Popular Science Monthly/Volume 23/May 1883/Physics in General Education
By Professor T. C. MENDENHALL.
THIS is an "Association for the Advancement of Science." But the forces which have to do with aiding or retarding this advancement are so various that we are in danger of losing sight of some of them. We are mistaken if we suppose that science is advanced only through contributions which are the result of original research in our laboratories and libraries. Even if so narrow a view be taken, it will be admitted that the talent for research is fostered and encouraged, if not indeed created, by an atmosphere of recognition and appreciation. The existence of such an atmosphere is in itself a blessing, and its production is certainly worthy of our highest efforts.
To this end it is desirable and necessary to bring about a more general diffusion of accurate knowledge concerning the elementary principles and propositions of the science of physics, as well as some degree of familiarity with the methods of physical investigation. I do not refer, of course, to the demands or the necessities of those who expect to undergo a course of training for the purpose of becoming themselves physicists, but rather to the diffusion of this knowledge among the masses of educated people in general.
That this diffusion is not taking place to any great extent, and will not, according to natural laws alone, is patent to any observing physicist, who can not fail to have come in contact with prevailing and pernicious errors, which often carry the weight of repetition, and now and then of recognized authority.
I am aware that this is not an association of educators, and that pedagogics is not, as yet, one of the sciences specifically indicated as worthy of advancement at our hands; but, if the growth of a tree is to be made healthy and permanent, it is not safe to neglect the soil into which its roots penetrate. Train it and prune it as you will, to grow into vigor and strength it must spring from a rich and generous earth which, though beneath it and below it, must be in harmony with it in order to supply the proper and necessary materials for its sustenance. It seems, therefore, not improper to raise the question, What can this Association do, or, more specifically, what can this section do, to increase the efficiency of instruction in physics?
I do this the more willingly for the reason that a considerable majority of the members of the section are engaged in this instruction during the greater portion of the year. In America a few only are privileged to devote themselves to original research. Here instruction and investigation, to a great extent, go hand in hand, and it is generally admitted that it is better so. The teacher does not reach his greatest efficiency, indeed he must fail completely, unless he continues a student, not of the works of men alone, but of Nature herself. On the other hand, some of the best and most fruitful inspirations of the investigator spring from his contact with those to whom he is communicating the finished products of his work. The history of science goes to show that many, perhaps most of those who have contributed to its advancement, have been great teachers. We neglect our duty, then, when we fail to give attention at proper times and under proper circumstances to the improvement of methods of instruction.
Perhaps in no other department of science has a greater change in these methods been wrought during the last ten years than in physics. And yet this change has been going on in an irregular, unmethodical sort of a way. There has been little or no concerted action among those interested and engaged in the work. Although all have had practically the same end in view, each individual has, in the main, worked out his own solution of the problem in accordance with his own views, modified and often largely controlled by the conditions and restrictions to which he was subjected.
It is not surprising, therefore, that results attained should in many cases be widely different and, on the whole, not entirely satisfactory.
In this new instruction many things have been attempted that could not be, and some things that ought not to be, accomplished. That overburdened and somewhat obnoxious word practical has found a place in our vocabulary, and we hear much of practical instruction in physics, whatever that may mean.
The subject, considered as a whole, naturally divides itself into two parts, pertaining respectively to higher instruction and elementary instruction: instruction in the colleges and instruction in the schools. Let us briefly consider each of these.
In referring to higher or collegiate instruction, it will be remembered that I do not include that of the post-graduate course in the university, properly so called, for which laboratories for research are equipped and maintained, and to which students are admitted only when thoroughly prepared by previous training. Fortunately for American students, a few such courses in physics are now open in this country, and it goes without saying that those who are conducting them do not need advice from us. It is for the large class of undergraduates who pursue the study of physics for a greater or less time that we may be concerned.
Contemporary with the recognition of the possibility of greatly improved methods of instruction was the recognition of the value of the more thorough study of physics as an element in what is called a liberal education.
