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"New York has seven per cent. and is buying more, while New Hampshire has seven per cent. and seems to like it." Mr. Turner disclaimed any intention to lay down details of a scheme for "parking" New England, but he recommended that "for the benefit of its own people, its own timber supply and its own watersheds, the section should promptly begin to formulate plans for the acquisition of at least eight or ten per cent. of its land area, or from three to four million acres. 99

THE ANTI-EVOLUTION STATUTE OF

TENNESSEE

VIOLATION of Tennessee's anti-evolution statute is now virtually impossible, under the interpretation placed upon the much-discussed law by the state supreme court, according to Henry E. Colton, counsel for the Tennessee Academy of Science in the appeal from the decision of the lower court after the Dayton trial. The only way in which a Tennessee teacher could now force himself into the law's clutches would be by directly inculcating doctrines of materialism or atheism in connection with evolution. Evolution pure and simple he can teach as much as he pleases, so long as he leaves religious denial out of the discussion. "The supreme court has rather clearly indicated that it wishes to get rid of this case, and the attorney-general is apparently likewise of the opinion that it is to the best interest of Tennessee not to prosecute this case further," Mr. Colton says. "In fact, under three opinions rendered in the case by the four judges now living it would seem probable that the state could not obtain a conviction in this case unless upon retrial and reappeal to the Tennessee supreme court it should win over the fifth judge, Swiggart, who did not participate in the case.

"An examination of the record indicates that John Thomas Scopes taught the generally accepted scientific theory as to the evolution of man without in any way denying the divine origin of man. Under liberal interpretation of the Biblical stories there is no conflict between the scientific theory of the evolution of man and the Biblical stories which teach the divine origin of man but do not specify the gradual process by and through which he was created.

"Two of the judges, Chambliss and McKinney, have held in substance that the mere teaching of the scientific evolution theory as to the origin of man does not constitute a crime under Tennessee law. Judge McKinney so holds because in his opinion the Anti-Evolution Act is unconstitutional for uncertainty. Judge Chambliss so holds because in his opinion the contention of the defense is correct that the teaching of the generally accepted scientific evolutionary theory as to the origin of man is not made an offense under the Anti-Evolution Act unless the teacher goes further and denies the divine origin of man. In other words, Judge Chambliss construes the statute as condemning the teaching of materialism or atheism, but not as condemning the mere teaching of the scientific theory of evolution of man as generally taught. Under the foregoing circumstances and facts, if the state, after having spent thousands of dollars

in the prosecution of Scopes, sees fit to dismiss Scopes without undertaking to convict him, it seems scarcely worth while for the defense to run the risk of antagonizing the court by arguing for a further hearing when it has already for all practical purposes won two out of the four judges now living who heard the case, and the state seems to be so tired of the prosecution that it is of its own accord dismissing the indictment against Scopes; and when it is known to all the world that he has taught the scientific theory as to the evolution of man.

"If the state does not have sufficient confidence in the act to proceed against Scopes under the foregoing circumstances it seems questionable whether it will ever undertake to enforce the act unless a teacher should not only teach the scientific theory as to the evolution of man but go further and undertake to teach materialism and deny the divine origin of man."

ITEMS

THAT the wave of influenza that has been sweeping over Europe is settling down before it touches our shores is the conclusion reached by officials of the U. S. Public Health Service based upon failure to receive further information on the progress of the epidemic. Both the Epidemiological Intelligence Department of the League of Nations and the Health Organization in England announced their intention recently of broadcasting radio reports on the character and progress of the disease. Up to date, however, no reports have been picked up, Surgeon-General Hugh S. Cumming declared recently. The fact that the Arlington Naval Wireless Station has been unable to pick up any of the signals for the Public Health Service is interpreted as meaning that the epidemic is subsiding and that no bulletins have been sent out from the European stations. The decision of the health section of the League of Nations to make available by broadcasting the information received by extensive epidemiological intelligence section it has been building up, was determined, it is said, by the numerous inquiries received from all over Europe as well as Australia and the United States.

