June 17. sunset. Image good; best in column (4).
The columns are sets of readings of the micrometer for the deflected image of slit.
| 112.81 | 112.80 | 112.83 | 112.74 | 112.79 |
| 81 | 81 | 81 | 76 | 78 |
| 79 | 78 | 78 | 74 | 74 |
| 80 | 75 | 74 | 76 | 74 |
| 79 | 77 | 74 | 76 | 77 |
| 82 | 79 | 72 | 78 | 81 |
| 82 | 73 | 76 | 78 | 77 |
| 76 | 78 | 81 | 79 | 75 |
| 83 | 79 | 74 | 83 | 82 |
| 73 | 73 | 76 | 78 | 82 |
| ------- | ------- | ------- | ------- | ------- |
| Mean = | 112.801 | 112.773 | 112.769 | 112.772 | 112.779 |
| Zero = | 0.260 | 0.260 | 0.260 | 0.260 | 0.260 |
| ------- | ------- | ------- | ------- | ------- |
| d = | 112.451 | 112.513 | 112.509 | 112.512 | 112.519 |
| Temp = | 77° | 77° | 77° | 77° | 77° |
| B = | + 1.500 |
| Corr = | - .144 |
| ------- |
| + 1.365 |
| 256.070 |
| ------- |
| n = | 257.426 | 257.43 | 257.43 | 257.43 | 257.43 |
| r = | 28.157 | 28.157 | 28.157 | 28.157 | 28.157 |
The above specimen was selected because in it the readings were all taken by another and noted down without divulging them till the whole five sets were completed.
The following is the calculation for V:
| 2d, 3d, |
| 1st set. | and 4th sets. | 5th set. |
| log | c = | 51607 | 51607 | 51607 |
| " | T = | 99832 | 99832 | 99832 |
| " | d = | 05131 | 05119 | 05123 |
| | ------- | ------- | ------- |
| | 56570 | 56558 | 56562 |
| " | r = | 44958 | 44958 | 44958 |
| | ------- | ------- | ------- |
| " | tan φ = | 11612 | 11600 | 11604 |
| φ = | 2694.7 | 2694.1 | 2694.3 |
| " | c = | 49670 | 49670 | 49670 |
| " | n = | 41066 | 41066 | 41066 |
| | ------- | ------- | ------- |
| | 90736 | 90736 | 90736 |
| " | φ = | 43052 | 43042 | 43046 |
| | ------- | ------- | ------- |
| " | V = | 47684 | 47694 | 47690 |
| V = | 299800 | 299880 | 299850 |
In the following table, the numbers in the column headed "Distinctness of Image" are thus translated: 3, good; 2, fair; 1, poor. These numbers do not, however, show the relative weights of the observations.
The numbers contained in the columns headed "Position of Deflected Image," "Position of Slit," and displacement of image in divisions were obtained as described in the paragraph headed "Micrometer," page 120.
The column headed "B" contains the number of "beats" per second between the electric Vt fork and the standard Vt3 as explained in the paragraph headed "Measurement of the Speed of Rotation." The column headed "Cor." contains the correction of the rate of the standard fork for the difference in temperature of experiment and 65° Fahr., for which temperature the rate was found. The numbers in the column headed "Number of revolutions per second" were found by applying the corrections in the two preceding columns to the rate of the standard, as explained in the same paragraph.
The "radius of measurement" is the distance between the front face of the revolving mirror and the cross-hair of the micrometer.
The numbers in the column headed "Value of one turn of the screw" were taken from the table, page 127.
| Date. | Distinctness of image. | Temperature, Fahr. | Position of def In the last two sets of June 13, the micrometer was fixed at 113.41 and 112.14 respectively. The image was bisected by the cross-hair, and kept as nearly as possible in this place, meantime counting the number of seconds required for the image of the revolving mirror to complete 60 oscillations. In other words, instead of measuring the deflection, the speed of rotation was measured. In column 7 for these two sets, the numbers 11 and 6 are the differences between the greatest and the smallest number of seconds observed. In finding the mean value of V from the table, the sets are all given the same weight. The difference between the result thus obtained and that from any system of weights is small, and may be neglected. The following table gives the result of different groupings of sets of observations. Necessarily some of the groups include others: | Electric light (1 set) | 299850 | | Set micrometer counting oscillations (2) | 299840 | | Readings taken by Lieutenant Nazro (3) | 299830 | | Readings taken by Mr. Clason (5) | 299860 | | Mirror inverted (8) | 299840 | | Speed of rotation, 192 (7) | 299990 | | Speed of rotation, 128 (1) | 299800 | | Speed of rotation, 96 (1) | 299810 | | Speed of rotation, 64 (1) | 299870 | | Radius, 28.5 feet (54) | 299870 | | Radius, 33.3 feet (46) | 299830 | | Highest temperature, 90° Fahr. (5) | 299910 | | Mean of lowest temperatures, 60° Fahr. (7) | 299800 | | Image, good (46) | 299860 | | Image, fair (39) | 299860 | | Image, poor (15) | 299810 | | Frame, inclined (5) | 299960 | | Greatest value | 300070 | | Least value | 299650 | | Mean value | 299852 | | Average difference from mean | 60 | | Value found for π | 3.26 | | Probable error | ± 5 |
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