These were alike the results of the tremendous strides made by physical science, beginning twenty-five or thirty years ago. Grand and beautiful generalizations commanded the admiration of men skilled in other departments of human knowledge, and equally wonderful applications of principles to practice touched our every-day existence upon so many sides as to draw forth applause from the millions who are without the "inner court." Physics thus found or forced its way upon the college curriculum to an extent much greater than had previously been thought possible or desirable.
A few keen-sighted men, combining in themselves, happily, the student and the teacher, recognized the fact that thorough instruction in physics implied and demanded the use of laboratory methods, such as had been utilized for some years in chemistry, and were rapidly coming into prominence in every other department of natural science.
Among these was, notably, Professor Pickering, whose establishment of a working physical laboratory for purposes of instruction, in the Institute of Technology at Boston, must be regarded as an epoch in the history of this progress; and with this also might be linked, although following at a little later date, the widely-known establishment made by Professor Mayer at Hoboken.
These were quickly followed by others in the East and in the West, and at the present time there are many institutions of learning in which the laboratory methods of instruction are in use, and whose equipment includes a so-called physical laboratory.
To all interested in the study of the present condition of this work I would especially recommend the very valuable "Report on the Teaching of Chemistry and Physics in the United States," prepared by Professor Clarke, of the University of Cincinnati, and issued about a year ago by the Bureau of Education. This report is full of facts of great value, and doubtless fairly represents the relative standing of collegiate instruction in these two important subjects at the present time.
Professor Clarke has classified the various courses of instruction in physics as follows:
1. Full course, including higher mathematical physics, advanced laboratory work, and research.
2. Full course, with mathematical physics and elementary laboratory work. 3. Course in general physics, involving a previous knowledge of trigonometry, and including laboratory work.
The other courses, up to ten in number, are elementary in their character, and do not concern the present investigation.
The report contains statistics gathered from nearly four hundred universities and colleges, agricultural colleges, and scientific schools. In nearly all of these the study of physics is pursued to a greater or less extent, although it appears that in some instances no report upon physics was forthcoming on account of ignorance as to what was meant by the word. Out of the whole number there were thirty-three institutions in which the instruction in physics fell within the limits established above. Of these there were four of the first rank, two of the second, and twenty-seven of the third.
In chemistry, however, laboratory instruction is to be found in at least one hundred and fifty institutions, the opportunities for instruction in this subject thus outnumbering those offered for similar instruction in physics in about the ratio of five to one. But it will be remembered that in this contest chemistry has many things in its favor, and that physics is handicapped by the great cost, relatively, of the first establishment, as well as by the lack of well-defined and systematic courses of instruction.
Taking it as a whole it will be admitted that there has been a rapid and, I believe, a permanent growth, and that the work has already become so extensive that it appears to be worth while to subject it to criticism, and to determine by conference and consultation what improvements, if any, might be suggested.
Admitting the necessity of the laboratory as a means of instruction in physics, two important questions present themselves: First, of the total amount of time given to the subject, what proportion should be spent in the laboratory? and, second, what should be the character of the work done there?
I shall not undertake to answer these questions, but will submit one or two conclusions which have been thrust upon me by observation and experience.
Concerning the first, something ought to be said. It will be remembered that the new instruction began at a time which was characterized not only by unusual scientific activity, but as well by what almost amounted to a revolution in educational processes. A great teacher. had told us that we studied Nature in books, and when we met her face to face she passed unrecognized. There sprang up a new method, the essence of which was that the mysteries of Nature could not be known at second-hand; that a knowledge of things could only be obtained by a contact with things themselves. The use of the text-book fell into disrepute, and the student was encouraged to become his own authority. It was as if all men were to cast aside their maps, globes, histories, books of travel, etc., and start out to obtain a knowledge of the world by visiting its different portions.
But it was soon found that many never succeeded in getting far away from home. It is true that there were those who, untrammeled by tradition, precedent, or authority, made bold excursions into the regions of the unknown, and returned richly laden with spoils, but these were the few; the many were found to require guidance and support for some time before they became able to carry on explorations on their own account.
The underlying principle of the new method was correct and must survive, but it was a mistake to give it universal and unrestricted application. The earlier and indeed much of the later instruction in physical laboratories was tinctured with this error.