NICOTINE, thus far practically unrivalled as an insecticide against plant lice, may soon have a serious competitor in the field through the results of experiments carried on at the U. S. Bureau of Entomology. An oil prepared from pyridine, which forms an essential part of nicotine, combined with sodium, has been found to be poisonous to plant lice. Like nicotine it destroys the lice without injuring the infested plants. Entomologists believe it possible that dipridyl oil, as the new compound is called, may prove more effective than nicotine for the practical control of some injurious insects. Thus far the economic phase of large-scale production of the new insecticide has not been thoroughly gone into, but it is believed that it can be made as cheaply as the manufacture of nicotine.

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Lancaster, Pa. Garrison, N. Y. New York City: Grand Central Terminal. Annual Subscription, $6.00. Single Copies, 15 Cts.

SCIENCE is the official organ of the American Association for the Advancement of Science. Information regarding membership in the Association may be secured from the office of the permanent secretary, in the Smithsonian Institution Building, Washington, D. C.

Entered as second-class matter July 18, 1928, at the Post Office at Lancaster, Pa., under the Act of March 8, 1879.

A MATHEMATICAL CRITIQUE OF SOME PHYSICAL THEORIES1 THE purpose of this paper was to review some of the mathematical-physical theories of the past and of the present, indicating briefly the nature of certain concepts upon which these theories rest as well as attendant logical difficulties, and proposing certain modifications. It goes without saying that geometry is the first and simplest of such theories. Some day, when the field of knowledge has extended so far that simplification becomes necessary, ordinary geometry may be approached somewhat as follows:

(1) Geometry treats of elements called points and the relation called distance between pairs of points.

(2) The complete tabulation of distances between pairs of points may be arranged as follows:

(a) the points P correspond to real number triples (x, y, z);

1

2

(b) the squared distance between P, and P, is (2x)2+(y2- Y1)2 + (Z2-Z1)2.

All geometry follows very readily from these agreements. Beginning in this way one may successively define line-segments, lines, planes, perpendicularity, rectangular coordinate systems, etc. The whole body of geometrical fact with corresponding analytic framework is easily deducible, and yet one may stop at the fundamental principles without taking up beautiful but less vital geometrical studies. In its origin the geometrical concept of space is always to be associated with that of a corresponding body of reference.

Classical dynamics arises in the attempt to use Euclidean space and absolute time as the means for expressing the laws of nature. There lie certain fundamental difficulties at the very basis of this attempt to make space the container of matter. The simplest illustration of them arises in dealing with a collection of "equal rigid elastic spheres." When only two spheres collide, the assumed laws of contact action determine uniquely their directions and velocities after collision; but when more than two spheres collide, the situation is entirely different.

1 Synopsis of address as retiring president of the American Mathematical Society before a joint meeting of the American Association for the Advancement of Science, the American Mathematical Society and the Mathematical Association of America. The full text will appear in an early number of the Bulletin of the American Mathematical Society.

Suppose that three equal spheres approach a point with equal velocities, the lines of motion being 120° apart and in the same place. If all three spheres collide at the same instant, considerations of symmetry alone demand that the spheres must rebound back along the same lines with a velocity equal to that of approach. But it is easily verified that if two of them collide ever so little before they collide with the third, the resultant motion will be decidedly different in character. Such a result seems to contradict the fundamental physical requirement of continuity. In fact the laws of action suffice to determine the behavior of two spheres which collide, but as more and more complicated simultaneous collisions between three or more spheres are considered, it is not possible to infer their behavior by an argument based on continuity or even symmetry, so that these laws need to be supplemented by indefinitely many others of arbitrary type, if the mathematical theory is to be determinate.

