plexity of qualitative distinctions than any other being known to science.

It is worthy of attention also that, in measuring and comparing phenomena, there are two different methods of procedure which correspond to the difference of quantity and quality. In the case of quantity, whether of a number of units or of magnitudes, the instrument of comparison is mathematics. Given a numerical or geometrical standard, all quantities of the same kind, or related to the same standard, can be mathematically compared. It is worthy of observation that the mathematical method finds its largest and surest application where the differences of quality are the fewest, and it becomes less and less fruitful as these differences increase in number. Thus, for example, the simple motions of the heavenly bodies are uniformly subject to exact mathematical calculation and predetermination, while the precise movements of an animal are less, and the complex conduct of a man least of all, capable of mathematical measurement and prediction.

As we rise in the scale of qualitative development from the chemical compound to the plant, from the plant to the animal, and from the animal governed by instinct to man governed by reason, we find mathematics less and less sufficient as an organ of investigation. While in the realms of color, temperature and other secondary physical properties quantity may furnish a key to the explanation of quality, we find ourselves at last in a sphere of being where quality is the matter of supreme interest, and where the mathematical method ceases to apply. The social life of man, the progress of civilization, the formation and development of political institutions, the rise and fall of empires, the relations between independent states-all these transformations belong to the sphere of qualitative change, defy mathematical calculation and demand a new instrument of comparison and comprehension.

III.

It is precisely this new and higher sphere of human activity. which is, by common consent, par excellence the field of history. The study of the successful transformations of quality may, however, go far back of this; and it is the appreciation of qualitative changes in the pre-human world that has illuminated the realms of astronomy and biology with the great principle of natural evolution. The point I wish here to establish is, however, the scientific necessity of qualitative as distinguished from quantitative measurement in estimating the phenomena of human life, which are the phenomena

of human history. One side of human science is built up with answers to the question, "How much?". There is another side, equally important to science in its totality, and far more rich in human interest, which depends upon the answers to the question, "Of what kind?" and this is the historical as distinguished from the mathematical aspect of science.

As mathematics answers the questions of the first series, so history answers those of the second. It deals with transformations of a qualitative character, while mathematics deals with quantitative relations. To make clear the difference, let us note the contrast between the mathematical and the historical methods. The former aim to discover the uniformities that exist in space and time; that is, to reach the largest attainable generalizations of the laws of invariable action. The aim of history is exactly the opposite. It does not seek for the law of recurrence, or any element of uniformity in either space or time; but to ascertain what particular changes have taken place in a definite time, with a view of estimating their relations as a series of acts, or of appreciating their value and significance as manifestations of the qualitative aspect of the universe. While mathematical science measures phenomena with reference to their quantity in terms of space or time, historical science measures them according to their value as elements of success or failure in the accomplishment of certain results as expressed in terms of human sensibility and rational worth; that is, according as they are beneficial or injurious, prudent or imprudent, ennobling or degrading, civilizing or barbarizing, commendable or reprehensible. In brief, while the sciences based on mathematics aim at the most universal generalizations of what happens in space and time in order to discover general laws, the historical sciences aim at a knowledge of the serial development of phenomena in a definite time and a definite place, showing the order in which they occurred, the conditions out of which they arose, the influence exercised by them and the consequent value of these phenomena, not in terms of number and magnitude, but as manifestations of reality ranked as inferior or superior in the scale of human utility or appreciation.

How fruitful the historical method may be, joined with the mathematical, in the study of nature is proved by the results that have followed from its application. Our whole conception of the universe has been changed by it under the influence of Laplace, Lamarck, Darwin and their successors. Instead of a rigid, static order of things, we now conceive of the universe as undergoing constant transformation; and it is in these processes of change that its

real nature is revealed. Even the elements of matter are now understood to have had their history, and it is in the course of their evolution from stardust to living organisms that their inherent potencies, which escape mathematical analysis, are brought to light.

IV.

There is one characteristic of human history, however, which separates it entirely from the history of nature, namely, the fact that a portion of it-or at least a specimen of its process-occurs in the individual consciousness, and can be examined from the point of view of man as a voluntary being, acting for definite purposes. I do not wish at this time to enter into the lively controversy carried on in recent years regarding the nature of historic causation, which is essentially a question of philosophy upon which opinions are still divided; and I here express no preference for one or another of the opposing theories that find the chief factor of historic change to be physical or psychical, individual or social, intellectual or moral. What I wish to insist upon is that, whether man be a really creative agent or merely a conscious mechanism put in motion by heredity and environment, whether he be impelled to action by blind and irresistible impulses or guided by intellectual enlightenment, the substance with which the history of man is concerned is personal conduct, and the reaction of conduct upon human development.

