Read Ebook: Experimental Determination of the Velocity of Light Made at the U.S. Naval Academy Annapolis by Michelson Albert A Albert Abraham

Font size: 10 px 15 px 20 px 25 px 30 px 35 px

Background color: BlackWhiteGrayLight GrayDark GrayDim Gray

Text color: BlackWhiteGrayLight GrayDark GrayDim Gray

Apply/Save settings

Ebook has 194 lines and 21192 words, and 4 pages

To measure the speed of rotation, a tuning-fork, bearing on one prong a steel mirror, was used. This was kept in vibration by a current of electricity from five "gravity" cells. The fork was so placed that the light from the revolving mirror was reflected to a piece of plane glass, in front of the lens of the eye-piece of the micrometer, inclined at an angle of 45?, and thence to the eye. When fork and revolving mirror are both at rest, an image of the revolving mirror is seen. When the fork vibrates, this image is drawn out into a band of light.

When the mirror commences to revolve, this band breaks up into a number of moving images of the mirror; and when, finally, the mirror makes as many turns as the fork makes vibrations, these images are reduced to one, which is stationary. This is also the case when the number of turns is a submultiple. When it is a multiple or simple ratio, the only difference is that there are more images. Hence, to make the mirror execute a certain number of turns, it is simply necessary to pull the cord attached to the valve to the right or left till the images of the revolving mirror come to rest.

The electric fork made about 128 vibrations per second. No dependence was placed upon this rate, however, but at each set of observations it is compared with a standard Ut? fork, the temperature being noted at the same time. In making the comparison the sound-beats produced by the forks were counted for 60 seconds. It is interesting to note that the electric fork, as long as it remained untouched and at the same temperature, did not change its rate more than one or two hundredths vibrations per second.

The Observer's Table.

Fig. 9 Represents The Table At Which The Observer Sits. The Light From The Heliostat Passes Through The Slit At S, Goes To The Revolving Mirror, &c., And, On Its Return, Forms An Image Of The Slit At D, Which Is Observed Through The Eye-piece. E Represents The Electric Fork Bearing The Steel Mirror M. K Is The Standard Fork On Its Resonator. C Is The Cord Attached To The Valve Supplying Air To The Turbine.

The Lens.

The lens was made by Alvan Clark & Sons. It was 8 inches in diameter; focal length, 150 feet; not achromatic. It was mounted in a wooden frame, which was placed on a support moving on a slide, about 16 feet long, placed about 80 feet from the building. As the diameter of the lens was so small in comparison with its focal length, its want of achromatism was inappreciable. For the same reason, the effect of "parallax" was too small to be noticed.

The Fixed Mirror.

The fixed mirror was one of those used in taking photographs of the transit of Venus. It was about 7 inches in diameter, mounted in a brass frame capable of adjustment in a vertical and a horizontal plane by screw motion. Being wedge-shaped, it had to be silvered on the front surface. To facilitate adjustment, a small telescope furnished with cross-hairs was attached to the mirror by a universal joint. The heavy frame was mounted on a brick pier, and the whole surrounded by a wooden case to protect it from the sun.

Adjustment of the Fixed Mirror.

The adjustment was effected as follows: A theodolite was placed at about 100 feet in front of the mirror, and the latter was moved about by the screws till the observer at the theodolite saw the image of his telescope reflected in the center of the mirror. Then the telescope attached to the mirror was pointed at a mark on a piece of card-board attached to the theodolite. Thus the line of collimation of the telescope was placed at right angles to the surface of the mirror. The theodolite was then moved to 1,000 feet, and, if found necessary, the adjustment was repeated. Then the mirror was moved by the screws till its telescope pointed at the hole in the shutter of the building. The adjustment was completed by moving the mirror, by signals, till the observer, looking through the hole in the shutter, through a good spy-glass, saw the image of the spy-glass reflected centrally in the mirror.

The whole operation was completed in a little over an hour.

Notwithstanding the wooden case about the pier, the mirror would change its position between morning and evening; so that the last adjustment had to be repeated before every series of experiments.

Apparatus for Supplying and Regulating the Blast of Air.

Fig. 10 represents a plan of the lower floor of the building. E is a three-horse power Lovegrove engine and boiler, resting on a stone foundation; B, a small Roots' blower; G, an automatic regulator. From this the air goes to a delivery-pipe, up through the floor, and to the turbine. The engine made about 4 turns per second and the blower about 15. At this speed the pressure of the air was about half a pound per square inch.

This arrangement was found in practice to be insufficient, and the following addition was made: A valve was placed at P, and the pipe was tapped a little farther on, and a rubber tube led to a water-gauge, Fig 12. The column of water in the smaller tube is depressed, and, when it reaches the horizontal part of the tube, the slightest variation of pressure sends the column from one end to the other. This is checked by an assistant at the valve; so that the column of water is kept at about the same place, and the pressure thus rendered very nearly constant. The result was satisfactory, though not in the degree anticipated. It was possible to keep the mirror at a constant speed for three or four seconds at a time, and this was sufficient for an observation. Still it would have been more convenient to keep it so for a longer time.

I am inclined to think that the variations were due to changes in the friction of the pivots rather than to changes of pressure of the blast of air.

It may be mentioned that the test of uniformity was very delicate, as a change of speed of one or two hundredths of a turn per second could easily be detected.

Method Followed in Experiment.

It was found that the only time during the day when the atmosphere was sufficiently quiet to get a distinct image was during the hour after sunrise, or during the hour before sunset. At other times the image was "boiling" so as not to be recognizable. In one experiment the electric light was used at night, but the image was no more distinct than at sunset, and the light was not steady.

