228 The American Geologist. October, i904. 
genesis and formation of that same hill is a philosophical and 
geological problem which cannot be solved by computation. 
Consequently, when we are told that a philosophical problem 
has been mathematically solved, as for instance, when G. H. 
Darwin "proves" bv mathematics that the moon almost touched 
the earth's surface some 50 or 100 million years ago, and that 
it revolved around the earth in about four days, then we must 
remember, that such speculation is simply an illusion. To 
give a rational solution of such a problem lies wholly outside 
the province of mathematics as we shall show more clearly 
in §13, when we come to speak of the true origin of the plan- 
ets. 
Next to and in connection with a clear understanding and 
a correct conception of the starting point, all sound inductive 
reasoning recjuires an equally thorough knowledge of all com- 
plications and conditions that may arise later in the course 
of reasoning; for logic, we must remember, can serve only as 
an aid or means, like a horse or a ship, which goes wherever 
we guide it. A navigator, for example, who sails from New 
York, bound for Liverpool, but lands in Porto Rico, gains 
little by claiming that Porto Rico or any part thereof is Liver- 
pool, because the ship brought him there. Thus it is also with 
the mathematician and the philosopher. The result gained is 
not a sufificient g-uarantee for the correctness of their reason- 
ing; because where due attention is not paid to nature and 
those of its laws that bear upon the problem, the result might 
so easily be "Porto Rico" instead of "Liverpool." 
Now, therefore, it is clear that one, who attempts to ex- 
plain the origin of the solar system by means of the nebular 
theory, must necessarily, in the first place, have a correct con- 
ception of the principal forces involved in his theory as a con- 
dition for a correct understanding of the genes'is or origin of 
the heavenly bodies, this to serve as a starting point on the 
basis of which he afterwards, by the aid of logic, tries to ex- 
plain the nature and inner relations of the whole svstem. 
Let us, then, remember this as we now proceed to the dis- 
cussion of the nebular theory; and let us remember also, that 
it is our duty to satisfy all reasonable demands which the prin- 
. ciples we have laid down, make upon us as we proceed, step 
by step. 
