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Show CONDITIONS AFFECTING THE and gradually distributed over the whole surface of the ]and. I want you now to trace out what will occur, and you will observe that I am not talking fallaciously any more than a mathematician does when he expounds his problem. If you show that the conditions of your problem are such as may actually occur in nature and do not transD'ress anv of the known laws of nature in 0 • 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. Pla.nts. 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 " 6t.h , 15,625,000,000 15,625,000,000 X 50 " 7th " 781,250,000,000 781,250,000,000 X 50 " Sth " 39,062,500,000,000 39,062,5.00,000,000 X 50 " 9th 1,953,125,000,000,000 51,000,000 sq. miles-the dry sur- .} face of the earthx27 878 400- =sq.ft. 1,421,798,400,000,000 ' ' I the number of 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. PERPETUATION OF LIVING BEINGS. 125 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. 'rhis is certainly quite enough to prove my point; that between the eighth and ninth year after being planted the single plant would have stocked the whole available surface of the earth. This is a thing which is hardly conceivable-it seems hardly imaginable-yet it is so. It is indeed simply the law of Malthus exemplified. Mr. Malthus was a clergyman, who worked out this subject most minutely and truthft1lly some years ago; he showed quite clearly,and although he was much abused for his conclusions at the time, they have never yet been disproved and never will be-he showed that in consequence of the increase in the number of organic beings in a geometrical ratio, while the means of existence cannot be made to increase in the same ratio, that there must come a time when the number of organic beings will be in excess of |