The revolving mirror was then adjusted by being moved about, and inclined forward and backward, till the light was seen reflected back from the distant mirror. This light was easily seen through the coat of silver on the mirror.

The distance between the front face of the revolving mirror and the cross-hair of the eye-piece was then measured by stretching from the one to the other a steel tape, making the drop of the catenary about an inch, as then the error caused by the stretch of the tape and that due to the curve just counterbalance each other.

The position of the slit, if not determined before, was then found as before described. The electric fork was started, the temperature noted, and the sound-beats between it and the standard fork counted for 60 seconds. This was repeated two or three times before every set of observations.

The eye-piece of the micrometer was then set approximately and the revolving mirror started. If the image did not appear, the mirror was inclined forward or backward till it came in sight.

The cord connected with the valve was pulled right or left till the images of the revolving mirror, represented by the two bright round spots to the left of the cross-hair, came to rest. Then the screw was turned till the cross-hair bisected the deflected image of the slit. This was repeated till ten observations were taken, when the mirror was stopped, temperature noted, and beats counted. This was called a set of observations. Usually five such sets were taken morning and evening.

Fig. 13 represents the appearance of the image of the slit as seen in the eye-piece magnified about five times.

Determination of The Constants.

Comparison of the Steel Tape with the Standard Yard.

The steel tape used was one of Chesterman's, 100 feet long. It was compared with Wurdeman's copy of the standard yard, as follows:

Temperature was 55? Fahr.

The standard yard was brought under the microscopes of the comparator; the cross-hair of the unmarked microscope was made to bisect the division marked o, and the cross-hair of the microscope, marked I, was made to bisect the division marked 36. The reading of microscope I was taken, and the other microscope was not touched during the experiment. The standard was then removed and the steel tape brought under the microscopes and moved along till the division marked 0.1 was bisected by the cross-hair of the unmarked microscope. The screw of microscope I was then turned till its cross-hair bisected the division marked 3.1 , and the reading of the screw taken. The difference between the original reading and that of each measurement was noted, care being taken to regard the direction in which the screw was turned, and this gave the difference in length between the standard and each succesive portion of the steel tape in terms of turns of the micrometer-screw.

To find the value of one turn, the cross-hair was moved over a millimeter scale, and the following were the values obtained:

Turns of screw of microscope I in 1mm--

Determination of the Value of Micrometer.

Two pairs of lines were scratched on one slide of the slit, about 38mm apart, i.e., from the center of first pair to center of second pair. This distance was measured at intervals of 1mm through the whole length of the screw, by bisecting the interval between each two pairs by the vertical silk fiber at the end of the eye-piece. With these values a curve was constructed which gave the following values for this distance, which we shall call D?:

Changing the form of this table, we find that,--

But the average value of D, for 140 turns is, from the preceding table, 38.130.

Therefore, the true value of D, is 38.130 x .996305mm, and the average value of one turn for 10, 20, 30, etc., turns, is found by dividing 38.130 x .996305 by the values of D;, given in the table.

This gives the value of a turn--

mm. For the first 10 turns 0.99570 20 turns 0.99570 30 turns 0.99573 40 turns 0.99577 50 turns 0.99580 60 turns 0.99583 70 turns 0.99589 80 turns 0.99596 90 turns 0.99601 100 turns 0.99606 110 turns 0.99612 120 turns 0.99618 130 turns 0.99625 140 turns 0.99630

NOTE.--The micrometer has been sent to Professor Mayer, of Hoboken, to test the screw again, and to find its value. The steel tape has been sent to Professor Rogers, of Cambridge, to find its length again.

Measurement of the Distance between the Mirrors.

Square lead weights were placed along the line, and measurements taken from the forward side of one to forward side of the next. The tape rested on the ground , and was stretched by a constant force of 10 pounds.

The correction for length of the tape was +0.12 of a foot.

To correct for the stretch of the tape, the latter was stretched with a force of 15 pounds, and the stretch at intervals of 20 feet measured by a millimeter scale.

The following are the values obtained from five separate measurements of the distance between the caps of the piers supporting the revolving mirror and the distant reflector; allowance made in each case for effect of temperature:

Rate of Standard Ut? Fork.

The rate of the standard Ut? fork was found at the Naval Academy, but as so much depended on its accuracy, another series of determinations of its rate was made, together with Professor Mayer, at the Hoboken Institute of Technology.

The fork was armed with a tip of copper foil, which was lost during the experiments and replaced by one of platinum having the same weight, 4.6 mgr. The fork, on its resonator, was placed horizontally, the platinum tip just touching the lampblacked cylinder of a Schultze chronoscope. The time was given either by a sidereal break-circuit chronometer or by the break-circuit pendulum of a mean-time clock. In the former case the break-circuit worked a relay which interrupted the current from three Grove cells. The spark from the secondary coil of an inductorium was delivered from a wire near the tip of the fork. Frequently two sparks near together were given, in which case the first alone was used. The rate of the chronometer, the record of which was kept at the Observatory, was very regular, and was found by observations of transits of stars during the week to be +1.3 seconds per day, which is the same as the recorded rate.

Specimen of a Determination of Rate of Ut? Fork.

The correction for temperature was found by Professor Mayer by counting the sound-beats between the standard and another Ut? fork, at different temperatures. His result is +.012 vibrations per second for a diminution of 1? Fahr. Using the same method, I arrived at the result +.0125. Adopted +.012.

Share on: WhatsApp @Hash Facebook Tweet