than half full of air. Record the levels of the mercury and the volume of the air. After this, the stop-cock in the air tube should be kept closed. Now lower the open tube until the air practically fills the graduated tube. Let the apparatus stand two or three minutes to permit the gas to recover its initial temperature, then read both mercury levels and the volume of the air. Raise the open tube a few centimeters, wait a few minutes and again take the three readings. Continue raising the open tube until the mercury levels are again equal, taking readings at each step. If the readings with levels alike are not the same as at the start of the experiment, probably the apparatus is leaking. If the difference is at all pronounced, consult the instructor. Keep on raising the open tube a few centimeters at a time, taking readings at a suitable interval after each shift, until at least six have been obtained with the air above atmospheric pressure and a similar number at less than atmospheric pressure. Finally restore the tubes to the original levels and again test for leakage.

Compute the pressures and then find the product of each pressure and the corresponding volume. Tabulate the data as follows:

Plot a curve using values of V as abscissæ and of P as ordinates. Does the shape of the curve indicate a direct or an inverse proportionality between P and V? What is your conclusion regarding the product of the pressure and volume of a constant mass of gas kept at the same temperature? How does this agree with Boyle's Law?

If the gas tube is closed by a stop-cock, change the mass of the enclosed gas and take another set of readings. In this case, the constant product, PV, will be a number different from that

STUDY OF A FALLING BODY.

rences: Stewart, Physics, Sect. 52-55; Kimball, College Physics, Sect. 100-101; Duff, College Physics, Sect. 66-67; Spinney, Text-Book of Physics, Sect. 22-26.

The procedure described here is known as Whiting's od. The general plan is to let a ball fall alongside a penm, the period of which provides a means of timing the fall e body. A wooden bar of rectangular cross-section, at least 4 cm and from 150 to 300 cm long, is used as the penm. The ball must be heavy enough to hold the pendulum reasonably large angle with the vertical, when suspended own in the figure. A strip of leather fastened in a slit at

the top of the pendulum makes a suitable support, but knife-edges may be arranged if desired. It is preferable that the surface turned toward the falling ball be at least 4 cm wide, but greater width than that leads to large damping effects. Set the pendulum vibrating and carefully determine the time for forty or fifty complete vibrations by the use of a watch or clock. A stop-watch may be used if available. A complete vibration means a swing to and fro. Try to estimate times to fractions of a second so as to obtain a value for the period as accurate as possible. This is essential because the period apig. 3. pears in the formula as a second degree factor. By means of thumb tacks or soft wax, attach a strip of e paper to the outer face of the pendulum near the bottom place a narrow strip of carbon paper over the white paper. ball is suspended by means of a thread running through -eyes or wire loops properly placed so it hangs just at the

upper end of the pendulum when the latter is drawn back by the thread. The ball must be so adjusted that it will just touch the pendulum anywhere along its length, when the bar is hanging vertically. Try lowering the ball carefully with the pendulum absolutely motionless and see if this condition is realized. A piece of lead, fastened by a single screw to one side of the pendulum, may be moved slightly to cause the front face of the pendulum to be exactly vertical. When ball, thread, and pendulum have all been adjusted, measure very carefully the distance from the center of the ball to the floor. In doing this the thread must not be allowed to slip and change the positions of pendulum and ball. Instead of using the carbon paper, one may smoke the ball, using a smoky gas flame, and it will then make black marks wherever it strikes the paper.

After seeing that the pendulum and ball are perfectly motionless, burn the string at the top with a match. This releases the ball and the pendulum at the same instant; and the pendulum, just as it completes a quarter oscillation, strikes the ball so that a black dot is printed on the paper. Measure carefully the distance from the center of this dot to the floor and compute how far the ball fell before it struck the pendulum. The time required for the ball to fall this distance is found by taking one quarter of the period found in the first part of the experiment. Make ten or twelve trials and measure the distances both in centimeters and feet. From the formula for distance covered by a body falling from rest, compute the acceleration due to gravity both in centimeters and feet per second per second.

