We are something in the condition of a man suspended on a balance with sharp-pointed spikes placed close to his body, and who must not stir for his life. Now the source of this fallacy (on which the whole turns, for without it it is null and abortive) lies here, namely in supposing that of the two ratios here connected together, the one is the cause of, or has any thing to do with the other. For the ratio in the upper line being at number 256 does not depend on the other ratio being at number 9, but simply on its being so many removes from the root or first number. It only expresses a possible or imaginary series, or the independent, direct, physical power of increase, or abstract tendency to increase in population at each step, and what that increase would amount to in a given number of steps, being left entirely to itself. If it expresses any thing else, or the actual increase of population combined with and in reference to the means of subsistence, it is utterly false and delusive, and a contradiction in terms. For population as regulated by, and arising out of the means of subsistence cannot have got the start of it in so prodigious a manner, and as unconnected with the increase of the latter cannot depend upon it. In the one case, population instead of being to the means of subsistence as 256 to 9, will only be a little a-head of it, or as 9½ to 9: in the other case it will be as 256, whether the food has in a given time increased from 1 to 9, or only from 1 to 6, or whether it has stood still at 1. The number of inhabitants from the beginning of the world, proceeding by the geometrical ratio, would have been going on just the same whether they had ever had any thing to eat or not (they are a kind of enchanted people who live without food) whether the quantity of food had been more or less, whether there has been any improvements in agriculture or not. Though the improvements in agriculture had stood still at 1 in the arithmetical scale this would not lessen or alter the height to which the geometrical scale would have mounted in the interval. ‘It keeps on its way unslacked of motion.’ By advancing in the arithmetical scale or increasing the means of subsistence, you do not advance the geometrical scale, much less by increasing the disproportion between the two, do you increase the _waste_ population of the world, which must be greater in proportion as less of it had been provided for. On the other hand, you necessarily lessen this disproportion. For instead of supposing that if we had remained at 1 in the lower scale, we should then have been at 1 in the upper, or that if we had advanced no further than 3, the disproportion would then only have been 4 to 3, and so on, whereas by going on it is now as 256 to 9, the fact is that the disproportion instead of being as 256 to 9, would have been 256 to 1, or 2, or 3: and that the further we go in the one scale, though we cannot keep up with,