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berlin (T. C.) was led by his study of glacial climates to formulate several hypotheses which have done much to advance geology (see "The Origin of the Earth'). The recently published work of Ellsworth Huntington concerning changes of climate is of notable interest to geologists. The data he has accumulated and the stimulating hypotheses he has advanced to interpret these data are worthy of most serious consideration. The importance of climate and the promised fruitfulness of its study has led the speaker to attempt to facilitate its study by summarizing what is known as to climate under the title "Laws of Climate." This summary will be published soon in The Monthly Weather Review.
A notable case of successive stream piracy in southern Indiana: CLYDE A. MALOTT. This paper deals with the Knobstone cuesta region lying between the Muscatatook and Ohio Rivers near the eastern margin of the driftless area of southern Indiana. Its purpose is to show specifically the responsibility of the geologic structure and topographic condition in drainage adjustment. Details shown how the particular lithologic units with their regional westward dip are important conditioning factors in giving rise to topographic forms. Other conditioning factors scarcely less important are the so-called time factors, such as various uplifts, rejuvenation and glaciation. The peculiarity of the streams flowing east from the Knobstone escarpment is noted. Blue River with its peculiar unchanging gradient is discussed in some detail, as it is representative of all the streams on the backslope of the cuesta. It is shown that the piracy of the Muddy Fork of Silver Creek has taken place as a result of the geologic structure and topographic condition along the Knobstone cuesta. It is not a single instance of piracy, but consists of successive piracy wherein a large number of tributaries belonging to a single system have been annexed one after another to the drainage system of the invading stream. Some 35 square miles have been stolen. The conditions are highly favorable for piracy to continue, and eventually the largest part of the Muddy Fork of Blue River will be taken over by the Muddy Fork of Silver Creek. Such piracy will continue until a balanced condition of the gradients of the two stream systems is reached. Such a condition will mark the beginning of old age of the stream systems, when stream adjustments are practically complete.
The Satsop formation and structure of the Cascade range: J. HARLEN BRETZ.
Geotectonic economy of thrust-faulting: CHARLES R. KEYES.
ROLLIN T. CHAMBERLIN,
THE AMERICAN MATHEMATICAL
THE two hundred and tenth regular meeting of the society was held at Columbia University on Saturday, April 24, extending through the usual morning and afternoon sessions. The total attendance exceeded one hundred and thirty and included eighty-two members. President Frank Morley occupied the chair, yielding it to ex-President R. S. Woodward during the presentation of the papers on relativity at the afternoon session. The Council reported the election of the following persons to membership in the Society: Professor H. S. Everett, Bucknell University; Dr. J. L. Rouse, University of Michigan; Professor Nilos Sakellariou, University of Athens; Mr. H. L. Smith, University of Wisconsin; Professor Eugene Taylor, University of Wisconsin; Professor W. P. Webber, University of Pittsburgh. Thirteen applications for membership were received.
Professor L. P. Eisenhart was reelected to the Editorial Committee of the Transactions, for a term of three years. Professor P. F. Smith will retire from the Editorial Committee on October 1, after nine years' service as editor, and Professor G. D. Birkhoff will fill out Professor Smith's unexpired term. Professor Oswald Veblen was appointed a representative of the society in the Division of Physical Sciences of the National Research Council for a term of three years. Professor Veblen's Cambridge Colloquium lectures on Analysis Situs will be published by the society in the fall. Committees were appointed to confer with a committee of the Mathematical Association on joint plans for future meetings and to prepare nominations for officers for the annual election next December.
ciety and which are a highly efficient instrument of government, well worthy of study, will remain practically as they stand.
The committee on reorganization of the society is actively engaged in preparing plans for carrying on the administrative work after the present year and enlarging the society's income. It will make specific recommendations at a later meeting. A report was received from the committee on the International Mathematical Union, and the formation of an American Section of the Union was approved. The report of the committee on bibliography, recommending the establishment of a journal of mathematical abstracts, was approved, and the committee was authorized to take steps toward securing the necessary financial support.
In the interval between the sessions over fifty members and friends took luncheon at the Faculty Club; thirty gathered there at the dinner after the meeting.
The greater part of the afternoon session was devoted to a symposium on Relativity at which the following papers were presented:
1. "The physical and philosophical significance of the principle of relativity," by Professor Leigh Page, of Yale University.
2. "Geometric aspects of the Einstein theory," by Professor L. P. Eisenhart, of Princeton University.
The regular program consisted of the following
N. A. Court: "On a pencil of nodal cubics.'' E. L. Post: "Introduction to a general theory of elementary propositions."
E. L. Post: "Determination of all closed systems of truth tables."'
Jesse Douglas: "The dual of area and volume.' J. K. Whittemore: "Reciprocity in a problem of relative maxima and minima."