I do not doubt that the historical process may be governed by general laws, and it may be that all qualitative differences in human experience may be or might be if our knowledge were sufficiently extended-reduced to purely quantitative elements, and the whole course of development explained upon a mathematical basis. What, on the other hand, seems to me most evident is, that history has no contribution to make to this enterprise, which, if it is ever to be rendered successful, must be accomplished by some other branch of science. Since history is the record of particular occurrences, no one of which has the property of universal necessity, and since -unlike the phenomena of nature-the phenomena of human history can never be exactly repeated, they contain no data that warrant absolute generalizations; and, therefore, disclose no necessary laws of action. As Treitschke has well said: "Wäre die Geschichte eine exakte Wissenschaft, so müssten wir im Stande sein, die Zukunft der Staaten zu enthüllen. Das können wir aber nicht, denn überall stösst die Geschichtswissenschaft auf das Rätsel der Persönlichkeit. Personen, Männer, sind es, welche die Geschichte. machen."

If there is any proposition upon which all schools of thought are agreed, it is that persons are the agents of historical movements. Each person, even the greatest, may be but a molecule in the moving mass of humanity; and social directions and velocities may be determined by physical conditions, but they operate always and everywhere through beings who are more or less dimly conscious. of whither and why they are moving. Nothing could be a better proof of this than the fact that in every great historical movement there is a conscious effort to rescue something, so to speak, from time, and to give it permanent endurance. Every monument, every inscription, every chronicle designed to commemorate a part played by a man or a nation in its impress upon a period bears witness to this human impulse. All the records of the past are the fruits of it. There seems to be in the current of the historic process something that rises above it and is not part of it, which judges, measures and estimates that which is fugitive and that which is permanent in it. There is in every generation of men a disposition to see in events some increase of good or some access of evil, some lesson for the enrichment of experience or some caution for the future. It is this effort to profit by the changes men are able to effect and to render permanent their achievements that has led to the making and preservation of historical documents, and it is this that inspires the historian to endure the labor and sacrifice of research.

Seen from within, the historic process opens new vistas to the historian. What is the signification of this ceaseless struggle with the evanescent and this endeavor to lift the contents of time to a position of permanent security? Does it not imply in the human. agent a sense of continuity through which he realizes his part in the general development of man, and his duty as a member of the human race? It is in the great crises of history that its true nature is made apparent. Only those who have lived through them and have had some part in them possess in its full sense the meaning of the historic process; for it is only as a part of it that the individual, in moments of victory or defeat, in the march of triumph or fainting on the field of battle, knows that the social unit counts for most when he is part of some great movement in which humanity moves on from one to another stadium in the realization of its destiny.

V.

If history is ever to throw any light upon the riddle of personality, beyond that which biology and psychology afford, it can be done in no other way than by bravely pursuing its own method

of recording the acts of men as they have actually occurred, and not by elaborating theories of causation. The temptation is strong to regard history as belonging in the same class with the inductive and nomological sciences, and to apply to it methods which pertain to them. Only thus, it has sometimes been represented, can history be shown to possess a scientific character. But this inference results from a failure to recognize the fact that, as we have shown, the sciences of quantity and the sciences of quality, though fundamentally different in conception and procedure, are co-ordinate in dignity and importance for mankind.

There is, it is true, no science where there are neither measurements nor relations upon which measurements can be based. For this reason it may be contended that no form of human knowledge is really scientific, unless it is based upon mathematics and can be expressed in exact and universal formulas. While it is undeniable that science of necessity requires measurement and comparison, it is an error to suppose that mathematical measurement and comparison are the only forms of human estimate or that scientific knowledge may not be based as firmly upon differences as upon resemblances and uniformities. While the observer of physical phenomena measures them upon a scale expressed in quantitative units, the observer of historical phenomena measures them upon a scale expressed in qualitative differences. The essential basis of science is variation of experience, which may be capable of expression in either of two ways: the mathematical, which measures it in terms of quantitative value; or the ethical, which measures it in terms of qualitative value.

I have used the term "ethical" in contrast to "mathematical ", because I understand by "ethics" the science of value in human conduct, and employ the adjective derived from it for want of a better term. Whatever criticism may be passed upon the expression, the distinction it is intended to represent is indisputable. There exist beyond question these two forms of value: that which is measurable in terms of duration and magnitude, and that which is measurable in terms of sensibility and utility. If, indeed, we undertake for a moment to compare them, we at once remark that quantitative or mathematical standards are in reality mere abstract units derived from the analysis of space and time; while qualitative or ethical standards, in the broad meaning here intended, represent those distinctions which affect our sensibilities or human purposes, and are, therefore, the measures of the most essential elements of our human experience.

AM. HIST. REV., VOL. XIV. —2.