Experimental Determination of the Velocity of Light Part 2

[Ill.u.s.tration: FIG. 10.]

The regulator, Fig. 11, consists of a strong bellows supporting a weight of 370 pounds, partly counterpoised by 80 pounds in order to prevent the bellows from sagging. When the pressure of air from the blower exceeds the weight, the bellows commences to rise, and, in so doing, closes the valve V.

[Ill.u.s.tration: FIG. 11.]

[Ill.u.s.tration: FIG. 12.]

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 a.s.sistant 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 antic.i.p.ated. 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 method followed in experiment was as follows: The fire was started half an hour before, and by the time everything was ready the gauge would show 40 or 50 pounds of steam. The mirror was adjusted by signals, as before described. The heliostat was placed and adjusted. The revolving mirror was inclined to the right or left, so that the _direct_ reflection of light from the slit, which otherwise would flash into the eye-piece at every revolution, fell either above or below the eye-piece.[2]

[Footnote 2: Otherwise this light would overpower that which forms the image to be observed. As far as I am aware, Foucault does not speak of this difficulty. If he allowed this light to interfere with the brightness of the image, he neglected a most obvious advantage. If he did incline the axis of the mirror to the right or left, he makes no allowance for the error thus introduced.]

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[3] and the revolving mirror started. If the image did not appear, the mirror was inclined forward or backward till it came in sight.

[Footnote 3: The deflection being measured by its tangent, it was necessary that the scale should be at right angles to the radius (the radius drawn from the mirror to one or the other end of that part of the scale which represents this tangent). This was done by setting the eye-piece approximately to the expected deflection, and turning the whole micrometer about a vertical axis till the cross-hair bisected the circular field of light reflected from the revolving mirror. The axis of the eye-piece being at right angles to the scale, the latter would be at right angles to radius drawn to the cross-hair.]

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.

[Ill.u.s.tration: FIG. 13.]

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 (feet) 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 (feet), 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--

7.68 7.73 7.60 7.67 7.68 7.62 7.65 7.57 7.72 7.70 7.64 7.69 7.65 7.59 7.63 7.64 7.55 7.65 7.61 7.63

Mean =7.65

Hence one turn = 0.1307mm.

or = 0.0051 inch.

The length of the steel tape from 0.1 to 99.1 was found to be greater than 33 yards, by 7.4 turns =.96mm +.003 feet.

Correction for temperature +.003 feet.

Length 100.000 feet.

-------------- Corrected length 100.006 feet.

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':

Turns of screw.

At 0 of scale D' =38.155 10 of scale D' 38.155 20 of scale D' 38.150 30 of scale D' 38 150 40 of scale D' 38.145 50 of scale D' 38.140 60 of scale D' 38.140 70 of scale D' 38.130 80 of scale D' 38.130 90 of scale D' 38.125 100 of scale D' 38.120 110 of scale D' 38.110 120 of scale D' 38.105 130 of scale D' 38.100 140 of scale D' 38.100

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

For the _first_ 10 turns the _average_ value of D' is 38.155 20 turns 38.153 30 turns 38.152 40 turns 38.151 50 turns 38.149 60 turns 38.148 70 turns 38.146 80 turns 38.144 90 turns 38.142 100 turns 38.140 110 turns 38.138 120 turns 38.135 130 turns 38.132 140 turns 38.130

On comparing the scale with the standard meter, the temperature being 16.5 C., 140 divisions were found to = 139.462mm. This multiplied by (1 + .0000188 16.5) = 139.505mm.

One hundred and forty divisions were found to be equal to 140.022 turns of the screw, whence 140 turns of the screw = 139.483mm, or 1 turn of the screw = 0.996305mm.

This is the _average_ value of one turn in 140.

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

This gives the value of a turn--