Several holes may be bored through the pendulum near the bottom and a piece of brass rod fitted into one of them. Shifting the rod from one hole to another will alter the period of the pendulum. If this arrangement is provided, trials should be made with pendulums having different periods.

Poor timing of the pendulum is one of the greatest sources of error in this experiment. In finding the average distanc fallen, it may be well to disregard any trial which differs radically from others of the same group. Such wide differences may arise if the ball has a slight swinging motion before it is let fall or if the pendulum has a twisting motion as it swings down. A box of sand or a thick pad should be placed below the pendulum to catch the falling ball.

EXPERIMENT NO. 110.

EFFECTS OF FORCE ON MOTION.

References: Stewart, Physics, Sect. 53, 59-65; Kimball, College Physics, Sect. 87-89, 94, 95, 98; Duff, College Physics, Sect. 64, 65, 69-76; Spinney, Text-Book of Physics, Sect. 23-26, 30.

The purpose of this experiment is to show that if different forces act on a certain mass, in each case there is produced a uniform acceleration which is directly proportional to the applied force. In mathematical form, this means that if a mass, m, moves under the action of a resultant external force, f, with an acceleration, a, the product, ma, is equal to the force, f.

In order to test this law experimentally, we make use of some form of the Atwood Machine. This is essentially a light pulley, over which runs a cord or paper tape with equal weights at the ends. If an excess weight is added at one side, there is set up an acceleration, the magnitude of which depends on the amount of excess weight used. The mass set in motion consists of the two large weights, the excess weights and the pulley. The force producing the motion is the excess weight (measured in dynes). The experiment consists in measuring the accelerations produced by different excess weights. The various forms of Atwood Machine differ mainly in the methods of timing employed.

In the Cussons type of Atwood Machine two equal brass weights are connected together by means of a strip of paper about 185 cm long hung over the wheel of the machine. A strip of paper 130 cm long connects the bottoms of the weights together and serves as a counter-balance. Place enough excess weight on the right-hand side to cause that weight to descend very slowly without acceleration. Friction in the machine is now counteracted and this small excess weight should be kept in place during the whole experiment.

Place this loaded weight on the upper "falling table" and put a rider of 5 grams upon it. The weight of this rider is the force producing motion. Set the vibrator so that it traces a line on the strip. (The writing brush should be charged with ink and stroked to a fine point by means of the larger brush.) Pull

the lever, releasing the vibrator and allowing the falling table to drop. The brass weight now descends till its rider is removed by the lower striking table, which should be carefully adjusted before the experiment. The vibrator traces a sinuous line on the strip, and if the brush is drawn across the paper tape while the brass weight is held at the point where its rider was removed, the distance traversed by the falling weight can be measured along the tape.

Let M be the mass of each large brass weight and m the mass of the rider. The total mass set in motion is then 2M+m+the equivalent mass of the wheel. The force causing this motion is mg. Hence if a is the acceleration of the whole system we have,

mg= (2M+m+E)a,

(1)

where E-equivalent mass of the wheel. This value will be furnished by the instructor.

If t is the time taken by the system in moving from the starting platform to the lower striking table, the whole motion being under the uniform acceleration a, and the distance from the upper platform to the lower striking table being s, it is known that,

1
S=- at2.
2

(2)

The value of t may be determined by counting the number of complete vibrations made by the vibrator in the distance s. The number of complete vibrations made per second by the spring is usually stamped on the vibrator. The value of s is to be measured along the paper strip. From equation (2) we may, therefore, calculate the value of a.

All of the quantities in equation (1) are now determined. Substitute your data and see whether this equation is satisfied.

Repeat with 8 and 10 gram riders. Tabulate the data.

In another type of machine the time intervals are indicated by dots on the tape made by a sounder placed at the top of the machine. A brush is fastened to the armature of the sounder and the sounder gives a click every time the clock pendulum passes its central position. The manipulation and computation are not essentially different from those already described.