The situation is similar with n mass particles, attracting one another according to the Newtonian law; and the concept of elastic bodies so fundamental in classical dynamics presents even more formidable logical objections. For example, suppose that two equal elastic spheres under no pressure approach along their line of centers with equal velocities which exceed the disturbance velocity. The parts of the spheres which collide can not then rebound without interpenetration. Thus it appears as if the spheres are converted into a kind of lamina of infinite density moving radially outward in the plane of symmetry. But this yields a total change of state, which the theory of elasticity does not contemplate.

These illustrations show that the classical theory of particles, rigid and elastic bodies, needs to be supplemented by further conditions if the central difficulty of indeterminateness is to be avoided, and also that such further conditions will of necessity be artificial in character. The question now arises: Is it possible to conceive of simple laws of motion for systems of particles, and for continuous bodies in empty space, which will be unified and determinate? To secure such a system of particles it suffices to assume that in addition to the ordinary Newtonian force of attraction there is a repulsive force inversely proportional to the cube of the distance. Since the potential energy of the system then increases indefinitely when any two particles approach collision, it follows that collision can never take place. In order to deal with a continuous distribution of matter, we may assume that the law of force for the continuous distribution is the same as for the system of particles just considered. It is obvious that such a fluid can not contract indefinitely since then its potential energy

would exceed the total initial energy; nor can it expand indefinitely unless sufficient kinetic energy is available. Evidently this fluid is entirely different in character from the elastic body under pressure, but it has at least the theoretical advantage of being free from indeterminateness. Two colliding bodies of this description will in general separate after a transitional period of interpenetration.

The chief mathematical instruments used by the physicists in dealing with space, time and matter in classical physics have been the Lagrangian and Hamiltonian equations. Poincaré proved it to be a general characteristic of equations of this type that small disturbances from stable periodic motion are essentially periodic.

It may be proved conversely that if a dynamical system is such that its state is determined by 2n coordinates, and if the perturbations from a periodic motion can be represented by trigonometric series, then the equations may be given Hamiltonian form.2 Thus perhaps the only significance of the Hamiltonian form of equations in classical dynamics is to insure automatically that the perturbations of certain periodic motions are oscillatory.

The equations of Maxwell, giving the interplay between the electric and magnetic forces in space, have never been modified. The space-time background appropriate to this form is that of the special theory of relativity, in which space and time are taken relative to some reference body and in which the velocity of light appears as a characteristic limiting disturbance velocity.

In the simple case of a number of electrified particles, there will be an indefinite radiation outward of electromagnetic energy as oppositely electrified particles fall into one another, while those similarly electrified tend to separate indefinitely under the mutual forces of repulsion. Evidently such a system of electrified particles is of little physical interest.

The use of an elastic fluid under tension as the carrier of electricity seems at first sight to offer prospects of success. Further examination of the problem shows that it is impossible to secure stability of the kind desired, no matter what the relation between tension and density may be. But, aside from this instability, which arises from the fact that electricity of one sign exerts strong forces of repulsion upon itself, there is another difficulty which arises even in the consideration of neutral matter. In fact, there are two types of disturbance velocities, firstly, that of light and, secondly, that of the elastic wave of

2 Cf. Paris Comptes rendus, September 20, 1926, and a paper which is about to appear in the American Journal of Mathematics for January, 1927.

the fluid. The same paradox might arise at collision as in the analogous classical situation.

The only possible elastic fluid would therefore seem to be one with a disturbance velocity equal to that of light at all densities. The fluid of this type may be termed the "perfect fluid," by analogy with the ordinary perfect gas. The expansive pressure is such a fluid is readily determined to be one half the density in absolute units, and so enormously great; on account of the relativistic character of this perfect fluid, the mass of a small part of it is not invariable but changes as the square of the density of the attached charge. Obviously the perfect fluid is a highly instable carrier of electricity.

