XII. MATHEMATICS.

To the President:

Sir: I have the honor to present herewith my report for the Department of Mathematics.

This Department has, during the past year, (a) maintained the instruction in the regular mathematical course. (b) We have taught the regularly assigned work in algebra, geometry, trigonometry, analytics, calculus, differential equations, subjects taken in whole or in part by students of all courses. (c) We have given the four courses in the Summer School in algebra, geometry and trigonometry. (d) The Department has assumed or been assigned three other courses in applied mathematics as special work for this year only-and extra hours in a fourth subject.

The total number of hours taught and the average number of hours per week per man has been greater than in any previous year.

The personnel of the instruction force is the same as at the time of my last report. During the fall, however, it was found necessary, as in years back, to engage temporary assistance.

The College was fortunate in being able to secure the services of Mr. J. Frank Shields, on leave of absence from the Adelphi College, Brooklyn, N. Y., to fill this position. Mr. Shields' departure was regretted by every member of the Department. It is a pity that the College is not in a position financially to make, if necessary, a permanent place for such a man. If possible, as our classes increase, the position should be made permanent for the good of the Department also. Mr. Louis L. Ansart, who has been at the College as a private tutor in mathematics, has been assigned occasional hours and has served us faithfully and satisfactorily.

The greatest difficulty met with in our work is the inadequate preparation of students in algebra and geometry.

Some students of course fail to make standing through no fault of their own. They perhaps do not have the advantages of high school or academic education, and are untrained in habits of study and expression.

But the main need is for more general thoroughness in preparation. Half the year and more is spent in doing work which ought to have been done in the preparatory school. In algebra, for instance, there is not so much a lack of ground covered as that a large number of students are absolutely unable to perform the ordinary and fundamental processes such as factoring ordinary problems, extracting

roots, solving quadratic equations and manipulating equations containing radicals, when met with outside of a book.

In

A second great need in our work is an increase in our library. the early history of the College apparently an attempt was made to start a mathematical alcove, but in late years the appropriations that could be made have been entirely inadequate to meet the needs of a rapidly growing Department. The books we have are put to good use by the young men but they do not cover the ground, and of some we ought to have duplicate copies. It is quite impossible to ask a class of seventy-five to consult a single volume before the next day, much less to compare it with books at the Physics or Engineering Buildings and expect it to be done. But further than that, the ordinary reference books are not at hand which we need for our work. It is certainly the part of economy to provide liberally for large bodies of students, and to put in the way of teachers every means of illustration, for every hour saved in explanation is money in the College treasury. Summer courses were conducted in algebra, geometry and trigonometry. A few students were present but, so far, the teachers of the vicinity have not realized how much of an opportunity the College has thrown in their way by opening its halls and turning over its laboratories and a good share of its teaching force to their use. The work done in the courses last summer was very creditable, and I think satisfactory to those who pursued the courses.

The time has come when students in the Latin science, chemical and biological courses are sufficiently numerous to justify making a separate section of the freshman class for their mathematical work.

The needs of students pursuing these courses are quite different from the needs of those pursuing engineering subjects. The College has been unable thus far, to provide separate work for these men. But now that their number is such as to make it probable that a separate section will be formed each year, we have set oureselves to the task of laying out such a course. The plan is not to change in any way the assigned hours but by cutting out some work and strengthening other work, to arrange a course better adapted to the wants of such students. The members of the Mathematical teaching force have had several conferences during the last session on this subject, and will, I believe, be able to present a definite plan to the various schools concerned and to the Trustees for revision before the opening of another year.

In this connection I wish to say that I hope in the near future that solid geometry will be required for entrance, at least for engineering students. It would very much simplify the making out of a separate couse of mathematical work for non-engineers and would certainly be the best, as I believe it to be the only, remedy for the congestion in the Fall Term of the freshman year.

Several students each year take examinations for advancd stand

ing, and it is certain that all the time given to trigonometry, analytics and calculus is necessary to enable students to begin mechanics and technical work before the opening of the Fall Session of the junior year. Again, the large number of hours now assigned to students in certain courses makes it all but impossible for them to asimilate so many new concepts as are presented to them, much less to get an adequate training in the practical side, sufficient to enable them without hesitation to solve the mathematical problems ordinarily met with in a professional career.

