to be no such physical necessity for the decay of a civilization as is found for the decay of a biological organism, but there are undoubted tendencies in the same direction. The very success of a race or a nation in building up a civilization seems to predispose it toward those habits which necessarily bring decay. The individual who has, by hard work and frugality, built up a fortune by producing more than he consumes will be difficult to convince that he should not stop working and begin to enjoy what he has accumulated. The difficulty will be increased with each generation of his heirs. Yet, nothing is more mathematically certain than the conclusion that if they do yield to this temptation, their consumption will soon exceed their production. If this tendency shows itself in the nation at large, it is equally certain that national wealth will thenceforward decline.

Again, even tho there are multitudes of people left in a state of poverty, the sight of so much wealth in the possession of other people will lead them to consider the cold-blooded question whether it would not be more profitable to try to rob them than to work for themselves. The sight of a conspicuously rich territorial group has never failed to arouse the cupidity of neighboring groups, provided the latter were strong enough to attempt inroads. Similarly, the sight of a conspicuously rich class does not fail to arouse an equal cupidity in the minds of other classes in the same territory whenever the latter feel strong enough to defy the laws of the land and make incursions over the class border. They who do not understand or appreciate this tendency in human nature will never have a very full understanding of the social problems of the present day. A careful reading of these three volumes should help the reader to such an understanding.

T. N. CARVER.

HARVARD UNIVERSITY.

NOTES AND MEMORANDA

ONE OF THE PHYSICAL FOUNDATIONS OF

ECONOMICS

So many attempts have been made to resolve economics into a psychological science as to make it seem advisable to call attention, in some detail, to some of the physical factors which are likely to remain unaffected by psychological changes, even assuming that these psychological changes are, first, possible, and second, desirable. Some of these physical factors are so fundamental as to give character to the science of economics under all possible conditions. It seems probable that, so far as these physical factors can be ascertained, they would have to be reckoned with under any form of social organization, and with any institutional background. In certain respects, therefore, communism and capitalism, socialism and individualism, would look very much alike if they ever got into working condition, because they would have to meet certain permanent and unchangeable conditions.

It is obvious that the prime factors of production are but two in number, nature and man. There is no reason why we cannot extend this assertion to the other departments of economics, and in fact to all the other fields whose objects are the goal of human research. Production requires relations between the various parts of nature, between man and nature and between the various types of men. Whatever be the relations, there are only these two terms implied, man and nature. When economics uses these terms, it must assume their essential characters, their reactions, and their interactions, as discovered by the different departments of positive science. Economics assumes these discoveries, for it is not the

business of the economist to engage in physical and biological research, except in so far as the scientist has not concerned himself with the phenomena which are of interest to the economist. All this may appear to be a truism, and yet it has not infrequently been forgotten. As Böhm-Bawerk says at the beginning of his Positive Theory, even those economists who preface their works with statements of physical fact, soon forget their declarations; these statements are mere ornaments, having no connection with the rest of the work. Now and then there appears one who insists upon a firm foundation before further investigation.

There are certain facts concerning production which, as Mill remarks, are true whether we like them or not, because they are inherent in the nature of physical things. (1) The law of diminishing returns is based, as I shall try to show, upon chemistry and physics, and, like certain chemical and physical laws, is capable of being reduced to a phase of the law of probabilities. (2) The primary advantages of a division of labor are not due to any preference of ours, or to the institutions that we have seen fit to adopt. (3) The Ricardian law of rent is based upon physical variations in land as well as upon diminishing returns from land of a given grade. (4) The laws of population, while in part psychological, have still a substantial physical and physiological basis and (5) physiology, as well as psychology plays a large part in determining the laws of consumption. In a general and fundamental sense, there are certain ways of doing things that are more economical than others regardless of social or legal institutions, and of popular philosophies, fashions, etc.

The law of diminishing returns probably has more ramifications in the field of economics than any other single generalization, therefore I shall elaborate this law as a sample of the physical laws which underlie the science of economics. This law has been the object of attack especially of those whose interest in economics is secondary to their interest in social reform. It is therefore most important for us to distinguish carefully between the law itself and any conclusions that may have been drawn from it thus far, whether right or wrong.

From the older treatises on economics, the impression is given that diminishing returns is applicable only to the special case of agriculture. It is due particularly to Professor Carver that this law has become more general, and made applicable to any group of factors in production. He has insisted that this is no fleeting social phenomenon, but is a fact which has its roots in physics and chemistry. It is perhaps impossible to trace all the manifestations of this law to any one allinclusive cause, but there is reasonable ground to suppose that it is traceable in great part to one fact which permeates all branches of science and even all activities of life. In the following attempt at a scientific explanation of this law, the procedure will be from the abstract to the concrete.

Let us take any fixed number of entities of a particular type which we may call x; then let us add to this successively increasing quantities of another type of entity which we may call y. Every time an addition is made let all the entities be paired off indiscriminately. Concerning the character of the resulting pairs as the number of y entities is increased, we can lay down this general proposition, that the number of mixed pairs, those composed of an x and a y, will increase as successive increments of y are added, but this increase in the number of mixed pairs will not be proportional to the increase in the number of y entities; the ratio of increase will be a diminishing one.

Let us next consider this case quantitatively. Suppose the number of x entities be 5, and the number of y entities added to this vary from 1 to infinity. If ly is added to the 5x, there will be 3 pairs of which 1 pair is certain to be mixed. In this case an addition of ly gave us a product of one mixed pair, which is both the most and the least that can be expected. In mathematical language, the probability is here certainty, in practical language we have 100 per cent efficiency. If now we add 2y to 5x, there will be a total of 3 pairs, of which we may have a maximum of 2 and a minimum of 0 mixed pair, but the probable number, or the average in the long run, will be something less than two mixed pairs but more than one. Thus by adding ly we have not increased the number of mixed

pairs by 1, but by something less than 1; whereas in the first case an addition of ly gave a certain result of 1 mixed pair. Continuing in this way we find that if we increase the number of y up to infinity, the greatest probable number of mixed pairs will be something less than 5. The following table may make this clearer:

It will now be apparent to those who know mathematics that the above is only an application of the theory of probability. Here pure probability alone was assumed. Certain concrete cases of pure probability can be found, for instance, in games of chance. Suppose we take 5x as meaning 5 red cards, and the various quantities of y as meaning so many black cards. If increasing quantities of black cards were mixed with a fixed quantity of red cards, and if the whole pack were then dealt out in pairs, the probable number of mixed pairs and the probability of each black card meeting a red card would work out in every case in the manner just described.

Let us take a still more concrete case. If in a certain community there were a thousand women all of marriageable age, and all desiring to be married, and if in this same community there were only one man of marriageable age also desiring to be married, and if furthermore polygamy were prohibited, the probability that this one man would, within a measurable

1 Only odd numbers of y may be taken, otherwise all will not be paired off.