XI PHENOMENA OF ORGANIC NATURE 437 
any more than a mathematician does when he ex- 
pounds his problem. If you show that the con- 
ditions 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 pro- 
position, 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 Ist year = 
50 x 50 ,, 2nd ,, = 2,500 
2,500 x 50,, 3rd 4, = 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 square miles—the 
oP g78 00 the manhen arp =S4-tt. 1,421,798, 400,000,000 
sq. ft. in 1 sq. mile 
being 531,326, 600,000,000 
square feet less than would be required at the end of the ninth 
year. 