I. A. Barnett: "Linear partial differential equations with a continuous infinitude of variables.'' I. A. Barnett: "Functionals invariant under one-parameter continuous groups in the space of continuous functions."'
T. R. Hollcroft: "A classification of plane involutions of order four."
Tobias Dantzig: "A group of line-to-line transformations."
A. R. Schweitzer: "On the iterative properties of the abstract field."
J. F. Ritt: "On the conformal mapping of a region into a part of itself."
L. R. Ford: "A theorem relative to rational approximations to irrational complex numbers.'
L. E. Dickson: "Recent progress in the theory of numbers."'
G. D. Birkhoff: "Note on the ordinary linear differential equation of the second order."'
Joseph Lipka: "The motion of a particle on a surface under any positional forces." Joseph Lipka: "Note on velocity systems in a general curved space of n dimensions.''
J. E. Rowe: "Testing the legitimacy of empirical equations by an analytical method." Oswald Veblen: "Relations between certain matrices used in analysis situs."
O. D. Kellogg: "A simple proof of a closure theorem for orthogonal function sets."
C. L. E. Moore: "Rotation surfaces of constant curvature in a space of four dimensions."
H. S. Vandiver: "On Kummer's memoir of 1857 concerning Fermat's last theorem." Nilos Sakellariou: "A note on the theory of flexion."
Abstracts of the papers will be published in the secretary's report in the July issue of the society's Bulletin.
The Chicago Section held a two-day meeting at Chicago on April 9-10, the program including a symposium on the Maxwell field equations and the theory of relativity. The San Francisco Section met at Stanford University on April 10.
The twenty-seventh summer meeting and ninth colloquium of the society will be held at the University of Chicago during the week of September 6-11. The colloquium will open on Wednesday, and will consist of two courses of five lectures each by Professor G. D. Birkhoff, of Harvard University, on "Dynamical systems," and Professor F. R. Moulton, of the University of Chicago, on "Certain topics in functions of infinitely many variables.'' F. N. COLE, Secretary
SUGGESTIONS FOR PHYSICAL IN-
SINCE diseased conditions imply deranged cell-processes-leading to failure of local functioning or to defective coordination between the activities of different parts of the organism-it is clear that the problem of preventing and rectifying such derangements in man (the problem of medicine) resolves itself ultimately into the means by which cellprocesses can be restored to the normal after disturbance. A scientific (as distinguished from an empirical) knowledge of how to restore normal conditions must be based on an exact knowledge of the conditions determining normal protoplasmic activity, and this knowledge presupposes a fuller insight into the fundamental physico-chemical constitution of protoplasm, since it is only through an understanding of the properties of the essential living substance that we can hope to understand how the living system acts under different conditions.
The fundamental questions are thus: what kind of a system, in the physico-chemical sense, is living protoplasm? and what are the conditions of equilibrium, i. e., of normal self-maintenance, of such a system?
As a physico-chemical system protoplasm is peculiar in various respects, of which perhaps the chief are:
1. The self-maintenance of the system through its own continued chemical activity; i. e., the preservation of the normal equilibrium or continued life-depends upon the active continuance of the chemical processes
1 Contribution to the discussion at the Conference on Biophysics held by the National Research Council, Division of Medical Sciences, at Washington, February 21, 1920.
of the protoplasmic system, i. e., upon metabolism.
2. This metabolism involves a continual construction of complex specific compoundstypically compounds of high chemical potential to replace those disintegrated (as a result or oxidation or otherwise) in the energyyielding or otherwise destructive processes of protoplasm.
3. The rate and in part the character of both the energy-yielding and the constructive metabolism are readily influenced by changes in the external conditions: i. e., protoplasm is a characteristically irritable system-one of unstable equilibrium.
4. The ratio of constructive to destructive metabolism may vary widely under different conditions; excess of construction over destruction involves growth; equality of the two is equilibrium, implying a stationary condition as regards size and properties; while excess of destruction leads to regression, as in starvation. Obviously regression, if sufficient, must impair functional capacity and eventually lead to death.
5. The power of growth is thus inherent or potential in all forms of protoplasm during life. Those pathological problems which relate to excessive or otherwise abnormal growth or proliferation (e. g., the case of tumors) thus require for their scientific solution a knowledge of the physico-chemical conditions of normal growth.
It is evident, since growth is an inherent property of the living system-i. e., since the continuance of the living state depends on this power of specific construction-that the problems just cited relate themselves directly to the general group of problems having reference to the essential physico-chemical constitution of protoplasm. The protoplasmic system is primarily a growing or synthesizing system, at the same time as it is a system which continually yields material and energy to the surroundings through the chemical breakdown of certain components. The chief aim of general physiology is to understand the type of physical and chemical constitution
that makes possible chemical activities of this general kind.
