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dT (3) tan f = c' ----; log c' = .51607 r
n (4) V = c ---; log c = .49670 f
D and r are expressed in feet and d' in millimeters.
Vt3 fork makes 256.070 vibrations per second at 65 Fahr.
D = 3972.46 feet.
tan a = tangent of angle of inclination of plane of rotation = 0.02 in all but the last twelve observations, in which it was 0.015.
log c' = .51607 (.51603 in last twelve observations.).
log c = .49670.
The electric fork makes (256.070 + B + cor.) vibrations per second, and n is a multiple, submultiple, or simple ratio of this.
Observations.
Specimen Observation.
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 f = 11612 11600 11604 f = 2694?.7 2694?.1 2694?.3 " c = 49670 49670 49670 " n = 41066 41066 41066 ------- ------- ------- 90736 90736 90736 " f = 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 Vt2 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 deflected image.
Position of slit.
Displacement of image in divisions.
Difference between greatest and least values.
B.
Cor.
Number of revolutions per second.
Radius of measurement, in feet.
Value of one turn of the screw.
Velocity of light in air, in kilometers.
Remarks.
June 5 3 76 114.85 0.300 114.55 0.17 1.423 -0.132 257.36 28.672 0.99614 299850 Electric light.
June 7 2 72 114.64 0.074 114.56 0.10 1.533 -0.084 257.52 28.655 0.99614 299740 P.M. Frame inclined at various angles June 7 2 72 114.58 0.074 114.50 0.08 1.533 -0.084 257.52 28.647 0.99614 299900 P.M. Frame inclined at various angles June 7 2 72 85.91 0.074 85.84 0.12 1.533 -0.084 193.14 28.647 0.99598 300070 P.M. Frame inclined at various angles June 7 2 72 85.97 0.074 85.89 O.07 1.533 -0.084 193.14 28.650 0.99598 299930 P.M. Frame inclined at various angles June 7 2 72 114.61 0.074 114-53 0.07 1.533 -0.084 257.42 28.650 0.99614 299850 P.M. Frame inclined at various angles June 9 3 83 114.54 0.074 114.47 0.07 1.533 -0.216 257.39 28.658 0.99614 299950 P.M. Frame inclined at various angles June 9 3 83 114.54 0.074 114.46 0.10 1.533 -0.216 257.39 28.658 0.99614 299980 P.M. Frame inclined at various angles June 9 3 83 114.57 0.074 114.47 0.08 1.533 -0.216 257.39 28.662 0.99614 299980 P.M. Frame inclined at various angles June 9 3 83 114.57 0.074 114.50 0.06 1.533 -0.216 257.39 28.660 0.99614 299880 P.M. Frame inclined at various angles June 9 2 83 114.61 0.074 114.53 0.13 1.533 -0.216 257.39 28.678 0.99614 300000 P.M. Frame inclined at various angles June 10 2 90 114.60 0.074 114.52 0.11 1.517 -0.300 257.29 28.685 0.99614 299980 P.M.
June 10 2 90 114.62 0.074 114.54 0.08 1.517 -0.300 257.29 28.685 0.99614 299930 P.M.
June 12 2 71 114.81 0.074 114.74 0.09 1.450 -0.072 257.45 28.690 0.99614 299650 A.M.
June 12 2 71 114.78 0.074 114.70 0.05 1.450 -0.072 257.45 28.690 0.99614 299760 A.M.
June 12 1 71 114.76 0.074 114.68 0.09 1.450 -0.072 257.45 28.690 0.99614 299810 A.M.
June 13 3 72 112.64 0.074 112.56 0.09 1.500 -0.084 257.49 28.172 0.99614 300000 A.M.
June 13 3 72 112.63 0.074 112.56 0.10 1.500 -0.084 257.49 28.172 0.99614 300000 A.M.
June 13 2 72 112.65 0.074 112.57 0.08 1.500 -0.084 257.49 28.172 0.99614 299960 A.M.
June 13 3 79 112.82 0.260 112.56 0.06 1.517 -0.168 257.42 28.178 0.99614 299960 P.M.