By many we were advised that the proper course to pursue was to put into the hands of the student who, in many instances, had little or no previous knowledge of the subject, a few pieces of simple apparatus and expect him to rediscover for himself principles of physical science which, although now commonplace, were at one time as completely surrounded by difficulties to the human mind as are now, for instance, the principles of the dissipation of energy and the vortex theory of atoms.
The result of the crude experiments of the student was often to disprove the law which he was expected to establish; for he lacked that knowledge and training which would enable him to take into consideration the influence of secondary causes and conditions, and to determine or properly interpret the errors of experiment. Something was gained, it is true, in the way of familiarity with the methods of manipulation, but very little in the acquisition of real knowledge.
Even if this method of instruction be made reasonably successful, the actual information concerning natural laws which the student obtains must be largely superficial, often erroneous, and the rate of acquisition extremely slow. Far better would, it be for him to begin his so called practical study of the subject after becoming tolerably familiar with its general outlines and prominent features through the study of some reliable text-book, and especially after having armed and equipped himself with such a training in mathematics as will enable him to discuss understandingly the results which he obtains, to consider the limitations to which they are subjected, and the influence which has been exerted upon them by errors of various kinds.
In this matter, as with most others, we are likely to fall into extreme views. Some of us maintain that experiment alone is the key, by the use of which Nature's mysteries are to be explored, and we fortify our belief by pointing to Faraday, the greatest experimental philosopher the world has yet produced. We forget that Faraday was ignorant only of the outward, conventional symbols of mathematical reasoning, and that one of the greatest works on mathematical physics, by one of the greatest mathematical physicists of modern times, is confessedly but little more than his interpretation.
Dazzled by the success of the leaders and representatives of another school, we proclaim that true success will depend on mathematical attainment, and that mathematical physics is the only physics worthy of the name. Here, again, the exceptionally brilliant few, who have succeeded under this training, stand as its exponents, and we fail to consider that, if adopted to the exclusion of the first, its results may be disastrous in the extreme. No better evidence of this need be furnished than is found in the remarks recently made by Mr. G. H. Darwin, concerning a contest for honors, in what is generally admitted to be the greatest school of mathematics and mathematical physics in existence. Mr. Darwin, who was one of the examiners, says: "The subject which exhibited the average weakness of grasp most flagrantly was thermo-dynamics. A great many men had read something of it, but very few really understood what they attempted to explain. Extraordinary muddle and confusion was sent up in answer to a question on the absolute scale of temperature. On another question, while the very elements of the subject were unknown to those who answered, the same men reproduced faultlessly the algebraic calculation of the thermo-dynamic function for a perfect gas."
Mr. Darwin also strongly recommends such a change in the style of questions as that half intelligence may be more stringently treated, and men induced to read less and master more, and to gain a comprehension of physical principles.
There can be little doubt but that the experimental and mathematical study of the subject should go on together, assuming, of course, a sufficient preliminary training in pure mathematics.
What seems desirable, therefore, at least in some instances, is less experimental work on the part of the student, and more thorough and exhaustive discussion and examination of what is done.
This leads at once to the consideration of what ought to be the nature of the work done in the laboratory. The limits to which I am confined will not allow me to enter into any lengthy discussion of this important question.
I will remark, however, that in my opinion there is much done which is neither desirable nor necessary. As a rule, quantitative work alone, and that the best possible under the circumstances, should occupy the time of the student. I would relegate to the lecture-table of the instructor all illustrative experiments and qualitative work necessary to a good understanding of the underlying principles of the subject, which every student should possess when he enters the laboratory. That which he gets which is of most worth in his course in a physical laboratory is not a familiarity with the principles of the science, but a training in the methods of investigation in use among physicists, including a knowledge of the use and abuse of experiment and the necessary limits of our knowledge derived therefrom. The study which he ought to make of errors, instrumental and accidental, will be of great value to him in other fields than this.
As an illustration of the lack of this sort of training, I may be allowed to mention a lecture to which I listened recently, delivered by the chief engineer of one of the leading railroads in the country. The subject was the "Great Pyramid," and in speaking of certain measurements taken in the interior he declared the results, which were given in feet, inches, and thousandths of an inch, to be absolutely accurate, taking especial care to disclaim anything in the nature of an approximation.
