period of time, be married, would amount, for practical purposes, to certainty. The same would be true of any small number of men. But if the number of men increased considerably and amounted, say to 500, we should not be at all certain that all of them would be married off within a given time. If the number of marriageable men reached 1000, the chances of marriage for each man, tho good, would be much less than before. If the number of men increased further to 2000, 3000, 4000, etc., each man's chances of marriage would gradually diminish, while the chances of each woman would increase.

Here some one will protest that human factors are being neglected. Men and women have qualities which are sometimes better and sometimes worse; in one instance there may be more likelihood of attachment than in another; in one community social life gives to each sex more opportunities to meet the other than in another. All this is true and even more. Despite this, however, the element of chance still remains, and we are justified in our conclusion that as the number of either sex increases, the number of the other remaining constant, the probability that any one of the first will be married diminishes.

Further study will convince us that the law of probability underlies most, if not all, natural phenomena, and where this is true when two or more factors are under consideration, the law of diminishing returns must hold true. Ever since the time of Laplace, who, at the end of the eighteenth century, was the first to make a systematic study of the theory of probability and its applications, more and more attention has been given to its applicability to science. Its real significance, however, was not apparent until the work of Professor Willard Gibbs of Yale University. In his Statistical Mechanics he showed that the second law of thermodynamics was only a deduction from the laws of probability, that in fact all physical and chemical laws which are concerned with molecular action are likewise deductions from the same laws. There are millions of molecules in any mass, moving about at a tremendous rate, going in all directions, and making in

numerable collisions; yet at any state of pressure and temperature, each molecule has an average mean velocity, there is on the whole an average direction and an average number of collisions.

The laws of chemical equilibrium, including the law of mass action, are corollaries of these laws of probability as applied to molecular activity. As this branch of chemistry is very technical, and as it would take us too far afield to go into detail, we cannot stop to derive these laws. Suffice it to say that when two substances react, the extent and the rate of the reaction is governed by the active mass of each substance. As the reaction proceeds, the rate gradually diminishes until an equilibrium is reached. Because of these laws, an increase of either one of the substances in reaction will increase the rate and extent of the reaction but not in proportion to the increase. For example, if we bring together ethyl alcohol and acetic acid, they interact to produce ethyl acetate and water. If we take these in equivalent ratio, action will cease when two-thirds of each is transformed into ethyl acetate and water. If the ethyl alcohol and acetic acid are brought together in the ratio of three to one, the action will go on until nine-tenths of the acetic acid is converted.

Enough has been said to show that diminishing returns is not an isolated phenomenon. Let us take an example from agriculture to which the law was first applied. The three important elements of plant food in the soil are potassium, nitrogen, and phosphorus. For proper plant growth these must exist in a certain ratio. If there is too little of any one element, the soil will not yield sufficient produce. If then we add some of this element to the soil in the form of a fertilizer, we shall have an increase of product. Up to a certain limit an increase in this element will bring an increase in the crop, but again not in proportion to the increase of the element. The following table, based upon the results of actual tests at the Rothamstead station, will illustrate this point:

In many cases it is more difficult to trace the cause of diminishing returns. Yet in every case we find chance as one of the factors. We saw before that in a community where there were few men and many women, every man would be fairly certain to meet a woman and enter into the relation of marriage. We can apply this to the three factors, land, labor, and capital. If the number of the units of any one of these is small, each unit will be more likely to meet units of the other factors. If, to take a concrete instance, there were only one plow in the community, this plow would combine with a large number of labor and land units, and it would be sure to meet some of these units all the time. If the number of plows became inordinately large, each plow could not be used as much as before, and plows would be idle a great part of the time. The important fact in each of these cases is the probability of idleness. A plow is capital, and an increase of plows is an increase of capital. The second plow would add a great deal to the product, and so also would the third and fourth, but not quite so much. The same applies to an increase of labor or land.

We can examine this fact more closely if we take an example from the manufacturing industry. Suppose a laborer is employed at a milling machine, milling the end of a steel rod. His task can be analyzed into a series of motions, which consist of those made to operate levers, to adjust the rod, take it out, and put another in its place. The laborer is capable of making a certain number of motions within a given time. If he operates only one milling machine, his motions can be adjusted almost perfectly to the milling process; that is to say, within a given time, the motions required to be made

will combine with the machine process to give a maximum result for each machine. If now, he operates two milling machines, the combinations of muscular motions with the processes of the two machines will be more effective from the point of view of total product, but less effective for each machine. In other words, there is a diminishing return for each increase in the number of milling machines. This will be true, whether the constant be the number of men or the number of motions each man is capable of performing.

In view of the preceding, it is hardly possible to deny that the law of diminishing returns is universally valid. If criticism is at all possible, it can refer only to the applications which economists have made. Yet it is evident that valid applications can and must be made. As we are not here concerned with the subject matter of economics, but rather with its fundamental notions, no attempt will be made to apply the law.

To those who might object that what has been said is not physical fact, and can have no foundation in positive science, I should point out again that all the laws of science may be said to rest on probability. The law of probability is as much a part of the eternal nature of things as any of the laws of physics or chemistry. A protest might properly be made if there were here any attempt to set up a permanent scale of probabilities with reference to any of the factors of production. The differences between the returns from one quantity of any factor and an increased quantity of the same factor may be reduced to a minimum, but physical fact requires that some difference remain.

JULIUS DAVIDSON.

A DEFINITION OF "CONDITIONS OF LABOR '

COLLECTIVE agreements between organizations of workmen and their employers generally provide that " wages, hours and working conditions" shall be determined by the joint decision of the representatives of both sides. What is meant by the terms wages and hours is of course clear, but the phrase "working conditions" (as well as its equivalents "conditions of employment" and "conditions of labor ") is distinctly ambiguous. Many indeed regard this phrase as similar to the "necessary and proper" clause in the federal constitution, thus giving elastic powers to the joint body created to administer the agreement.

In the contests over interpretation, labor is almost invariably the broad constructionist party while management is the narrow. A study of collective bargaining in several industries cannot fail to impress one with the belief that the interpretation which is given to this term depends more upon the relative strength of the two parties than to the logic or rhetoric of the respective sides.

The very obscurity of the term, however, is leading many employers at least to be more cautious in agreeing to submit "working conditions" to the process of collective bargaining. They are typically beginning to inquire what the phrase includes, and some are insisting that its definition be written in the bond. Somewhat fearful of the increasing powers of organized labor, they are unwilling to trust to the process of evolution to define this term, since evolution may go against them. The formation of a joint agreement in one important industry has indeed been prevented at least temporarily by the uncertainty over this very phrase.

Plainly it is time that we should begin to define our terms and determine what this phrase means. The present definition is largely based upon the interpretation which the Shipbuilding Labor Adjustment Board gave to it. The following