ends of the iron pipes; mn, plane glass plates silvered on front surface, and provided with adjustments in two planes; omnb, the path of the pencil of light. The apparatus was set up in the vertical east and west plane, the light traversing the entire circuit of the Ryerson Laboratory, a path about 200 feet long and 50 feet high.
2.
It was found that under ordinary conditions the temperature disturbances in this length of air made it impossible to measure the position of the fringes; and the difficulty was only slightly remedied by enclosing the whole path of the light in a wooden box. By making this enclosure an iron pipe and exhausting the air to within a hundredth of an atmosphere, it was found possible to measure the position of the central bright fringe to within something like a twentieth of the fringe-width.
A difficulty is encountered in the selection of a fiducial mark. The double image of the source does not remain on the cross hairs of the observing telescope for any great length of time, notwithstanding the precaution of the double reflections at the corners, but by using this double image itself as the fiducial mark, any possible errors due to daily temperature changes, etc., are eliminated. This double image and the interference fringes are not in focus at the same time, but by sacrificing a very
little in the definition of each, the measurements may be made with very considerable precision.*
The observations were taken in the morning, at noon, evening and night; no special care being taken as to the exact hour. The results are summed up in the table containing the observations taken and reduced by Mr. Mann, as follows:—
The micrometer was set on one spot, then on the central fringe, then on the other spot, giving three readings of the micrometer. The first reading was subtracted from the third, giving the distance between the spots in divisions of the micrometer head. The second reading was subtracted from the third, giving the distance of the central fringe from the lower in divisions of the micrometer head. This last remainder was divided by the first, giving the distance n of the central fringe from the lower spot in fractions of the distance between the spots regarded as unity.
Each reading was reduced this way and the mean of ten taken as the result for any given time. The weights p were calculated as usual from the formula: p = c/e2.
|
Date. |
6 A. M. |
12 Noon. |
6 P. M. |
11 P. M. | ||||||||
|
n |
P |
pn |
n |
P |
pn |
n |
P |
pn |
n |
P |
pn | |
|
March 11 |
0.500 |
67 |
33.50 |
0.515 |
40 |
20.60 |
0.503 |
12 |
6.03 |
0.480 |
20 |
9.60 |
|
0.513 |
38 |
19.49 |
0.506 |
10 |
5.06 |
0.490 |
32 |
15.68 | ||||
|
March 13 |
0.495 |
11 |
5.44 |
0.530 |
33 |
17.49 | ||||||
|
March 16 |
0.507 |
55 |
27.88 |
0.499 |
50 |
24.95 |
0.492 |
13 |
6.40 |
0.479 |
60 |
28.74 |
|
0.509 |
120 |
61.08 |
0.491 |
45 |
22.09 |
0.488 |
40 |
19.52 |
0.487 |
22 |
10.71 | |
|
March 17 |
0.490 |
40 |
19.60 |
0.504 |
80 |
40.32 |
0.500 |
35 |
17.50 |
0.488 |
105 |
51.24 |
|
0.488 |
50 |
24.40 |
0.502 |
60 |
30.12 |
0.498 |
30 |
14.94 |
0.496 |
100 |
49.60 | |
|
March 18 |
0.501 |
80 |
40.08 |
0.492 |
80 |
39.36 |
0.493 |
40 |
19.72 |
0.498 |
25 |
12.45 |
|
0.507 |
50 |
25.35 |
0.488 |
25 |
12.20 |
0.498 |
35 |
17.43 | ||||
|
Sums. |
461 |
231.47 |
438 |
220.28 |
205 |
101.37 |
399 |
195.45 | ||||
|
Means. |
0.502 ± 0.002 |
0.503 ± 0.003 |
0.494 ± 0.002 |
0.490 ± 0.002 | ||||||||
12 Noon – 11 p. m. = 0.013
1 fringe = 0.250 ∴maximum displacement 13/250 = 1/20 fringe.
The conclusion from these results is that if there is any displacement of the fringes it is less than one-twentieth of a fringe.
If we consider the times occupied by the two pencils in com
* On account of the inequality of the angles of incidence and reflection there will be a slight difference between the real and apparent positions of the double image. This difference will be altogether too minute to produce any appreciable error. Again, this difference in direction produces a difference in the length of the two paths—which is however of the second order and can also be neglected.
Am. Joint. Sci.—Fourth Series, You III, No. 18.—June, 1897.