I need hardly explain that he was declaiming against the introduction and adoption of a system of metrology which has done and will continue to do much to increase the simplicity and accuracy of all measurements.
I have said that this quantitative work should be of the best quality possible. It is better for the laboratory to contain a few instruments of real precision than a large number of inferior performance and accuracy. It is not a matter of great importance upon which particular department of physics a student shall spend his time and strength. The underlying principles of this method of study are common to all, and it is a matter of experience that when a student has successfully accomplished a tolerably exhaustive investigation of one topic, involving, it may be, but a single instrument with its accessories, he is upon his feet for the remainder of the course.
To sum up, the course of study in physics for the undergraduate collegian, which I have tried to indicate, should include a sufficient training in mathematics to enable him to apply his knowledge with ease and facility to the more common physical problems; a thorough and exacting course of text-book and lecture-work, in which the application of his mathematical knowledge would be made, and during which all illustrative experiments necessary to a complete understanding of the text should be exhibited by the instructor from the lecture table; and, finally, this to be supplemented by a course in the laboratory in which more attention is paid to the quality than to the quantity of work done; during which every problem is discussed, as far as possible, both mathematically and experimentally, and especial attention is given to the discussion of the results of experiment, and of the more elementary portions of the theory of errors.
Considering the work as thus divided into three parts, I am unable to see which is the least essential.
I desire to say a few words in regard to instruction in physics in the school, about which we are, apparently, more remotely concerned. Even greater reform is demanded in this direction than in the other. Although there are numerous American text-books, I venture the remark that none have properly combined, in their making, the experience of the class-room with the critical knowledge of the scholar. We may import them from Europe, it is true, as we must also our more advanced text-books, but, although in the main vastly superior to our own, they are still not entirely suited to the wants of American schools and American pupils. These books, in the hands of teachers who know little or nothing outside of the books they use, and often falling far short of that, serve to put the instruction in elementary physics in this country in a condition over which no one can grow very enthusiastic; and this, in spite of the prominent place which has been given it and the considerable attention it has received. Unsound doctrines and absurd theories are promulgated because of an inability to distinguish the ring of genuine metal. These become so deeply rooted that it is difficult and often impossible in after-years to clear them away.
I believe it to be possible for this Association to exert a strong influence in favor of an improvement in the character of the instruction in physics in both elementary and higher institutions of learning in America. Much of it at present does us no credit, and must eventually do us much harm. At a meeting of this Association in Nashville, five years ago, a committee was appointed to report upon science-teaching in the public schools. At the Boston meeting, two years ago, this committee presented a report which embodied much thought upon the subject, and was replete with just and keen criticisms of present systems. It is greatly to be regretted that this report can not have found its way into the hands of those whom it would most benefit. A wide distribution ought to have been secured, and I am convinced that it is not yet too late to remedy this error.
The same gentlemen were continued as a committee to report upon the "Best Method of Science-Teaching in Public Schools," and it is to be hoped that a scheme may be presented at no distant day. I will venture the opinion, however, that the best results will not be obtained until this, or a similar, committee shall work in co-operation with representatives of the public schools themselves, and I would suggest the feasibility of securing such co-operation through the National Educational Association.
No such difficulty is in the way of securing an improvement in the teaching of physics in colleges and universities, for those most interested are, in the main, a part of this Association and of this section.
I will not venture to suggest in what manner the Association might best make itself felt in this matter, although I think that would not be difficult to ascertain. I have only endeavored to direct attention to some of the salient features of the problem, and to ask its consideration at the hands of many members of the section who come in almost daily contact with it, and who will, I am convinced, sustain me in the belief that it is not unworthy to be brought before this body.
In preparing this discussion of the subject, I have not had access to such information as would have been desirable concerning the work which is being done in many institutions, nor have I been able to consult with others who are especially engaged in its management. Indeed, it was this very lack of accessible information, this very impossibility of personal consultation, with which I met in the outset, that convinced me of the importance of directing the attention of the section to the subject.
What the section could do in the direction indicated seems to be tolerably clear and certain. Whether it is wise or desirable that it should undertake to do anything is a matter which I willingly leave for it to determine.