an advertising agent and a lobbyist, and to shape his institution so as to suit the tastes of legislators rather than the best interests of the community. An appeal for further appropriations often requires to be backed by a showing of increased attendance, and a detailed departmental budget is apt to be allotted by a board of regents or trustees on the same basis of attendance. The result is that deans of engineering schools, without intending to do so at all, sometimes become more lax in their requirements, in order that the number of engineering students may show up favorably enough to draw the needed appropriations. The standards which President Atkinson specifies for the Polytechnic Institute of Brooklyn are attainable in any of our state institutions. The fact that an engineering school is a state institution should by no manner of means be considered a reason for permitting an incompetent student to secure a degree.

SOME CLASSROOM EXPERIMENTS IN

MECHANICS.

BY JAMES E. BOYD,

Professor of Mechanics, Ohio State University.

In teaching mechanics at the Ohio State University we give a limited number of classroom demonstrations to illustrate the fundamental conceptions of the subject. We aim to have these experiments on a sufficiently large scale to be clear to all the members of the class. The experiments are usually quantitative. The actual readings are generally taken by some of the students, and they are at once worked out on the blackboard, sometimes by the instructor or some one member of the class, more frequently by the entire class. The method used depends, of course, upon the nature of the problem and the state of the students' knowledge of it. As a general proposition, each student profits most by what he himself does. At the same time, it is not economical to permit a class of beginners to flounder around after something which only a few can reach.

The experiments which I am about to describe are some of those which we used during the past yearapparently with profit.

I make no apology for their extremely elementary nature, for it is impossible to make work of a physical character too elementary for the average student; and I am convinced that, if the fundamental conceptions are really mastered, only a little common sense

and a working knowledge of mathematics are needed to solve the complex problems.

Figs. 1 and 2 represent a cantilever beam made of 2 x 6-inch pine. A chain A takes the tension. In Fig. 1 the compression is taken by a light cylinder B.

The distance between the chain and the cylinder is measured and multiplied by the tension in the chain as given by a spring balance to get the resisting moment. The weight and location of the center of gravity of the portion to the left of the section being determined, the resisting moment and the external moment may be compared.

There remains the vertical shear, usually a rather vague idea to the beginner. To measure this we place a cylinder C under the right end of the free portion and support this cylinder by a platform scale (shown reduced) reading to one fourth ounce. The reading of the scale is found to be the weight of the portion of the beam to the left of the section, as we already know deductively.

We now lift the right end of the chain till we reach the position shown by the broken line in Fig. 1. The weight on the scale becomes zero and the cylinder C may be removed. If we extend a line parallel to the chain, we find that it intersects the horizontal line through the cylinder at a point directly below the

center of gravity of the left hand portion of the beam -the condition of equilibrium for three forces.

Fig. 2 shows the same thing with the tension horizontal and the compression taken by a square block D held at the right angle. Or both block and chain

FIG. 2.

may be placed at an angle with the horizontal, illustrating the fact that shear may be regarded as made up of tension and compression. Again the block D may be put in with its faces parallel to the section. If the surfaces are smooth, it is probable that the friction will not be equal to the shear when the block is near the bottom. It may then be raised so as to increase the normal pressure, and equilibrium secured.

In Fig. 3 we have a simple beam. The compression is now at the top and the tension at the bottom.

G
B

FIG. 3.

The shear is taken by the cylinder C, which is placed between the left portion of the beam and the projection G attached to the right portion. be up or down, depending upon the

This shear may

position of the

supports and the loads. If, in Fig. 3, we move the right support E toward the left, we find a position of zero shear. We may now determine the left reaction by means of our platform scale and we find that it is equal to the weight of that portion of the beam between the left support and the section.

In Fig. 4 we have placed a block H between the chain and the right hand portion of the beam and

B

H

FIG. 4.

removed the cylinder C. The shear is now taken by the vertical component of the tension. If we extend a line parallel to the chain and a horizontal line through the compression cylinder B, we find that these lines intersect to the left of the left support. We now measure the end reaction, and knowing the weight and the position of the center of gravity of that portion of the beam to the left of the section, we calculate the position of the resultant of these two oppositely directed vertical forces. We find that this resultant passes through the intersection above mentioned-the condition of equilibrium for four forces.

For the elastic curve and deflection of simple beams and cantilevers, it is easy to devise experiments adapted to the lecture table. For instance, as a cantilever, we use a 2 x 2-inch yellow pine, ten feet in length, which is securely fastened at one end to a pair of 4 x 6-inch beams. As the end cannot be made absolutely "fixed," we attach a long light pointer to the