College Teaching Part 13

These latter especially are encouraged, as this does much to offset current ideas that physics is a subject of unmitigated severity. The particular topics put into these demonstrations will be discussed in paragraphs below, which take up in more detail the organization of the special subdivisions of the material in a general physics course.

=Mechanics a stumbling block--How to meet the difficulty=

Mechanics is a stumbling block at the outset. As we have indicated above, it must form the beginning of any course that is a.n.a.lytic in aim. There is no question of sidestepping the difficulty: it must be surmounted. A judicious weeding during the first week is the initial part of the plan. Interest may be aroused at once in the demonstration lectures by mechanical tricks that show apparent violations of Newton's Laws. These group around the type of experiment which shows a modification of the natural uniform rectilinear motion of any object by some hidden force, most often a concealed magnetic field. The instinctive adherence of every one to Newton's dynamic definition, that acceleration defies the ratio of force to inertia, is made obvious by the amus.e.m.e.nt with which a trick in apparent defiance of this principle is greeted. Informality of discussion in such experiments, questions on the part of the instructor that are more than rhetorical, and volunteer answers and comment from the cla.s.s increase the vividness of the impressions. A mechanical adaptation of the "monkey on the string" problem, using little electric hoists or clockworks, introduces interesting discussion of the third law in conjunction with the second. A toy cannon and target mounted on easily rolling carriages bring in the similar ideas where impulses rather than forces alone can be measured.

There follow, then, the laboratory experiments of the Atwood machine and the force table, where quant.i.tative results are demanded. It is desirable to have these experiments at least worked by the cla.s.s in unison. Whatever may be the exigencies of numbers and apparatus equipment that prevent it later, these introductions should be given to and discussed by all together. In the nature of things, fortunately, this is possible. A single Atwood machine will give traces for all in a short time under the guidance of the instructor.

The force table experiment is nine-tenths calculation, and verifications may be made for a large number in a short time.

Searching problems and discussion are instigated at once, and the notion of rotational equilibrium and force moments brought in. Because of the very great difficulty seeming to attach to force resolutions, demonstration experiments and problems using a bridge structure, such as the Harvard experimental truss, will amply repay the time invested.

Another experiment here, which makes a.n.a.lysis of the practice of weighing, is possible, although there will be divergence almost at once due to the personality of the instructor and the equipment by which he finds himself limited. The early introduction of moments is important, however, because it seems as if a great amount of unnecessary confusion on this topic is continually cropping out later.

At this point, if limitations of apparatus present a difficulty, a group of more or less independent experiments may be started. Ideas of energy may be ill.u.s.trated in the determination of the efficiency and the horse power of simple machines, such as water motors, pulleys, and even small gas or steam engines.

In discussion of power one should not forget that in practical problems one meets power as force times velocity rather more frequently than as rate of doing work, and this aspect should be emphasized in the experiments. Conservation of energy is brought out in these same experiments with reference to the efficiencies involved.

In sharp contrast here the principle of conservation of momentum may be brought in by ballistic pendulum experiments involving elastic and inelastic impacts. Most students are unfamiliar with the application of these ideas to the determination of projectile velocities, and this forms an interesting lecture demonstration. Elasticity likewise is a topic that may be introduced with more or less emphasis according to the predilection of the instructor. The moduli of Young and of simple rigidity lend themselves readily to quant.i.tative laboratory experiments. Any amount of interesting material may be culled here from recent investigations of Michelson, Bridgman, and others with regard to elastic limits, departures from the simple relations, variations with pressure, etc., for a lantern or demonstration talk in these connections.

