does not have a broad training in general engineering.

Students in that course have always had physical laboratory practice, and now should have the advantages of the new engineering laboratories so far as they are able in the time allowed. It appears probable that the course would be much improved if a student could take four years and thus broaden the general engineering training. So far as can be learned, the theoretical training in Naval Architecture is much like our own in quality and extent, and somewhat more time has been given to ship ́design, though it is not certain that a correspondingly better training is given. The advantages and disadvantages of having the course under a distinguished practising naval architect have already been discussed.

The particular advantage that this course presents is the good opportunity it presents for parallel work in the profession on the so-called "sandwich" system. A Scotchman who has made himself familiar with their course and our own expressed the idea that we taught more and they gave better practical training. It should be considered whether the Institute cannot in practice obtain that every student in Naval Architecture shall get practical training in shipyards during the summer, and see that opportunities are provided; it may be said that many of our students have taken that course, and that no instance is known in which the opportunity was lacking.

The English technical colleges all have three-year courses, but in general have fairly long terms. The Armstrong College, for example, has about eight months. They have developed to a large extent the tutorial system, and in particular arrange to have students solve numerous engineering problems of graded difficulty in the drawing-room under the eye of the instructor, who is not very likely to help them too much, as the classes for that kind of work are large. This method has an advantage over handing in problems in that students must in all cases do each one his own work, and there can be no question of improper or undesirable assistance.

Of all the courses examined, the one that appeared to show

the greatest similarity to our own was that at Berlin, though there must be some reserve in such a statement, for the national differences are marked and none of my acquaintances has taken the course there. If the resemblance is real and not superficial, it is most interesting, because American and German technical schools seem to have started from diametrically opposite educational ideals. It is perhaps not too much to say that New England colleges and all that pattern after them began as exalted district schools in which definite tasks were set in textbooks and truths were driven home by good disciplinarians. Much that is good in that system remains, though we use the lecture system where desirable and broaden the choice by options when possible. The Germans, though committed to lectures by doctors who speak with personal authority, and though adhering to the form of academic freedom, have practically confined students of engineering to the comparatively narrow path which experience has indicated as essential to an engineering education. The general belief appears to be that young men come to the technical schools better trained, and especially in Mathematics, though of this I have no direct evidence. The ideal of academic freedom appears even yet to have some adverse influence on the efficiency of teaching, especially in engineering laboratories, where work can best be done by groups. The requirement of extensive experience in shipyards and engine works is a step further than either British or American colleges have been able to go. The amount of drawing and design, especially if we include the Diplom-arbeit, is much more than we can obtain or desire to obtain from our students.

Since the German naval constructors are drawn from graduates of the schools at Berlin (or Danzig), it is proper to compare with their training our Course for Naval Constructors. In such a comparison it should be borne in mind that the officers designated for instruction at the Institute have had four years at Annapolis of severe drill that covers a wide field, after which they have two years at sea, and then come to us for three

years. In the three years at the Institute they have the theoretical work of our regular Course in Naval Architecture, together with Applied Mechanics, Steam Engineering, Dynamics of Machines and Marine Engines, and also an extensive course in Electricity, with laboratory practice. There are also advanced courses in Mathematics. The work accomplished in warship design is believed to be at least as good as that given at Berlin to students who elect that branch of their profession. A very important part of the training for constructors is obtained during the summer vacations at the electrical works and steel works.

As was pointed out in the description of the course for naval constructors at the Royal Naval College, their main source of supply has been from the dockyards apprentices, with a supplemental supply from men who have undertaken a course for naval engineers. These men, especially the dockyards apprentices, have good practical training before coming to the colleges, and there is less reason for supplementing it than exists at any other college for naval constructors; nevertheless, they have considerable laboratory work and are drafted into the dockyards in summer. The standard in Mathematics is purposely put on a par with that for honor men at the Universities, a fact which appears to be an element at once of strength and of weakness; of strength, in that there can be no question that the graduates of the school can grapple with any problem that will yield to mathematical treatment; of weakness, in that the desire to make the standard equal has tended to make it identical with that at the Universities, and in consequence apart from the proper engineering ideal. The teaching of Applied Mechanics. and Steam Engineering is under revision, and is likely closely to resemble our own. My impression is that the work in electricity is better at our school. Warship design is carried on with the advantage of supervision by a constructor who is in active service, with, however, the consequence that the instructor must change from time to time.

The course for naval constructors at Paris is at once very theoretical and much cumbered with descriptive lectures, which go into the minute details of materials, tools, and processes which could better be learned at navy yards. There can be no question of the mathematical training of the students, but their facility in Mathematics appears to lead them occasionally to fill lacunæ in reasoning and information with mathematical operations, as will be found in many works on Naval Architecture by men in the corps of constructors. They have no laboratory work at the École d'Application du Génie Maritime and but little at the École Polytechnique. At the present time they have some shop work, as was stated in the description of the course. They have extensive lectures in electricity, but mainly of a theoretical nature. During the summer they inspect work in dockyards and make written reports, The warship design and engine design is carried through in a thorough and systematic manner.

In conclusion, it may not be too much to assert that our courses for private students and for naval constructors need not fear comparison with those of any college. And, further, it may be said that there appears to be no reason why any American should go abroad to study Naval Architecture, even though it be admitted that residence at a foreign school or university has distinct advantages in giving variety and breadth of education, and for that and other reasons has always been favored by our faculty for men seeking an advanced degree, even when we are prepared to offer equal facilities. To be specific, attention may be called again to the fact that the English and French governmental schools are not open to foreigners. On the other hand, the policy of the German technical schools appears purposely to make the acquisition of the degree of doctor of engineering so difficult that a disproportionate effort and time would be required by an American, even if he did not find the language an additional obstruction. The University of Glasgow requires a residence of three academic years at some

British university before the bachelor's degree can be attained, and offers the doctor's degree only to its own graduates after five years' practice, in consideration of private research. Should a young man desire the advantages of foreign residence with the object of broadening his professional training in Naval Architecture, he is advised to try for a place in some shipbuilding establishment or in the office of some consulting naval architect, and in any case should give his attention to the examples and methods of construction and yard management.

C. H. PEABODY.

DEPARTMENT OF MATHEMATICS.

The year has been one of gradual progress along lines indicated in previous Reports. The increase in the assignment of time to Differential Equations for students in Mechanical Engineering, Chemical Engineering, and Naval Architecture has enabled the Department for the first time to give a satisfactory course to these students. In the Calculus Professor Osborne has carried through a revision of his text-book, making important changes, but his health has not proved equal to the completion of publication in time for use this year. There is every reason to count on the use of the new text next October. The revision of the first-year course by Professors Woods and Bailey has been carried on with energy, and the new text-book will be ready for the next entering class.

One of the important objects of the revision of these fundamental mathematical courses is their better adaptation to later actual use in engineering study and practice. The Department will welcome suggestions from graduates or others reading this Report which may facilitate the attainment of this end.

A conference with principals and teachers of Mathematics was held by the Department, with the co-operation of the Faculty Committee on Entrance Examinations, last May, with interesting and helpful discussion of the results of entrance examinations