examinations are decided pedagogic aids in engineering courses. Perhaps they are not needed in the lower grades. Professor Kent says he never heard until recently that examinations were too great a strain on the intellect. If you will go back several years in our proceedings you will find that there have been numerous discussions on that subject. But apparently we all think now that examinations are good things, though we do not all hold the same reasons for our beliefs.

DESCRIPTIVE GEOMETRY-ITS IMPORTANCE IN THE ENGINEERING CURRICULUM AND THE METHODS OF TEACHING IT.

BY OTIS E. RANDALL,

Professor of Mechanics and Mechanical Drawing, Brown University.

Since projection has been universally adopted as the medium of graphic representation, and since this medium is so extensively used in engineering practice, everyone admits that the student of engineering should in some way or other acquire a working knowledge of the fundamental principles of the system. But whether the study of pure descriptive geometry, which of course deals with the fundamental principles of projection, is absolutely necessary or at least worthy of the assignment of so much space as is usually given in engineering curricula, and what are the best methods of treating the subject, are questions upon which there are differences of opinion.

The direct or apparent results of the study of descriptive geometry, the ability to intelligently and skilfully use the various forms of projection in the representation of magnitudes of great complexity, is only one of the advantages derived from such study. The unique and vital part which the study of descriptive geometry plays in the development of the mind is the one thing which makes the subject of such importance in the engineering curriculum.

There is a tendency in the modern engineering schools to lay stress upon those courses which are

practical in nature, which supply the student with needed information, but without requiring mental effort or resulting in mental development. We are inclined to forget that intellectual development is the prerequisite of breadth of vision, depth of insight, and soundness of judgment, qualifications without which a man will make poor use of the best of opportunities.

The nature of the material with which the subject deals and the character of the medium through which the subject is approached and treated, a medium which differs radically from the usual pictorial method of representation and which requires the simultaneous observation from a number of standpoints of magnitudes and the operations performed upon them, calls for a form of mental exercise whose value is seldom appreciated.

The study of descriptive geometry greatly increases the power of comprehensive thinking. The power of concentrating the thoughts upon a single matter to the exclusion of all others is of great value and is rightly regarded as a sufficient reward for years of study. But this power is often acquired at the sacrifice of another equally rare and sometimes more valuable power, the power of simultaneous consideration, comparison, and combination of the numerous parts of which a whole may be composed.

These parts are frequently so closely related that it is not safe to consider any one apart from the others. Of course our system of projection enables us to place upon a single sheet many views of the same object and through this medium to comprehend

at a glance the nature relation and combination of the various parts which make up the whole, but frequently in the field of design, before the design has reached the stage where it can be represented on paper, or even in model, the mind is called upon to consider simultaneously the details of a large assemblage of parts. The importance of this power in the realm of thought is not confined to the field of engineering but should be recognized in all branches of analytic and synthetic work. Is there any subject the study of which can do more toward the development of this altogether too uncommon power than descriptive geometry? Many men to-day who use this power with so much freedom and find it such a valuable possession, little know how much they owe to the study of descriptive geometry. The practical results of such study, valuable as they may be, are small in importance when compared with the subtle influence which the oft-repeated and still fruitless efforts to understand had upon the development of the mind.

The classroom work connected with the study of descriptive geometry, when properly conducted, furnishes unique practice and dicipline in vocal expression of thought. Practice in word expression of ideas which are easily and definitely formed in one's own mind and which are more or less understood by others, is of daily occurrence, but practice which comes from the attempt to express in correct and intelligible language that which is intangible and difficult of expression is uncommon but most valuable.

The real worth of the study of descriptive geom-. etry depends very largely upon the way in which the

subject is taught. If the student is simply to sketch upon paper and in a conventional way the various views which he may obtain of an object from a number of standpoints, he will acquire little more than a very convenient method of representation, the value of which is comparable with any manual skill which comes from years of practice, and which is not an expression of intellectual effort. If this is all we wish to secure from such study, the student would do better to omit the courses in solid and projective geometry and enter at once upon the work of machine drawing, as is frequently done, or better still go directly to the drafting room of the manufacturer. But statistics show that men of this training seldom rise above the subordinate's position. They soon reach the point where the undeveloped and unimaginative mind fails to supply the material for future growth.

Concerning the best method of treating the subject, it would be impossible to formulate a universally applicable method of procedure owing to the widely differing circumstances under which the subject must be taught. The writer simply offers the following suggestions which are based upon his experience for the last twenty years.

The preliminary training of the student of descriptive geometry should include thorough courses in plane and solid geometry, elementary mechanical drawing, and freehand drawing. A knowledge of plane and solid analytic geometry is very desirable but owing to the fact that descriptive geometry must come early in the college course it will rarely happen