It would then appear that a demand for a slowly advancing standard of admission is made, by the necessities of the case and by the patrons of the institution, and justified by the example of nearly every first rate technical school in the country.

Of my associates, I can only speak in the highest terms of the fidelity, vigor and intelligence in their work, and to you, sir, and to the Trustees through you, express my thanks for your patient consideration.

Respectfully submitted,

J. M. WILLARD, Professor of Mathematics.

June 1, 1899.

XIII. MECHANICAL ENGINEERING.

To the President:

Sir: I have the honor to make the following report for the Department of Mechanical Engineering for the College year 1898-99. There have been practically no changes made in the curriculum during the past two years and the work has, therefore, followed the same lines as heretofore, with the exception of such additions to the different departments of study as have been required in order to keep up with new developments in machine practice.

The revival of business has made a great demand for technical men, so that not only do our graduates experience no difficulty in securing positions, but, during the past year calls for men have enabled us to offer better positions to those already employed, in this way securing to them either improved conditions of work or more lucrative employ ment.

The success of our graduates has been most gratifying. In certain cases the advancement made during the past year has been phenomenal. Observation leads me more strongly than ever to the conviction that a course in mechanical engineering, properly developed, fits young men for great possibilities. This is true in its fullest sense as, in addition to the technical course itself—which must be as wide as the time allotted will permit, every man is given the broadest possible general training. The ideal preparation for a manager, superintendent or one at the head of any manufacturing enterprise as well as for the engineer, is the acquirement of an intimate technical knowledge of the things which enter into the manufacturing processes, added to the liberal training of a college course.

The tendency to differentiate early in the college work or training between different courses in engineering, is to be deplored. A knowledge of steam, fuel, physics, electricity, magnetism, structural materials, the structure and economy of machines, economy in design, illustrated by shop practice, and of shop methods as secured by practical experience in conjunction with a thoroughly good education, is essential to the training of any engineer-it matters not whether he be civil, electrical, mechanical or mining. It is a common experience to find that the work of a College graduate seems to be more closely allied to some other of the engineering courses than to that in which he was trained. The experiences of certain of our own graduates give striking examples of this fact. Not a few have attained a high degree of success in work that, to the casual observer, would be considered in a line other than that for which they were prepared.

The course pursued in college determines, as a rule, the first position after graduation. After that, nearly every young man's future is governed more or less by circumstances, and his engineering training should be broad enough to meet every demand that is likely to be made upon him in a professional life. The mechanical or electrical engineer should be able to design a bridge or a roof if called upon and the civil engineer should be able to design a machine and should have a full appreciation of the points in pattern making, moulding and casting. Machine design is not one whit less important to the electrical engineer than to the mechanical engineer, and it is also of decided importance to the civil engineer.

Though considerable differentiation is of course essential it is undoubtedly true that, with the present requirements for admission to engineering schools, much beter results would be reached if the undergraduate courses were more thoroughly unified, and if much that is now done as undergraduate work of the "narrowly special" order were left to be done as graduate work, the time being given to subjects which underlie all departments of engineering.

I have tried to show, in previous reports, the desirability of general cultural training for the engineer. It is my present desire to emphasize the importance of a close co-ordination of the engineering courses. This is counter to the tendency narrowly to specialize that prevails in many of our engineering schools. It is believed, however, that the best engineering thought of the present, is tending in the direction here indicated, and further, that the experience of graduates from technical colleges leads to this conclusion. Institutions whose courses are laid out on the basis of close co-ordination are the ones whose graduates are found in the places of greatest prominence and responsibilty.

We believe that the courses offered by the School of Engineering of The Pennsylvania State College rank with those in the forefront; no better evidence of this is needed than the success of our own graduates, yet even here a closer co-ordination of the engineering departments would, I am convinced, give more fruitful results, and, if the College year were to be divided into two sessions, as you, Mr. President, have suggested, an opportunity would be afforded to recast the engineering work so as to improve where needful the sequence of studies and at the same time bring about a closer relation between the work of the different departments.

There is no question in my mind but that a division of our College year into two sessions is desirable. Without affecting the efficiency of the examinations the time consumed in conducting them would be much reduced; the introduction of new subjects would be greatly facilitated; the work after vacation would be taken up with more promptness and vigor; the problem of securing text books on time