June 13 3 79 112.82 0.260 112.56 0.13 1.517 -0.168 257.42 28.178 0.99614 299960 P.M.
June 13 3 79 112.83 0.260 112.57 0.07 1.517 -0.168 257.42 28.178 0.99614 299940 P.M.
June 13 3 79 112.82 0.260 112.56 0.06 1.517 -0.168 257.42 28.178 0.99614 299960 P.M.
June 13 3 79 112.83 0.260 112.57 0.11 1.517 -0.168 257.42 28.178 0.99614 299940 P.M.
June 13 3 79 113.41 0.260 113.15 11 1.517 -0.168 258.70 28.152 0.99614 299880 P.M. Set micrometer and counted oscillations.
June 13 3 79 112.14 0.260 111.88 6 1.517 -0.168 255.69 28.152 0.99614 299800 Oscillations of image of revolving mirror.
June 14 1 64 112.83 0.260 112.57 0.12 1.500 +0.012 257.58 28.152 0.99614 299850 A.M.
June 14 1 64 112.83 0.260 112.57 0.05 1.517 +0.012 257.60 28.152 0.99614 299880 A.M.
June 14 1 65 112.81 0.260 112.55 0.11 1.517 0.000 257.59 28.152 0.99614 299900 A.M.
June 14 1 66 112.83 0.260 112.57 0.09 1.517 -0.012 257.57 28.152 0.99614 299840 A.M.
June 14 1 67 112.83 0.260 112.57 0.12 1.517 -0.024 257.56 28.152 0.99614 299830 A.M.
June 14 1 84 112.78 0.260 112.52 0.06 1.517 -0.228 257.36 28.159 0.99614 299790 P.M. Readings taken by Lieut. Nazro.
June 14 1 85 112.76 0.260 112.50 0.08 1.500 -0.240 257.33 28.159 0.99614 299810 P.M. Readings taken by Lieut. Nazro.
June 14 1 84 112.72 0.260 112.46 0.08 1.483 -0.228 257.32 28.159 0.99614 299880 P.M. Readings taken by Lieut. Nazro.
June 14 1 84 112.73 0.260 112.47 0.09 1.483 -0.228 257.32 28.159 0.99614 299880 P.M.
June 14 1 84 112.75 0.260 112.49 0.09 1.483 -0.228 257.32 28.129 0.99614 299830 P.M.
June 17 2 62 112.85 0.260 112.59 0.09 1.517 +0.036 257.62 28.149 0.99614 299800 A.M.
June 17 2 63 112.84 0.260 112.58 0.06 1.500 +0.024 257.59 28.149 0.99614 299790 A.M.
June 17 1 64 112.85 0.260 112.59 0.07 1.500 +0.012 257.58 28.149 0.99614 299760 A.M.
June 17 3 77 112.80 0.260 112.54 0.07 1.500 -0.144 257-43 28.157 0.99614 299800 P.M. Readings taken by Mr. Clason.
June 17 3 77 112.77 0.260 112.51 0.08 1.500 -0.144 257.43 28.157 0.99614 299880 P.M. Readings taken by Mr. Clason.
June 17 3 77 112.77 0.260 112.51 0.11 1.500 -0.144 257.43 28.157 0.99614 299880 P.M. Readings taken by Mr. Clason.
June 17 3 77 112.77 0.260 112.51 0.09 1.500 -0.144 257.43 28.157 0.99614 299880 P.M. Readings taken by Mr. Clason.
June 17 3 77 112.78 0.260 112.52 0.08 1.500 -0.144 257 43 28.157 0.99614 299860 P.M. Readings taken by Mr. Clason.
June 18 1 58 112.90 0.265 112.64 0.07 1.500 +0.084 257.65 28.150 0.99614 299720 A.M.
June 18 1 58 112.90 0.265 112.64 0.10 1.500 +0.084 257.65 28.150 0.99614 299720 A.M.
June 18 1 59 112.92 0.265 112.66 0.07 1.483 +0.072 257.62 28.150 0.99614 299620 A.M.
