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this for the instructor, but it is the only way to good results.

Teach the consideration of accuracy as a relative matter. Let the effect upon the result of an error in the work or in the conditions be determined. Give short methods, teach quickness and correctness in operations, and make a trustworthy computer.

But the difficulties do not lie wholly in the instruction; the fault lies largely in the student himself. If only the dreaded tradition about mathematics could be overcome, the remainder of the task would be easier. Get out of the student's mind the idea of a bugbear and let him see its importance and usefulness. The elements of these branches and their use are not difficult to acquire.

But the teaching of mathematics must go beyond its first presentation. The professor of pure mathematics must not be charged with the whole responsibility. The average student may forget the best training and declare that he never heard of some precept which has been fairly hammered into him. It is the privilege and duty of the instructor in many of the later subjects in a technological course to supplement and strengthen the student's mathematical equipment. The application to the varied technical subjects and the wide range of field and laboratory work gives ample opportunity for this, and repeated references should be made and drill given in mathematical matters previously treated. It is a mistake to assume that since the student has passed his previous examination, no further study of the subject need be made, and the various instructors should feel the responsibility. The writer's observation indicates that the value of this training is quite generally felt and and that good results are shown.

The teaching of mathematics bears so important a part in the training of the engineer that it should be carefully discussed. It seems not to have kept pace with the improvement in technological education. The text-books generally used have not been written with the engineering student in mind. Many of the teachers of mathematics are not engineers—although engineering graduates. But they are usually workers, and their aid has been invaluable in the training of that grand body of young men who are such an honor to our engineering schools and to the engineering profession.




Director of the Rensselaer Polytechnic Institute, Troy, New York.

The number of topics into which the general subject of engineering education has been divided for purposes of discussion at this conference necessarily restricts each paper and confines it within narrow limits. A general treatment of the subject to be here considered would permit, and perhaps demand, a careful historical review of the development of the methods of education of the engineer in this and other countries. Again, an enunciation of the writer's idea of the ideal engineering education and a comparison with the methods at present in vogue would be a rational method of treatment of the special heading to which he is confined. But since both the historical review and the ideal education are special topics for which provision is elsewhere made, it would not be proper to develop the subject from either of these standpoints. In fact the general scheme of the conference and the method of sub-division wisely provide that the matter presented should be of the nature of concise opinions within narrow prescribed limits, rather than general papers in which repetitions would naturally often be found.

It is not necessary here to prove the wide acknowledgment of the value of a technical training, as well for persons desiring to prepare themselves for business pursuits as for those intending to confine themselves strictly to professional work. Nor are we called upon to discuss the relative values of a classical and of a scientific education as a preparation for a business life. The youngest of us here remembers how many of the academic schools were unwillingly forced to add scientific departments in compliance with public demand and that it took years for some of them to look upon these additions as other than unwelcome though necessary attachments.

It is not the want of appreciation of the value of scientific knowledge but the admission of its usefulness which brings to our consideration an unfavorable tendency in engineering education. Some universities and colleges throughout the country are adding engineering courses without making proper provision for their maintenance. This arises, on the part of the authorities, partly from ignorance of what constitutes an engineering school, and partly from a desire to increase the number of their students without having sufficient capital to provide properly for their instruction. With the “university' bee buzzing in their bonnet they inaugurate a series of departments, for most of which no proper provision is made, and the cause of engineering education suffers with the rest. One such “university'' gives three engineering courses and two other scientific

courses with six instructors. Another school gives four engineering

courses and one course in natural science with seven instructors all told. In another a professor and assistant give the pure mathematics and civil engineering Other such examples could be given. In consequence of this instruction, or want of it, deluded students are graduated each year who labor under the belief that they have obtained an education which fits them for the practice of their profession. In many cases the knowledge imparted has qualified them to act only as country surveyors. Speaking now, not as au instructor but as an engineer, the writer wishes to unqualifiedly condemn such practices as a far reaching injury to the profession, and he would impeach the honesty of those who send broadcast over the land young engineering graduates who are not only wanting in knowledge of the fundamental principles of engineering, but who are unaware of their own ignorance of the subject.

This brings to our minds another tendency, having a different origin, but which acts in a lesser degree, to produce the same result. The opinion is often expressed that the practical engineer in his ordinary work never has occasion to use the higher mathematics; that his calculations are confined to the simple operations of geometry, algebra, and trigonometry. Does the skilled designer and constructor of difficult foundations, it is said, differentiate to find the depth to which he will sink them? Does the computer of stresses in the pieces of structures integrate to find them? Can you not proportion a sewer or determine

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