Experiment shows that destroying the structure of protoplasm, by mechanical or other means, destroys most (though not all) of its chemical activity (including the latter's susceptibility to electrical influence), and in particular its power of specific synthesis or growth. Hence this power must depend on the special structure of the system. The chemical reactions constituting metabolism take place within a field or substratum having a special type of structure (i. e., arrangement of phases); and the nature and rate of the metabolic reactions are controlled by the structural conditions present. These structural conditions are themselves produced by the growth of the system itself, or of another system having similar properties.
It must be recognized that the problem of the fundamental constitution of living protoplasm underlies all of the problems of biology -including ultimately those of medicine, as a branch of applied biology. It is therefore all-important from the practical as well as from the purely scientific standpoint that this problem should be the subject of continual and active study and investigation.
Physical Processes of Fundamental Importance in Protoplasmic Activities.—The re search of the past fifteen years has made especially clear the importance of surfaceprocesses in the activity of living matter. The behavior and properties of colloids (the substances composing most of the solid material of protoplasm) are largely determined by surface conditions (adsorption, variations of phase-boundary potentials, interfacial tensions). Electrical stimulation depends upon sudden changes in the electrical polarization of the semi-permeable surfaces of the irritable cell. Protoplasmic movement (muscular contraction, etc.) is almost certainly due in most cases to the changing surface-tension of the structural elements composing the contractile fibrils. Growth processes show various significant resemblances to structure-forming processes occurring under the influence of local electrolysis at metallic surfaces in contact
with electrolyte solutions (formation of precipitation-tubules of zinc or iron ferricyanide, rust-patterns, etc.). Transmission-effects in protoplasmic systems (i. e., in nerve, etc.) may be closely paralleled by processes of chemical transmission or distance-action in film-covered metallic systems, like passive iron in nitric acid or mercury in hydrogen peroxide. Many cell-processes are associated with changes in the osmotic properties or permeability of the protoplasmic surface-films or plasma-membranes. The high development of surface layers or membranes is in fact a longrecognized structural peculiarity of living matter. The prevalence of the cellular type of organization is in itself evidence of the fundamental importance of this condition.
These general facts indicate strongly that for the purpose of gaining further insight into the physico-chemical constitution of living matter a more thorough and detailed study (1) of the general properties of surfaces (their structure, tension, electrical properties, etc.), (2) of the layers of material formed at surfaces (surface-films, etc.), and (3) of phenomena dependent on surface conditions (adsorption, catalytic effects, flocking and peptization of colloids, etc.), is all-essential. Probably the purely physical or chemical investigation of these problems will best be undertaken by students trained in the methods of physics and physical chemistry. Data or principles so obtained can then be applied to biological or medical problems by those specially qualified to deal with such problems.
There is much evidence that living protoplasm is essentially emulsion-like in its fundamental physical constitution; and it is known that the properties of emulsions are largely determined by the presence of interfacial films and by the electrical and other conditions resident at the phase-boundaries. The general physical and chemical conditions affecting the stability and properties of emulsion-systems are thus in large part identical with those affecting the stability and properties of living protoplasm. As is well known, emulsions are mixtures of two (or more) mutually insoluble liquids, of which one is in
a state of fine division and dispersed throughout the other; for stability a third substance (e. g., soap), forming a surface-film between the two phases, is usually required. Recent work has shown that the properties of oilwater emulsions may be made to vary in a remarkable manner by varying the salt-content of the system, and that these changes depend upon the solubilities of the soaps formed and upon their surface-activity. Many surprisingly close parallels between the effects of different combinations of salts on emulsionsystems and on living protoplasmic systems have been demonstrated. It is well known that the presence of inorganic salts in definite proportions is essential to the normal activity of most living cells. Such results, therefore, indicate the importance of initiating and extending researches which will have as their object the determination of the relation between the soluble substances (both electrolytes and non-electrolytes) present in emulsionsystems and the general physical properties and behavior of such systems. Light may thus be thrown upon the general properties of protoplasm (mechanical properties, structure, permeability, electrical properties), in so far as these properties are determined by the emulsion-like constitution of the system.
This emulsion-structure, however, furnishes only the field or substratum in which the essential chemical reactions (or metabolism) of the living protoplasm proceed. The special nature of these chemical processes determines the special properties and behavior of the protoplasmic system. Hence the relation of the film-pervaded or emulsion-like structure of protoplasm to the special type of chemical activity exhibited by the living system should be thoroughly studied and investigated. There are many indications that the extraordinary chemical capabilities of living matter are dependent upon the extent of its surface development: i. e., that the influence of protoplasm in inducing chemical reactions not found elsewhere is essentially the result of the special predominance of surface influences of a peculiar kind. And since the sensitivity of living matter to the electric current is one of