Human life is immediately sustained by food, clothing, shelter, and fuel. Food and clothing are principally derived from fish, fowl, sheep, cattle, and grain, all of which _tend_, more so than man, to increase in _geometrical_ ratio, although actually their increase in this progression is checked by man or by Nature. As regards shelter there can be no increase at all, either arithmetical or geometrical, apart from the work of human hands. Again, the stock of fuel in or on the earth cannot increase of itself, and is gradually becoming exhausted. On the other hand, within living memory, new sources of fuel, such as petroleum, have been made available, and old varieties of fuel have been used to better advantage, as witness the internal-combustion engine driven by smoke from sawdust. Moreover, in the ocean tides is a vast energy that one day may take the place of fuel. (c) Thirdly, before anyone can reasonably maintain that overpopulation is the cause of poverty and disease, it is necessary to prove that overpopulation actually exists or is likely to occur in the future. By overpopulation we mean the condition of a country in which there are so many inhabitants that the production of necessaries of livelihood is insufficient for the support of all, with the result that many people are overworked or ill-fed. Under these circumstances the population can be said to _press on the soil_: and unless their methods of production could be improved, or resources secured from outside, the only possible remedy against the principle of diminishing returns would be a reduction of population; otherwise, the death-rate from want and starvation would gradually rise until it equalled the birth-rate in order to maintain an unhappy equilibrium. Section 3. THE ROOT FALLACY