The failure of attempts to make use of an elastic fluid as the carrier of electricity leads one to inquire whether it is not in the nature of the case that the elementary bodies such as the protons and electrons must have some sort of autonomous existence. Now the kinetic and elastic energy of the perfect fluid at low velocities can be defined, in such wise that the principle of conservation of energy holds. Let us suppose in addition that there is an individual "atomic potential" energy of positive volume density, v, where V has a value fixed for all time at each point of the fluid. This leads to a supplementary body force, proportional to the gradient of in space, and also to a surface pressure inward, proportional to . In this way indefinite expansion is prevented, for it would involve an indefinite increase in the atomic potential

energy.

At first sight this seems to insure a stable spherical form of equilibrium. However, further examination shows that the nucleus is amorphous under radial displacement. But now suppose that the protons are made of very small parts of the fluid with charge + e, while the electrons are also made of parts of the fluid carrying the charge -e, both with suitable atomic potentials. Let us suppose furthermore that such an electron can be penetrated freely by the proton. Under these circumstances there will be a stable spherical form of equilibrium, in which the proton coincides with the electron; the tendency tovards amorphous shape of the electrons and protons will be destroyed by the attractive forces between bem.

Here perhaps is a kind of two substance theory of atter and electricity which will be found to meet the undamental mathematical requirements of determinteness and stability.

The space-time framework of general relativity is dapted to the concept of atomic potential; for this urpose the energy tensor T1, may be defined as consting of the elastic and electromagnetic energy

tensors due to the protons and electrons, and of a further term, vg11, where is the atomic potential. If we grant the four-dimensional nature of spacetime, the argument of continuity seems to make it imperative that the atom is an oscillating electromagnetic system. The central facts about the atomic oscillator are essentially two: first, it acts like a number of simple resonators of perfectly definite frequencies, such as those given by the Balmer formula in the case of the hydrogen atom; and secondly, these frequencies are excited only by means of certain quanta of energy. Now there need be no essential difficulty in accounting for this second fact. Imagine a pendulum to swing in a viscous medium whose viscosity diminishes rapidly as the distance from the position of equilibrium increases. Only with sufficient initial velocity will it oscillate back and forth, traversing the viscous region in damped hormonic motion. Consequently it is possible to conceive of the so-called "energy levels" as defining the amount of energy necessary to carry the oscillators so far from equilibrium that they will move back and forth past the position of equilibrium. Thus the first and most fundamental task appears to be to find an oscillator possessing the desired frequencies. Afterwards one may investigate in detail the rate of electromagnetic radiation, which may correspond to viscosity.

In particular it will be of interest to consider the small oscillations of the fluid proton and electron as specified. The three equations determining the frequencies are analogous in type to the "wave equation" of Schrödinger.

It seems to be of decided importance to develop theories, like the above, which meet the elementary mathematical demands of actual determinateness and stability. This does not seem to have been done in a single case hitherto.

In conclusion the statistical properties of non-Hamiltonian equations were referred to. These seem to be best suited to represent atomic systems taken as possessing a finite number of degrees of freedom; for such equations only can there be a set of periodic motions to which every other motion is in general very near. Hence such differential equations may yield the effect of quantum orbits without any quantum conditions.

HARVARD UNIVERSITY

GEORGE D. BIRKHOFF

3 A development of the theory outlined will be published in a forthcoming number of the Proceedings of the National Academy of Sciences. On proper choice of the "substance coefficients" and "atomic potentials," the theory leads to a formula of Balmer type for the frequencies.

▲ Cf. Göttinger Nachrichten, 1926.

THE CHINA FOUNDATION FOR THE PROMOTION OF EDUCATION AND CULTURE

THE First Report (Peking, 1926) of the China Foundation should be widely read by all who are interested in Oriental problems. It constitutes a definite landmark in the development and maintenance of cordial relations between China and the United

States. In it will be found a detailed statement of the arrangements which have been made for the expenditure of the unremitted portion of the Chinese Boxer Indemnity, amounting to a little over twelve and a half million dollars United States currency. Of this amount $1,422,217.75 has already been released by the American Government.

