ou show that the
conditions of your problem are such as may actually occur in nature and
do not transgress any of the known laws of nature in working out your
proposition, then you are as safe in the conclusion you arrive at as
is the mathematician in arriving at the solution of his problem. In
science, the only way of getting rid of the complications with which a
subject of this kind is environed, is to work in this deductive method.
What will be the result, then? I will suppose that every plant requires
one square foot of ground to live upon; and the result will be that,
in the course of nine years, the plant will have occupied every single
available spot in the whole globe! I have chalked upon the blackboard
the figures by which I arrive at the result:--

Plants. Plants
1 x 50 in 1st year = 50
50 x 50 " 2nd " = 2,500
2,500 x 50 " 3rd " = 125,000
125,000 x 50 " 4th " = 6,250,000
6,250,000 x 50 " 5th " = 312,500,000
312,500,000 x 50 " 6th " = 15,625,000,000
15,625,000,000 x 50 " 7th " = 781,250,000,000
781,250,000,000 x 50 " 8th " = 39,062,500,000,000
39,062,500,000,000 x 50 " 9th " = 1,953,125,000,000,000

51,000,000 sq. miles--the dry surface of the earth x 27,878,400--the
number of sq. ft. in 1 sq. mile = sq. ft. 1,421,798,400,000,000 being
531,326,600,000,000 square feet less than would be required at the end
of the ninth year.

You will see from this that, at the end of the first year the single
plant will have produced fifty more of its kind; by the end of the
second year these will have increased to 2,500; and so on, in succeeding
years, you get beyond even trillions; and I am not at all sure that I
could tell you what the proper arithmetical denomination of the total
number really is; but, at any rate, you will understand the meaning of
all those noughts. Then you see that, at the bottom, I have taken the
51,000,000 of square miles, constituting the surface of the dry land;
and as the number of square feet are placed under and subtracted from
the number of seeds that would be produced in the ninth year, you can
see at once that there would be an immense number more of plants than
there would be square feet of ground for their accommodation