Scientific Culture, and Other Essays / Second Edition; with Additions

by Jr. Josiah P. Cooke

Of course, the faculty of observation thus early exercised in childhood only attains the highest degree of development after long experience and continued practice. The acuteness which practice gives is frequently very remarkable, and rude men often surprise us by the extent to which their power of observation has been cultivated in certain special directions. The sailor who recognizes the outlines of to him a well-known coast, where the ordinary traveler sees nothing but a bank of clouds, or the miner who recognizes in the rock indications of valuable ores, are illustrations which may give a clearer conception of the nature of the power we have been attempting to describe.

Naturally following the power of observation in the order of education is the power of conception with the cognate power of abstraction; that is, the power of forming in the mind distinct and accurate images of objects, and relations, which have been previously apprehended either by direct observation, or through description; and also the power of confining the attention to certain features which these images may present to the exclusion of all others. This is a power which depends very greatly on the imagination and is capable of being cultivated to a very high degree. There is no study which is so well suited to the training both of the powers of conception and of abstraction as the study of geometry.

To this end the study of geometry should be begun at an early period in school-life, and it should be studied at first not as a series of propositions logically connected, but as a description of the properties and relations of lines, surfaces, and solids—what has sometimes been called "the science of form." A text-book prepared on this idea by Mr. G. A. Hill forms an admirable introduction to the study.

I esteem very highly the system of geometry of Euclid, either in its original form or as it has been modified by modern writers, as a means of developing the logical faculty. The completeness of the proof of the successive propositions and their mutual dependence by means of which, as on a series of steps, we mount from simple axiomatic truths to the most complex relations, furnish an admirable discipline for the reasoning power; but too often the whole value of this discipline is lost by the failure of the pupil to form a clear conception of the very relations about which he is reasoning, and the study becomes an exercise of the memory and nothing more. Often have I seen a conscientious and faithful student draw an excellent figure, and write out an accurate demonstration, without noticing that the two were not mated; and in a recent meeting of teachers of our best secondary schools it was gravely asserted that solid geometry is the most difficult study with which the teachers had to deal. In solid geometry, however, the reasoning is no more difficult than in plane geometry, but the conceptions are far more complex, and, if the teacher insisted that the pupil should not take a single step until his conceptions were perfectly clear, all the difficulties would disappear. Of this I am fully persuaded, for I have had to encounter the same difficulties over and over again in teaching crystallography. In beginning the study of geometry, of course the power of conception should be helped in every possible way. Let your pupil find out by actual measurement that the sum of the angles of a triangle is equal to two right angles, and he will easily discover the proof of the proposition himself. So, also, if he actually divides with his knife a triangular prism made from a potato or an apple into three triangular pyramids, he will find no difficulty in following the reasoning on which the measurement of the solid contents of a sphere depends. Let me assure teachers that the study of geometry, taught as I have indicated, is a most valuable introduction to the study of science. But, as it has been usually taught as a preparation for college, it is almost worthless in this respect, however valuable it may be as a logical training.

I consider practice in free-hand drawing from natural objects a most valuable means of training both the power of observation and the power of conception, besides giving a skill in delineation which is of the greatest importance to the scientific student. Accuracy of drawing requires accuracy in observation, and also the ability to seize upon those features of the object which are the most prominent and characteristic. Hence, in a course of scientific training, the importance of practice in drawing can hardly be exaggerated, and it should be made one of the most important objects of school-work from an early period.

To the scientific student the powers of observation and conception are not sought as ends in themselves, but as means of studying Nature. The precise portions of this wide field to which the attention of the student shall be directed will be determined by many circumstances, and it is not our purpose in this address to lay down a plan of study. To most students the natural history subjects offer the most attractive field; but all, I think, will admit that the experimental sciences should form a considerable portion, at least, of the course of all scientific students, whatever specialty may subsequently be chosen. That on which I desire particularly to dwell is the spirit in which all these studies should be pursued; and I can best illustrate what I mean by confining my remarks to that subject in which I am most interested, and in regard to which I have the greatest experience.

In a course of scientific study, chemistry can not be dissociated from physics, and the two sciences ought to be studied to a great extent in connection with each other. Not only does the philosophy of chemistry rest upon physical conceptions; but, moreover, chemical methods involve physical principles. There is, however, a distinction to be made; for, while some of the departments of physics are best studied as a preparation for chemistry, there are other subjects which are best deferred until the student has some knowledge of chemical facts. Among the preliminary subjects we should mention elementary mechanics, including hydrostatics and pneumatics, and also thermotics; while electricity, acoustics, and optics, including the large subject of radiant energy, may well be deferred until after the study of chemistry.

In the study both of chemistry and physics there are of course two definite objects to be kept in view: In the first place, a knowledge of the facts of the science is to be acquired; in the second place, the student must learn by experience how these facts have been discovered. It would be obvious, from a moment's reflection, that a knowledge of the circumstances under which the facts of Nature are revealed to the student is essential to a complete apprehension of the facts themselves. The child who is taught that the earth moves in an elliptical orbit around the sun in one year does not in the least grasp the wonderful fact thus stated, and will not come to realize it until he connects the statement with the nightly procession of the stars in the heavens. And it is just such a connection as this which the teacher must seek to establish in all scientific teaching. In experimental science such a connection is most readily established in the mind of the student by means of a series of well-arranged experiments, which each one repeats for himself at the laboratory table. Obviously, however, it is impossible, in a limited course of teaching, to go over the whole ground of chemistry and physics in this way, or even over that small portion of the ground with which the average scientific student can expect to become acquainted. Nor is this necessary; for, after one has realized the connection between phenomena and conclusion in a number of instances, the mind will fully comprehend that a similar connection exists in other cases, and will understand the limitations with which scientific conclusions are to be received.

Hence, it seems to me that, in teaching chemistry or physics, it is best to combine a course of lectures which should give a broad view of the whole ground with a course of laboratory instruction, which must necessarily be more or less restricted. Experimental lectures are, I am convinced, much the best way of presenting these subjects as systematic portions of knowledge. It is not necessary that the lectures should be formal, but it is all-important that they should be given in such a way that the interest of the student should be awakened, and that they should be fully illustrated by specimens and experiments. What we read in a book does not make one half the impression that is produced by the words of a living teacher, nor can we realize the facts unless we see the phenomena described. There is undoubtedly an advantage to be gained in subsequently reviewing the subject as presented in a good text-book, and such a book may be of great use in preparation for an examination. But how far examinations are of value in enforcing the acquisition of knowledge of an experimental science is a question on which I feel a grave doubt. Certainly their value is very small if, as is too frequently the case, they lead the student to defer all effort to make his own the knowledge presented in the lectures, until a final cram.

The management of lectures, text-books, and examinations, will not, however, offer nearly so great difficulties to the teacher as the management of the parallel experimental course of laboratory teaching. In the last the methods are less well tried and demand of the teacher a very considerable amount of invention and experimental skill. To follow mechanically any text-book would result in a loss of the proper spirit with which the course should be conducted and which constitutes its chief value. No experiments are so good as those which have been devised by the teacher, or, still better, by the pupils themselves. A mere repetition of a process, according to a definite description, has no more value than a repetition of a form of words in an ordinary school recitation. The teacher must make sure that the student fully understands what he is about, and comprehends all the connections between observations and conclusions which it is his aim to establish. Moreover, he must constantly encourage his students to think and work for themselves, and direct them in the methods of inductive reasoning. The failure of an experiment may be made most instructive if the student is led to discover the cause of the failure. A leak in his apparatus may be turned to a similar profit if the student is shown how to discover the leak, by carefully eliminating one part after another until the weak point is made evident.