extremes, the differences of velocity are less and the 

 rotatory effects less, whatever their phases. 



The average or residual effects of collisions in the limiting cases 

 may be gathered from the case represented at the left in Fig. 30, in 

 which planet esimals in small orbits are overtaken by the nucleus near 

 its perihelion point, and from the case at the right in which the plan- 

 etesimals in the large orbit overtake the nucleus near its aphelion point. 

 By inspecting the figure, it will be seen that the areas which represent 

 the possibilities of overtake favorable to forward rotation exceed those 

 favorable to backward rotation. This holds true on the assumption 

 of an equable distribution of planetesimals, which may fairly be assumed 

 as the 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 axis 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. 



The order in which the contingencies of collision come into play — 

 There is a supplementary factor arising from the order in which the 

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

 equal contingencies of collision with the planetary nucleus, of opposite 

 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 reference to Fig. 31 it will be seen 



