=The laws of multiplication.=--Implicit or explicit approval of a falling birth-rate involves opposition to the opinion of the man in the street, the general opinion of the medical profession,[23] the bench of bishops and the social prophet and publicist in general. Nevertheless a fall in the birth-rate is a factor in organic progress, and, in general, the level of any species is in inverse proportion to its birth-rate, from bacteria to the most civilised classes of men in the most civilised countries of to-day. But in truth the uninformed opinion, totally contrary to the whole history of life and to the most obvious comparative facts of the birth-rate amongst and within present day human societies, was utterly disposed of forty years ago in the closing chapter of the greatest contribution yet made to philosophic biology--Herbert Spencer's _Principles of Biology_. The last chapter of that masterpiece is entitled “The Laws of Multiplication.” Unfortunately it has not been read by one in ten thousand of those who think themselves entitled to hold, and even to express, opinions about the birth-rate. Spencer's discovery is the complementary half-truth to the discovery of Malthus, and just as the law of Malthus is pessimistic, so the law of Spencer is optimistic. In a word, Malthus assumed--indeed, formally declared--that there was no natural factor of an internal kind tending to limit the rate of vital fertility. Spencer discovered that there is such a factor, which can and does limit and has been limiting vegetable, animal, and human fertility since the dawn of life. All reproduction involves an expenditure of energy in some degree on the part of the parent. Now the energy available by any individual is finite. If he expends it all upon reproduction, he himself, or she herself, must cease to exist. This happens in all the lowest forms of life, which multiply by fission or simple splitting. The young bacteria are their sub-divided parent. At the other extreme is the case of the individual who retains the whole of his energy for his own development and life, and has no offspring at all. Such consummate bachelor philosophers as Kant and Spencer may be quoted, and the list of childless men of genius might be extended quite indefinitely. This is not to declare this last state to be the ideal, but merely to point out the logical extremes.