By this time the student should have found himself sufficiently prepared to take up problems of rotational motion. The application of Newton's Laws to pure rotations and combinations of rotation and translation, such as rolling motions, are very many. We would emphasize here the dynamic definition of moment of inertia, I = Fh/_a_ rather than the one so frequently given importance for computational purposes, S_mr_^{2}. Quant.i.tative experiments are furnished by the rotational counterpart of the Atwood machine. Lecture demonstrations for several talks abound: stability of spin about the axis of greatest inertia, Kelvin's famous experiments with eggs and tops containing liquids, which suggest the gyroscopic ideas, and finally a discussion of gyroscopes and their mult.i.tudinous applications. The book of Crabtree, _Spinning Tops and the Gyroscope_, and the several papers by Gray in the _Proceedings of the Physical Society of London_, summarize a wealth of material. If one wishes to interject a parenthetical discussion of the Bernouilli principle, and the simplest laws of pressure distributions on plane surfaces moving through a resisting medium, a group of striking demonstrations is possible involving this notion, and by simple combination of it with the precession of a rotating body the boomerang may be brought in and its action for the major part given explanation.

Rotational motion leads naturally to a discussion of centripetal force, and this in turn is simple harmonic motion. This latter finds most important applications in the pendulum experiments, and no end of material is here to be found in any of the textbooks. The greatest refinement of experimentation for elementary purposes will be the determination of "g" by the method of coincidences between a simple pendulum and the standard clock. Elementary a.n.a.lysis without use of calculus reaches its culmination in a discussion of forced vibrations similar to that used by Magie in his general text. Many will not care to go as far as this. Others will go farther and discuss Kater's pendulum and the small corrections needed for precision, for here does precision find bold expression.

It is not our purpose to give a synopsis of the entire general physics course. We have made an especially detailed study of mechanics, because this topic is the one of greatest difficulty by far in the pedagogy. It is too formally given in the average text, and seems to have suffered most of all from lack of imagination on the part of instructors.

=Suggested content for the study of phenomena of heat and molecular physics=

In the field of heat and molecular physics in general there is much better textbook material. Experiments here may legitimately be called precise, for the gas laws, temperature coefficients, and densities of gases and saturated vapor pressures will readily yield in comparatively inexperienced hands an accuracy of about one in a thousand. In the demonstrations emphasis should be given to the visualization of the kinetic theory points of view. Such models as the Northrup visible molecule apparatus are very helpful. However, in absence of funds for such elaboration, slides from imaginative drawings showing to scale conditions in solids, liquids, and vapors with average free paths indicated and the history of single molecules depicted will be found ideal in getting the visualization home to the student. Where we have a theory so completely established as the mechanical theory of heat it seems quite fair to have recourse to the eye of the senses to aid the eye of the mind. Brownian movements have already yielded up their dances to the motion picture camera. Need the "movies" be the only ones to profit by the animated cartoon?

Nor should the cla.s.sical material be forgotten. Boys' experiments in soap bubbles have been the inspiration of generations of students of capillarity. And if the physicist will consult with the physiological chemist he will find a ma.s.s of material of which he never dreamed where these phenomena of surface tension enter in a most direct fashion to leading questions in the life sciences.

=The teacher of scholarship and understanding is the teacher who uses sound methods=

Enough has been said to indicate what we consider the methods of successful teaching of college physics. It is quite obvious, we think, that physics const.i.tutes no exception to the rule that the teacher must first of all know and understand his subject. Right here lies probably nine tenths of the fault with our pedagogy. No amount of study of method will yield such returns as the study of the subject itself. The honest student, and every teacher should belong to this cla.s.s or he has no claim to the name, is well aware that most of his deficiency in explaining a topic is in direct ratio to his own lack of comprehension of it. In physics, as in every other walk of life, we suffer from lack of thoroughness, from a kind of superficiality that is characteristically human but especially American. We have yet to know of any one who really ranks as a scholar in his subject from whom students do not derive inspiration and enthusiasm. Such a one usually pays little attention to the methods of others, for the divine fire of knowledge itself does not need much of tinder to kindle the torches of others. Our greatest plea is for our teachers to be men of understanding, for then they will be found to be men of method.

