courses, and my feeling has been in connection with the school where I am located, that just at present the mathematician stands almost nowhere. He can classify himself neither in the science department nor in the engineering department. The people in the science department talk of zoology, of chemistry and things of that kind, so he doesn't belong with them; the people in the engineering department look at him askance. They will not own him because he is visionary and impractical. He wastes the time of his students. Much that he does must, in their opinion, be undone. And so the mathematician has no place to put the soles of his feet. I think, however, the tendency is to divide the mathematical departments, forming a section on one side which shall teach mathematics from the standpoint of the liberal arts, and a section on the other side from the standpoint of engineering.

PROFESSOR C. FRANK ALLEN: Apparently there is opportunity for discussion upon the matter of the standpoint from which descriptive geometry shall be taught. The tendency of the institution with which I am connected is in the direction of making descriptive geometry a part of drawing and teaching from the drawing side rather than from the mathematical side, and there are many other institutions in which the same course is pursued. I did not rise for the purpose of saying this point of view is the correct one, but I do wish to say it is a point of view that does prevail to a considerable extent; and there does appear a good deal of reason and belief that it may be right from the fact that great success does attend the teaching of descriptive geometry from that standpoint; I presume that is

a sufficiently disputed point so it may not be well for us to waste a large amount of energy at this time in discussing that particular feature. It would perhaps be better to leave it as one of the disputed points, and possibly later we can take it up and thresh it out.

PROFESSOR A. N. TALBOT: I merely want to second the suggestion that in any institution the department of mathematics in so far as it affects the engineer should be in the department of the college or school of engineering. The man at the head of the department should be a part of the engineering school and should be a thorough engineer or a man who is in sympathy with engineering training.

PROFESSOR SWAIN: The point I made was that the teaching of mathematics should be the same for all students. I am unable to see why we should have different ways of teaching students of engineering from the methods followed in teaching students in college.

PROFESSOR WALDO: If I may answer briefly, my sympathies, of course, have been for a good many years in the line of trying to make mathematics understandable by giving it physical illustration from the beginning, and I do not know that I have any objection to saying that for the kind of elementary mathematics required of students in the so-called liberal arts course this is also the best method of treatment. But much of modern mathematics which enters into the equipment of the well-read pure mathematician can have no possible physical representation. Here, of course, some other treatment is necessary.

PROFESSOR SWAIN: I do not think I made myself clear. I agree that there are certain parts of mathematics which the engineer does not need; but why should there

be a difference in the method of teaching mathematics in one class from that in another? That I cannot understand.

PROFESSOR FORD: There was one point made, and that was the question of thermo-dynamics. The reason I put it in physics was that it is required not alone by the steam engineer, but by the chemist.

PROFESSOR SWAIN: While I do not teach mathematics, if I did I should teach it in the same way to any student who had the same preparation, whether a civil engineering student or a student of any other branch, though I do not mean to say that I should teach the same portions of the subject to all students. I further wish to urge here the importance of training the imagination, and the great advantage in this direction that is possessed by the study of descriptive geometry. This branch trains the imagination as few mathematical branches do, and imagination is one of the most important faculties of the engineer. Many engineers lack this faculty in great degree. It can also be trained in the analytical branches of mathematics, if the student is required to interpret his own equations, and, as it were, visualize his results. The distinction which Leibnitz made between knowledge that is intuitive and knowledge that is symbolical is of great importance. I think the great trouble in mathematical courses as they are taught, especially in colleges, is due to the idea that they should be taught simply as a means of so-called mental training, without any idea of ever using it. Most of the men who study it in this way, when they have completed their course, find themselves powerless to make any use of what they have studied.

PROFESSOR H. P. TALBOT: I am not quite sure that I

clearly understand Mr. Ford's point of view with respect to the chemical instruction for chemical engineers. It must be confessed that chemical engineering is a profession which has not yet fully taken shape, and it is a little difficult to properly define what belongs to it. The chemical engineer has, I believe, been defined as one who is not only familiar with the written chemical equation and its meaning, but has also the ability to ultimately surround that equation by a plant, thus endowing it with productive capacity, so to speak. Such a man, it seems to me, must be primarily a chemist, and must have received a fundamental training in that science, together with so much of the training of an engineer as the available years will permit. Assuming the truth of this, it seems to me that the chemical instruction, because it is of such prime practical importance, should rather be under the general supervision of those more closely in touch with engineering and technical interests than is often the case in the university; that is, as has been said in regard to mathematics, the instruction should be given with due reference to the ultimate use which the student will make of the information acquired. Such instruction must include a liberal amount of pure science and chemical theory. What has been said applies less directly to subjects of this character than to analytical, organic or technical chemistry.

PROFESSOR FORD: The contemplated relation of the department of chemistry to that of chemical engineering is the same as that of physics to mechanical or electrical engineering, namely, the former concerns itself with general chemical phenomena and theory, while the latter concerns itself with the application of these laws to chemical manufacture.

ENGINEERING INSTRUCTION IN LARGE TECH

NICAL SCHOOLS.

BY HENRY H. NORRIS,

Professor of Electrical Engineering, Cornell University.

The rapid growth of the technical schools throughout the country has forced upon those responsible for their success a more careful study of the conditions governing the efficient instruction of large numbers of students. A pedagogical plan which is perfectly satisfactory with a small student body, utterly fails when the classes become larger.

Most of the technical schools are now facing this problem and the purpose of the present paper is to bring about a discussion of this important topic.

A number of salient facts in this connection are as follows:

1. The bulk of technical instruction must be given in large schools. This follows from (a) The expensive equipment necessary; (b) the expensive corps of specialists required; (c) the attractiveness of the large schools to the students. As evidence of this proposition it is only necessary to cite the unprecedented growth of the large schools.

2. The efficient instruction of large classes is difficult. Teaching cannot be done in a wholesale manner. Members of very large classes are apt to lose many advantages of smaller groups. Some of the losses are: (a) Personal contact with the mature members of the faculty; (b) coordination of the several courses of the curriculum; (c) ample facilities for laboratory work.