Full responsibility for the use of these funds is placed in the China Foundation, an organization established by presidential mandate, consisting, in the first instance, of fifteen trustees, of whom five are Americans and ten are Chinese. According to the constitution, vacancies occurring in the board of trustees shall be filled by election by the trustees. There is no stipulation as to nationality; but an agreement on this point may be contained in some other document. It is provided that "Representatives of the Minister of Foreign Affairs and of the Minister of Education and of the Minister of the United States to China shall have the right to attend the meetings of the board of trustees to observe the proceedings." These representatives are, however, without power, and, according to the published minutes, have not availed themselves of this privilege.

The present American trustees are: Mr. J. E. Baker, Mr. C. R. Bennett, Mr. R. S. Greene, Professor Paul Monroe, and Dr. W. W. Willoughby, the last named having been appointed to take the place of Professor John Dewey, who has resigned. Not all these persons are resident in China. It is to be hoped that they will soon be replaced by Chinese.

The Chinese trustees, with whom the responsibility really lies, are as follows: Dr. W. W. Yen, Dr. V. K. Wellington Koo, Dr. Sao-Ke Alfred Sze, Mr. Fan Yuan-lien, Dr. Huang Yen-pei, Dr. Chiang Monlin, Dr. Chang Poling, Dr. P. W. Kuo, Dr. V. K. Ting, and Mr. Y. T. Tsur.

Probably no other group of ten Chinese could be chosen in which Chinese and foreigners, alike, would repose such implicit confidence. It will be recalled that Dr. W. W. Yen is the distinguished and internationally well-known Chinese minister of foreign affairs, that Dr. V. K. Wellington Koo is the Chinese minister to Great Britain, and that Dr. Sao-Ke Alfred Sze is Chinese minister to the United States. Fan Yuan-lien, the director of the foundation, has had much experience as minister of education. Dr.

Mr.

Chang Poling is president of the Nankai College and Dr. P. W. Kuo is president of the National Southeastern University, two institutions financed and con trolled by Chinese and worthy of the highest praise Dr. V. K. Ting is director of the Geological Survey Mr. Y. T. Tsur is a well-known banker. Indeed almost every important walk of life is represented by a leader in it. Most of the members have attended

foreign universities: one in Japan, one in both En gland and Germany, and at least six in the Unite States. Many of them have been and still are teach ers. No one can deny that these trustees are qualifie to deal wisely with problems of education.

It has been unanimously resolved by the trustee that these indemnity funds shall "be devoted to th development of scientific knowledge and to the appl cation of such knowledge to the conditions in Chin through the promotion of technical training, of scien tific research, experimentation and demonstration, an training in science teaching, and to the advancemen of cultural enterprises of a permanent character, suc as libraries, and the like."

In order, perhaps, that this remission by the Unite States shall stand as a permanent gesture of goo will, the trustees have decided to establish a perm nent endowment fund "to consist of present accum lations, plus an annual addition sufficient to provi at the end of twenty years a principal which will yie an annual income of about half a million go dollars."

Grants made during the year 1926–1927 amou to $850,000 silver (approximately $400,000 Unit States currency). The largest item is $250,000, beir the first of four annual contributions toward t establishment of a Metropolitan Library in Pekin in fulfillment of a definite agreement with the Min try of Education. The National Southeastern U versity receives a total of $184,000, Nanyang U versity, $50,000, Hsiang Ya Medical College, $45,00 and the China Institute in America, $30,000. Oth grants are made for special purposes, but the d bursements are in no sense diffuse. Each is direct to a concrete purpose, preference being given existing institutions with a record of efficient serv and administration, rather than to newly founded stitutions which base their applications solely future prospects."

Never before have such large funds been pla under Chinese control for philanthropic purposes foreigners, but, in consideration of the personnel the board, the outlook is very bright. The maste administration of the North Manchurian Plague P vention Service from its inception on October 1, 19 by its director, Dr. Wu Lien Teh, and the continu of its activities through periods of famine, fore

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