=The method of a.n.a.lysis dominant in physics=

The sequence in which heat, electricity, sound, and light follow mechanics seems quite immaterial. Several equally logical plans may be organized. Preference is usually accorded one or the other on the basis of local conditions of equipment, and needs little reference to pedagogy. If one gives to mechanics its proper importance, the difficulty in giving instruction in the other topics seems very much less. The momentum acquired seems to serve for the balance of the year. Always must a.n.a.lysis be insisted upon, if our college course is going to differ from that of the high school. If we are to let students be content to read current from an ammeter with a calibrated scale and not have the interest to inquire and the ambition to insist upon the knowledge of how that calibration was originally made, we have no right to claim any collegiate rank for our courses. But if we define electrical current in terms of mechanical force which exhibits a balanced couple on a system in rotational equilibrium, there can be no dodging of the issue, for in no other way than by the study of the mechanics of the situation can the content and the limitations of our definition be understood. Any college work, so called, that does less than a.n.a.lyze thus is nothing more than a review and amplification of the material that should be within the range of the high school student and in that place presented to him. The first college course reveals a different method, the method of a.n.a.lysis. Science at the present time is so far developed that in no branch is progress made by mere description and cla.s.sification. The method of a.n.a.lysis is dominant in the biological and the earth sciences as well as in the physics and chemistry of today.

=Teaching of advanced courses in physics=

On the more advanced college courses which follow the general physics course little comment is needed. Problems and questions here also exist, but they have a strongly local color and are out of place in a general discussion. The student body is no longer composed of the rank and file, half of whom are driven, by some requirement or other, into work in which they have but a pa.s.sing interest at best. It is no longer a problem of seeing how much can be made to adhere in spite of indifference, of how firm a foundation can be prepared for needs as yet unrecognized in the subject of the effort. A very limited number, comparatively, enter further work of senior college courses, and these have either enthusiasm or ability and often both. Of course, a cold neglect or bored indifference in the att.i.tude of the teacher will be resented. It will kill enthusiasm and send ability seeking inspiration elsewhere. But any one who is fond of his subject, and of moderate ability and industry, should have no difficulty in developing senior college work. If our instructor in the general course must be a scholar to be successful, the man in more advanced work must be one _a fortiori_. If he is not, few who come in contact with him have so little discernment as to fail to recognize the fact.

=Organization of advanced courses=

Organization of senior college work may be in many ways. One method where an inst.i.tution follows the quarter system is the plan of having eight or ten different and rather unrelated twelve-week major courses which may be taken in almost any order. Half of these are lecture courses, the other half exclusively laboratory courses. There should be a correspondence of material to some extent between the two.

Lectures on the kinetic theory of gases should have a parallel course in which the cla.s.sical experiments of the senior heat laboratory are performed,--such experiments, for example, as vapor density, resistance and thermocouple pyrometry, bomb calorimetry viscosity, molecular conductivity, freezing and boiling points, recalescence, etc. A course of advanced electrical measurements should have a parallel lecture course in which the theoretical aspects of electromagnetism, the cla.s.sical theories, and the equations that represent transitory and equilibrium conditions in complex circuits are discussed. In optics, likewise, there is ample material of great importance: physical, geometrical optics, spectroscopy, photography, X-ray crystallography, etc. The advanced student in these fields finds more elasticity and opportunity for cultivating a special interest in having a large number of limited interest courses from which to choose than in having such material presented in a completely organized course covering one or two years of complete work. Instructors who are specialists have opportunity of working up courses in their own fields which they do more efficiently under this plan. Research begins at innumerable places along the way, and the senior college courses so organized are the feeders of all graduate work.

=Dangers of formalizing methods of instruction=

In all of the above discussion it should be clearly remembered that no single plan or no one particular method has the final word or ever will have. As long as a science is growing and unfinished, points of view will continually be shifting. We are largely orthodox in our teaching. If brought up on the laboratory method of instruction it may seem the best one for us, but others may prefer another way which they have inherited. Let us appeal, then, for a constructive orthodoxy. Let us be as teachers of a subject to which we are devoted, truly and sincerely open-minded, quick to recognize and sincere in our efforts to adopt what is better wherever we meet it: waiting not to meet it, either, but going out to seek it. From the humblest college to the greatest university we shall find it here and there. Not alone in schools but in the legion of human activities about us on every hand are people who are doing things more efficiently, more thoroughly, and more skillfully than we do things. If we would be of the number that lead, we must be among the first to recognize these facts and profit by them.

