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attaining a capacity to submit the acquisitions of the first to the operation of common
and well trained judgment, and thus make them applicable to the real conditions of professional practice. In the latter, the engineer has to treat precisely of the same things as in the former, but not under the same simple conditions nor with the same accuracy of definition. The determinate characteristics of pure theory transform themselves into the most elusive indetermination. Nevertheless, qualitatively they are still the same, and it is the whole essence of modern engineering practice to so control and adapt the laws and quantitative deductions of the ideal conditions of engineering physics as to make them fit with reasonable accuracy its very varying and complicated conditions. That is the highest art of the engineer. There is nothing beyond it, and anything less is crude and unsatisfactory. It is evident from the very nature of this result that its accomplishment can only follow a thorough scientific training in the professional school. There should, however, be made at this point a very sharp distinction between the abstract scientific training of the student in engineering and the corresponding instruction given to the student in pure physics. These two students are acquiring scientific knowledge for two very different purposes, although many portions of the two fields overlap and indeed are identical in many characteristics. The study of pure science requires a wide range of investigation and a thorough knowledge of the inter-relation of all the departments of physics; this includes exceptional facility in the experimental and analytical treatment of all problems under ideal conditions. The student in engineering should also be given a sound elementary grounding in the main departments of physics, but his advanced physical studies must necessarily be limited by the requirements of his future profession. The selection of subjects and the mode of treatment must be governed by the same motive. Whatever he does, should be adapted to his life work, and so clearly and evidently adapted that he can see and appreciate the purpose of his efforts. His powers of investigation and analysis should be developed into a condition of vigor and facility in those directions along which he is to work. In order to accomplish these objects, without which the probability of his marked professional success remote, his mathematical training must be of the best. This point cannot be too strongly insisted upon. It matters little that the engineer is seldom required in his practical life to use the pure mathematics for purposes of investigation. He needs them most urgently in his course of study as affording a foundation for his mechanics and for the subsequent analytical treatment of such subjects as the elasticity and the resistance of materials, hydraulics and the general theory of machines, the theory of bridge structures, water and wind motors, thermo-dynamics and the steam engine, electrostatics and electro-dynamics, and every other branch of engineering physics. These are intensely practical applications of pure mathematics, and engineers cannot hope in the future to attain to a high grade of professional success without facility in their use. They illustrate and emphasize the meaning of the statement that the mathematical and physical portions of a course of study in engineering should be so constituted as clearly to show their relationship to subsequent professional work. There is another advantage gained by mathematical training which is less important only than that just stated, namely, mental discipline of a logical character. If mathematics are anything, they are logical, and no student can intelligently and rationally pursue the study without acquiring close logical habits of thought of the greatest value in his subsequent practice. It is precisely this mental discipline which will give value to his professional advice on the comparative merits of various proposed works to accomplish a given end. It trains him to carefully weigh all evidence for and against any proposition, and teaches him to avoid that common and frequently fatal error of assumption of conditions not known to exist. If every engineer should make as thoroughly critical and accurate an examination of all the governing circumstances of every work he undertakes as is required for the correct solution of a mathematical problem, a great many machines that have been constructed either would have been designed very differently or not at all, and at least a few completed structures would be found in other locations than those they occupy. In short, it it difficult to form any rational conception of a course of study in engineering other than that in which a thorough study of mathematics is the main feature of fundamental strength. Without it, study in engineering is degraded to a mere descriptive superficiality of technique. An intimate relation exists between mathematical and physical science and the professional practice of engineering which is most essential to the well-being of the latter. This principle has clearly been recognized in some of the oldest and strongest engineering schools of this country and Europe, but there are some quarters in which it has not been admitted.
The first of the James Forrest lectures before the Institution of Civil Engineers of Great Britain was recently delivered by Dr. William Anderson (superintendent of the Royal Woolwich gun factory) and its prescribed subject was the “Inter-relation of Abstract Science and Engineering.” The accomplished lecturer, who is an eminent engineer, deplored the well known fact that the engineering profession of Great Britain has in the past clearly disregarded the scientific elements in the education of young men intending to become engineers. He frankly admitted that continental and American engineers had, by pursuing the other course, gained such material advantages over those of Great Britain that the latter had lost perhaps irretrievable ground. At least he maintained that they could never even hope to recover it except by making an advanced and thorough study of abstract science a prominent and indispensable portion of the educational training of young engineers. He did not admit that there could be any alternative; on the contrary, he based his thesis squarely on the present condition of engineering practice in the United Kingdom, and con
tended that the results demonstrate the positive necessity of abstract scientific knowledge to the engineer. On the continent, this has always been true of the German polytechnics and the French professional schools in engineering, and largely so of the most advanced engineering schools in this country, yet there is not entire absence of the danger, that in the fierceness of competition for large numbers of students in the greater universities of the United States, a requisite degree of scholarly excellence may be forced to give place to a condition of things more conducive to a greater number of graduates. Another most significant fact is the late change in the prescribed qualifications for the grade of students in the Institution of Civil Engineers, by which a scientific education is now deemed essential where it was heretofore scarcely or indifferently recognized. These are very important facts; they are not the opinions of theorists nor the erratic and irresponsible utterances of impracticable men, but they are the spontaneous expressions of needs born of a radically different system from that of the ideal engineering education, which is not only consistent with the present condition of engineering practice, but imperatively demanded by it. The engineer without that which such an education supplies, works under serious direct and indirect curtailment of his powers, and they are the more serious because by their nature they are scarcely discoverable by the sufferer. It is one of the commonest matters of observation that the uneducated or imperfectly educated man possesses, in general, but crude powers of observation and interpre