that the sex-linked genes are carried by the X-chromosome left no plausible ground for believing that that proof did not hold for the ordinary characters and the ordinary chromosomes. However, the present case offers a direct and positive identification between particular ordinary Mendelian characters and a particular autosome, so that we need no longer depend upon an extension to ordinary characters of a proof that was complete only for sex-linked characters. Taken in connection with the immense body of general proof for the chromosome theory, and with the many established parallels between hereditary behavior and chromosome behavior, these direct proofs in the case of both sex-linked and autosomal characters may be regarded as decisive. 1 Paper read before the Genetics Seminar of the University of California, Dec., 1920. 2 Bridges, C. B., Genetics, 2, Sept., 1917 (445-465). 1 Muller, H. J., Jour. Exp. Zool., 17, Oct., 1914 (325–537). 'Hoge, M. A., Am. Nat., 49, 1915 (47). 'Bridges, C. B., Genetics, 1, Jan.-Mar., 1916 (1-52, 107-163). Bridges, C. B., J. Gen. Physiol., 1, July, 1919 (645-656). 8 Dr. Little has recently reported such an identification (Science, 53, Feb. 18, 1921 (167)); but as I have pointed out in a note to Science (53, April 1, 1921 (308)) the facts as stated are more in conformity with the assumption of a "weak" allelomorph of eyeless, or of a linked dominant "minus" modifier of eyeless. (Since the above was written, triplo-fourth individuals have been identified among the offspring of triploid females (Science, 54, Sept. 16, 1921 (252)). 'Bridges, C. B., Proc. Am. Soc. Zool., 1918. NOTE ON THE ECONOMIC CONVERSION FACTORS OF ENERGY' BY ALFRED J. LOTKA BROOKLYN, NEW YORK Communicated by R. Pearl, June 20, 1921 That there is some relation between physical energy and economic value has been more or less clearly recognized by several authors. So G. Helm, for example, conceives of an "economic energy," whose capacity factor is quantity (of commodity), and whose intensity factor is measured by the price paid per unit quantity. A certain justification for this standpoint may be found in the fact that on the one hand goods having economic value can be exchanged for, and in this sense converted into energy; while on the other hand the movement of commodities in an economic system, that is to say, the transfer of property by sale and purchase, is determined by differences in economic value in much the same way as the transfer of energy from one portion of a physical system to another is determined by differences in the intensity factor of the energy concerned in the change. From Helm's standpoint, money would represent the most fluid form of economic energy, convertible freely into any other form of economic energy. Attention to this rôle of money is also drawn by Ostwald, who, however, expressly makes the reservation that money, although bearing a certain resemblance to energy, is not essentially identical therewith.3 Nevertheless, as we all know, money is convertible, by purchase upon the market, into various forms of energy, at rates somewhat variable, yet in some manner determinate. The question therefore arises, what is it that determines the ratio of conversion of various forms of energy by exchange upon the market? The physicist is familiar with two kinds of conversion factors of energy. The first kind of factor is that which enters into the analytical expression of the first law of thermodynamics, the expression of the constancy in ratio of the amounts of several forms of energy replacing each other in physical transformations. The second kind of factor relates to that fraction of energy transformed, which can be recovered in a selected form, and expresses the "efficiency" of the transformation or of the transformer taken in view.. It is one of the central data of thermodynamics that the equivalence factor is always independent of the mechanism by which the transformation is effected, while the efficiency factor is thus independent in the ideal case of a reversible transformation It is this independence which makes the two laws of thermodynamics so fertile as tools for drawing conclusions regarding the course of physical events. Anyone who has ever sought to show a perpetual motion inventor just why his machine cannot work will appreciate the economy of thought and language which is secured by direct application of these principles. Now in the transformation of energy by economic exchange upon the market we are dealing with a third type of conversion factor. The physical relations here involved are so complex that we are apt to overlook altogether that they are physical. Still less do we ordinarily recognize their precise character. A simple example may help to clarify the view: the case of the automatic vending machine, the penny-in-the-slot chocolate dispenser, for instance. The salient facts here are: 1. A definite amount of money brings in exchange a definite amount of commodity (and of energy). 2. The physical process is a typical case of "trigger action," in which the ratio of energy set free to energy applied is subject to no restricting general law whatever (e.g., a touch of the finger may set off tons of dynamite). 3. In contrast with the case of thermodynamic conversion factors, the proportionality factor is here determined strictly by the particular mechanism employed. Reflection shows that all transformations of money or of economic assets of any kind into energy by exchange upon the market are of this character. It is always a case of trigger action. Somewhere there is a store of available energy, which can be tapped with an expenditure of greater or less effort. The payment of the price sets in motion the requisite machinery for the release of that energy (or for its transfer of ownership, the release being delayed at the discretion of the buyer). In view of the entire absence of any general law regulating the ratio of energy released to energy applied in such case of trigger action, we may ask the question, how does it come about that economic conversion factors, economic ratios-in-exchange of different forms of energy, display any regularity whatever? We have been accustomed, in thermodynamics, to disregard mechanism. In dealing with energy conversions by trigger action we must make a complete change of attitude. Here everything depends on mechanism. If we find any degree of regularity in the conversion factors, this must be due to regularities in the mechanism, i.e., in the human organism, and its social aggregations; and we cannot hope to make any progress in our understanding of the physical principles involved except by taking due account of the mechanism. In view of the extreme complexity of the systems in which economic phenomena have their course, it may appear hopeless to attempt analysis. But reflection shows that the complexity is in the details; the broad underlying features resolve themselves into comparatively simple lines. Our vital interest in physical energy arises out of the following facts: 1. The body of a living organism is not in equilibrium with its surroundings. In other words, the living body (and also the dead body, for some time after death, as popularly conceived), in its natural environment, is a source of available energy. 