First, let our work be organized with respect to that of others--the high schools; not discounting their labor but having them truly build for us.

Second, let us be open-minded enough to see that all methods of instruction have their advantages and make such combinations of the best elements in each as best suit our purpose.

Above all things, let us know our subject. Here is a task before which we quail in this generation of vast vistas. But there is no alternative for us. No amount of method will remove the curse of the superficially informed. Let us devote ourselves to smaller fields if we must, but let us not tolerate ignorance among those who bear the burden of pa.s.sing on, with its flame ever more consuming, the torch of knowledge.

HARVEY B. LEMON _University of Chicago_

VII

THE TEACHING OF GEOLOGY

=Values of the study of geology diverse=

So wide is the scope of the science of the earth, so varied is its subject matter, and so diverse are the mental activities called forth in its pursuit, that its function in collegiate training cannot be summed up in an introductory phrase or two. Geology is so composite that it is better fitted to serve a related group of educational purposes than a single one alone. Besides this, these possible services have not yet become so familiar that they can be brought vividly to mind by an apt word or phrase; they need elaboration and exposition to be valued at what they are really worth. Geology is yet a young science and still growing, and as in the case of a growing boy, to know what it was a few years ago is not to know what it is today. Its disciplines take on a realistic phase in the main, but yet in some aspects appeal powerfully to the imagination. Its subject matter forms a const.i.tutional history of our planet and its inhabitants, but yet largely wears a descriptive or a dynamic garb.

=Geology a study of the process of evolution=

Though basally historical, a large part of the literature of geology is concerned with the description of rocks, structural features, geologic terrains, surface configurations and their modes of formation and means of identification. A notable part of the text prepared for college students relates primarily to phenomena and processes, leaving the history of the earth to follow later in a seemingly secondary way.

This has its defense in a desire first to make clear the modes of the geologic processes, to the end that the parts played by these processes in the complexities of actions that make up the historical stages may be better realized. This has the effect, however, of giving the impression that geology is primarily a study of rocks and rock-forming processes, and this impression is confirmed by the great ma.s.s of descriptive literature that has sprung almost necessarily from the task of delineating such a mult.i.tude of formations before trying to interpret their modes of origin or to a.s.sign them their places in the history of the earth. The descriptive details are the indispensable data of a sound history, and they have in addition specific values independent of their service as historical data. But into the multiplicity and complexity of the details of structure and of process, the average college student can wisely enter to a limited extent only, except as they form types, or appear in the local fields which he studies, where they serve as concrete examples of world-forming processes.

=Disciplinary worth of study of geology=

The study of these structures, formations, configurations, and processes yields each its own special phase of discipline and its own measure of information. The work takes on various chemical, mechanical, and biological aspects. As a means of discipline it calls for keenness and diligence in observation, circ.u.mspection in inference, a judicial balancing of factors in interpretation. An active use of the scientific imagination is called forth in following formations to inaccessible depths or beneath areas where they are concealed from view.

While thus the study of structures, formations and configurations const.i.tutes the most obtrusive phase of geologic study and has given trend to pedagogical opinion respecting its place in a college course, such study is not, in the opinion of the writer, the foremost function of the subject in a college curriculum that is designed to be really broad, basal, and free, in contradistinction to one that is tied to a specific vocational purpose.

=This study concerned primarily with the typical college course, not with vocational courses=

While we recognize, with full sympathy, that the subject matter of geology enters vitally into certain vocational and prevocational courses, and, in such relations, calls for special selections of material and an appropriate handling, if it is to fulfill these purposes effectively, this seems to us aside from the purpose of this discussion, which centers on typical college training--training which is liberal in the cosmic sense, not merely from the h.o.m.ocentric point of view.

