this difficulty, and that is, the partial consideration of factors entering into a practical problem chosen to illustrate a principle. This very often results in too much importance being placed upon minor factors. Sometimes we find ridiculously accurate results obtained in the solution of certain problems and no account taken of other factors not particularly needed in illustrating the principle, which factors, should they be included, would partially or entirely overshadow the principle that is desired to be demonstrated. Sometimes very false and harmful impressions are left in the student's mind, and are a source of much difficulty in getting the student to fully comprehend problems of a similar nature arising in his subsequent work. Even though it may not be necessary to use all the factors entering into a practical problem, the partial solution of which illustrates the principle, it certainly should be called to the student's attention.

Another matter that should not be neglected is the pointing out of the limitation of formulas based on irrational theories. There seems to be no way to avoid the improper use of formulas other than to thoroughly drill the student in their derivation. Most students have great faith in everything printed in books and can hardly realize that formulas have limitations. There is so much matter at the present time appearing in the various technical papers from which improper conclusions represented by formulas have been deduced that gross errors are liable to arise by their improper application. As well as requiring the student to analyze the foundation and limi

tation of formulas, I believe that too much stress cannot be put upon the student's direct interpretation of formulas. There is quite a common belief among students that when a formula has once been derived that there remains merely the remembering of the formula as a formula only and not the laws which it may express. This can only result in the blind solution of problems.

One of the most useful means for getting the student to properly interpret formulas is laboratory instruction. Here, as in no other place can it be required that the student use his thinking powers. Laboratory courses of instruction are quite different in the many schools throughout the country, but I believe that most of the schools are beginning to recognize the fact that the best results are obtained when the student is required to apply what he knows to the determination of fundamental laws rather than to merely go through with routine standard tests. If the student is given some real problem to solve with facilities at his disposal for testing his ideas and obtaining the data which his general understanding of the problem shows him that he needs, he begins to understand what he is about. He is required to think, and not merely to fill in certain columns of log sheets which may or may not have a meaning to him. How easy it is for a student to come into the laboratory with the experiment already set up, be assigned to reading a certain instrument, record his readings in one of the columns of the log sheet, get certain results from printed instructions and formulas and utterly fail to understand what it

is all about. It can hardly be disputed that this is a very convenient way to get students through the laboratory without much trouble to the instructor, but can it be said that it is the best for the student? Let the student be given real problems to solve in the laboratory, so that he must prepare his own log sheet and decide what data he must obtain in order to solve his problem. No student should be allowed in the laboratory until he has proved to his instructor that he knows what he is after and has a full understanding of his problem.

The tendency in engineering practice is to standardize as much as possible, but when it is realized that this standardization permits of the employment of less competent help who need not necessarily be very strong in analysis, how foolish it seems to apply this to methods of instruction primarily intended to instruct the student in fundamental laws. With these few remarks, I have attempted to point out some of the principal features in the teaching of applied mechanics which my experience has shown me must continually be kept in mind in order that the work in that subject may become more efficient. One who has had engineering experience can easily realize the importance of these remarks. He understands the engineer's point of view, how he must attack his problem and apply his theories and I believe such an one can more satisfactorily lead his students to correct understanding of the subject than one who looks at the subject from the academic point of view, and cannot fully comprehend all the relations of the principles he is explaining to engineering practice.

JOINT DISCUSSION.

DEAN KENT: "Much careful repetition by the instructor" is said to instil the principles into the boy. I think the trouble with the teachers is they do too much oral repetition. They forget that nine tenths of what they say goes into one ear and out of the other. The proper thing is to have a textbook written in good English, in words that cannot be misunderstood. One trouble with the textbooks is, they have not been carefully edited for the purpose of seeing whether the sentences are rhetorically correct and clear. They lack unity. In regard to teaching mechanics, the other day I sprang a quiz on the senior class, calling for the fundamental equations of elementary dynamics. I asked them to explain how they got the equations and give an example showing that they understood how to apply them in a practical example. The result was rather startling; they had the formulæ by memory, but they could not show their derivation, and in their application many of them showed a lamentable lack of knowledge of the first principles.

DEAN WOODWARD: I think three hours a week is not too much, and is not extending a subject over too long a time. Some of the principles require a good deal of study. They should have the same course in mechanics, in my judgment. The examples brought in are from all the realms of applied mechanics. These things should be taught as early as the middle of the sophomore year, and go on continuously. The examples we bring in should not all be from engineering work. They should be abstract, some of

them; some of them should be ideal till the ideals are clear. Then they should be applied to real problems until they get a clear grasp of the important truth that every ideal solution is a more or less close approximation to a real solution, or to the solution of a real problem. Thus the student learns that ideal problems become useful in dealing with real ones.

I don't think it is wise to give men purely numerical examples. The general underlying thought is best given in general terms, so they are not too much distracted by numerical values. I would have them learn the best arrangement for their work, the best style for their work, the clearness of it on paper and the logical order in which they should put things down, and finally the necessity for the absolute numerical accuracy of all their results. While you are emphasizing the arrangement and accuracy you should begin with something perfectly familiar in principle.

In regard to the language we find in our books, I endorse what Professor Kent says. We find problems stated so badly that they may mean one thing or they may mean another. Sometimes you have to guess at the meaning by the answer that is given. There is too much looseness in the English.

PROFESSOR BENJAMIN: At this time of the year I am. always in a particularly humble frame of mind. I feel that if the Lord will forgive me for what I have left undone during my teaching the past year; I will try to do better next year. So I do not feel like criticising anybody. I suppose those who take my men after I have taught them will have the same feeling toward me that I have toward those who pre