2. Though not in equilibrium with its surroundings, the living body is in an approximately steady state; furthermore, it is one of the essential conditions for the continuance of life that this approximately steady state be maintained. Extreme departures therefrom result in permanent displacement from the steady state, and, ultimately, in the dissipation of the available energy presented in the substance of the organism. 3. In the course of events a certain amount of available energy, varying according to the nature of the organism, is unavoidably dissipated, per unit of time. It follows that every organism, in order to maintain the steady state necessary for its survival, must be provided with devices for capturing available energy. Furthermore, in the competition which takes place among organisms, the advantage must go to those whose energy-capturing devices are most effective in directing available energy into such channels as are favorable to the preservation of the species. In man, as an organism of the animal type, the mechanism for capturing available energy comprises three elements: 1. Sense Organs, or Receptors, whose function is to establish a certain rather close correlation between the state of the environment and that of the individual. Their function, in fact, is to depict the external world in the organism, to apprise him of the state of his environment. 2. Organs of Operation, or Effectors, such as hands, feet, etc., by means of which the individual reacts physically upon his environment so as to modify it, or to modify his relation to it (as, for instance, by locomotion). 3. Organs and Faculties of Adjustment, or Adjustors, whereby the action of the Effectors is adjusted in accordance with the indications furnished by the sense organs (receptors), and with the needs of the organism. Among these adjustor faculties one which figures prominently and plays an important rôle is what we may call the sense of values, that faculty which we exercise when we are confronted with two or more alternative courses of action, from which one must be selected. In such a situation we choose the course which appears to us, subjectively, the more desirable, and we do not ordinarily give any thought to the question as to what may be, objectively, the significance of "desirability," any more than we do ordinarily concern ourselves, in viewing a landscape, as to the particular wave-length, the objective characteristic, of the light which to our subjective judgment appears "green." And yet, for the interest of the species, it is evidently far from indifferent what may be the objective characteristics of those things which to us appear, subjectively, desirable. Upon the proper adjustment of the sense of values, of the "tastes," to certain objective realities depends the welfare of the species. A nation of drunkards, for example, is not destined to figure among the winners in the struggle of evolution. If, then, the physicist has been interested in discovering the objective significance of the indications of our sense organs, if he has thought it within his province to investigate the relation between color and wavelength, between musical pitch and frequency, then it is equally a problem for the physicist to enquire into the physical basis of economic value. The ground has been prepared for this enquiry by the mathematical economists in their hedonistic calculus. A person having at his disposal a given sum of money, and being confronted with the necessity of choosing between different ways of spending it, will seek so to apportion his ex penditures as to procure for himself a maximum of pleasure. So, for example, if the choice lies between two commodities C1 and C2 (which may, in particular, be certain forms of energy) he will purchase quantities q1 and q2, respectively, such that, if his total pleasure derived from the purchase is, then where dqi, dq2 are small, arbitrary increments in the quantities of the commodities C1, C2 purchased. If P1, P2 are the prices upon the open market, say, per unit quantity, of commodities C1, C2, respectively, then evidently the corresponding increment in expenditure is p1dqı + p2dq2. But the sum of money to be spent is fixed. We must have, therefore, P1 dqi + p2dq2 = 0 (2) It follows, then, from (1) and (2), that the individual will so apportion his purchases, that If the commodities C1, C2 are "necessities of life," whose influence upon the life of the species is to increase r, the proportional rate of increase of the species, then, evidently, the interests of the species demand that the purchases be so apportioned as to make r a maximum, and thus, by similar reasoning, to make If we regard the sense of values as a device for attaining, as nearly as may be, the adjustment (4), then we see that a perfect sense of values would make So that, in a community of organisms endowed with a sense of values thus ΖΩ perfectly adjusted, the marginal utilities. (and hence the prices on да Dr да In an open market) would be proportional to the partial derivatives practise this proportionality will not be actually reached; but it represents the limiting state towards which a race must tend to evolve. For, a race having tastes radically at variance with the exigencies of race propagation (measured by the rate of increase r), could not long survive, as pointed out years ago by Herbert Spencer.4 It is this tendency to approximate (perhaps somewhat remotely) to the adjustment (5), which gives rise to fairly definite economic interconversion factors of different forms of energy, as purchased upon the market, and applied to specific uses. There is no need to invoke a specific "economic |