=Knowledge of geology contributes to a truly liberal education=

To subserve these broader purposes, geology is to be studied comprehensively as the evolution of the earth and its inhabitants. The earth in itself is to be regarded as an organism and as the foster-parent of a great series of organisms that sprang into being and pursued their careers in the contact zones between its rigid body and its fluidal envelopes. These contact zones are, in a special sense, the province of geography in both its physical and its biotic aspects. The evolution of the biotic and the psychic worlds in these horizons is an essential part of the history of the whole, for each factor has reacted powerfully on the others. An appreciative grasp of these great evolutions, and of their relations to one another, is essential to a really broad view of the world of which we are a part; it is scarcely less than an essential factor in a modern liberal education.

=Geology embraces all the great evolutions=

Let us agree, then, at the outset, that a true study of the career of the earth is not adequately compa.s.sed by a mere tracing of its inorganic history or an elucidation of its physical structure and mineral content, but that it embraces as well all the great evolutions fostered within the earth's mantles in the course of its career.

Greatest among these fostered evolutions, from the h.o.m.ocentric point of view, are the living, the sentient, and the thinking kingdoms that have grown up with the later phases of the physical evolution. It does not militate against this view that each of these kingdoms is, in itself, the subject of special sciences, and that these, in turn, envelop a mult.i.tude of sub-sciences, for that is true of every comprehensive unit. Nor is it inconsistent with this larger view of the scope of geology that it is, itself, often given a much narrower definition, as already implied. In its broader sense, geology is an enveloping science, surveying, in a broad historical way, many subjects that call for intensive study under more special sciences, just as human history sweeps comprehensively over a broad field cultivated more intensively by special humanistic sciences. In a comprehensive study of the earth as an organism, it is essential that there be embraced a sufficient consideration of all the vital factors that entered into its history to give these their due place and their true value among the agencies that contributed to its evolution. A true biography of the earth can no more be regarded as complete without the biotic and psychic elements that sprang forth from it, or were fostered within its mantles, than can the biography of a human being be complete with a mere sketch of his physical frame and bodily growth. The physical and biological evolutions are well recognized as essential parts of earth history. Although the mental evolutions have emerged gradually with the biological evolutions, and have run more or less nearly parallel with them--have, indeed, been a working part of them--they have been less fully and frankly recognized as elements of geological history. They have been rather scantily treated in the literature of the subject; but they are, none the less, a vital part of the great history. They have found some recognition, though much too meager, in the more comprehensive and philosophical treatises on earth-science. It may be safely prophesied that the later and higher evolutions that grace our planet will be more adequately emphasized as the science grows into its full maturity and comes into its true place among the sciences. It is important to emphasize this here, since it is preeminently the function of a liberal college course to give precedence to the comprehensive and the essential, both in its selection of its subject matter and in its treatment of what it selects. It is the function of a liberal course of study to bring that which is broad and basal and vital into relief, and to set it over against that which is limited, special, and technical, however valuable the latter may be in vocational training and in economic application.

=Physical and dynamic boundaries of geology--Implications for teaching=

In view of these considerations--and frankly recognizing the inadequacies of current treatment--let us note, before we go further, what are the physical and dynamic boundaries of the geologic field, that we may the better see how that field merges into the domains of other sciences. This will the better prepare us to realize the nature of the disciplines for which earth-science forms a suitable basis, as well as the types of intellectual furniture it yields to the mind.

Obviously these disciplines and this substance of thought should determine the place of the science in the curriculum of any course that a.s.sumes the task of giving a broad and liberal education.

Earth-science is the domestic chapter of celestial science. Our planet is but a modest unit among the great celestial a.s.semblage of worlds; but, modest as it is, it is that unit about which we have by far the fullest and most reliable knowledge. The earth not only furnishes the physical baseline of celestial observation, but supplies all the appliances by which inquiry penetrates the depths of the heavens. Not alone earth-science, as such, but several of the intensive sciences brought into being through the intellectual evolutions that have attended the later history of the earth, have been prerequisites to the development of the broad science of the outer heavens. The science of the lower heavens is a factor of earth-science in the definition we are just about to give. At the same time, the whole earth, including the lower heavens, is enveloped by the more comprehensive domain of celestial science.