Part 6
June 18
2
75
112.79
0.265
112.52
0.09
1.483
-0.120
257-43
28.158
0.99614
299860
P.M.
June 18
2
75
112.75
0.265
112.48
0.10
1.483
-0.120
257-43
28.158
0.99614
299970
P.M.
June 18
2
75
112.76
0.265
112.49
0.08
1.483
-0.120
257-43
28.158
0.99614
299950
P.M.
June 20
3
60
112.94
0.265
112.67
0.07
1.517
+0.063
257.65
28.172
0.99614
299880
A.M.
June 20
3
61
112.92
0.265
112.65
0.09
1.517
+0.048
257.63
28.172
0.99614
299910
A.M.
June 20
2
62
112.94
0.265
112.67
0.07
1.517
+0.036
257.62
28.172
0.99614
299850
A.M.
June 20
2
63
112.93
0.265
112.66
0.03
1.517
+0.024
257.61
28.172
0.99614
299870
A.M.
June 20
2
78
133.48
0.265
133.21
0.13
1.450
-0.156
257.36
33.345
0.99627
299840
P.M.
June 20
2
79
133.49
0.265
133.23
0.09
1.500
-0.168
257.40
33.345
0.99627
299840
P.M.
June 20
2
80
133.49
0.265
133.22
0.07
1.500
-0.180
257.39
33.345
0.99627
299850
P.M.
June 20
2
79
133.50
0.265
133.24
0.13
1.483
-0.168
257.39
33.345
0.99627
299840
P.M.
June 20
2
79
133.49
0.265
133.22
0.06
1.483
-0.168
257.38
33.345
0.99627
299840
P.M.
June 20
2
79
133.49
0.265
133.22
0.10
1.483
-0.168
257.38
33.345
0.99627
299840
P.M.
June 21
2
61
133.56
0.265
133.29
0.12
1.533
+0.048
257.65
33.332
0.99627
299890
A.M.
June 21
2
62
133.58
0.265
133.31
0.08
1.533
+0.036
257.64
33.332
0.99627
299810
A.M.
June 21
2
63
133.57
0.265
133.31
0.09
1.533
+0.024
257.63
33.332
0.99627
299810
A.M.
June 21
2
64
133.57
0.265
133.30
0.11
1.533
+0.012
257.61
33.332
0.99627
299820
A.M.
June 21
2
65
133.56
0.265
133.30
0.13
1.533
0.000
257.60
33.332
0.99627
299800
A.M.
June 21
3
80
133.48
0.265
133.21
0.06
1.533
-0.180
257.42
33.330
0.99627
299770
P.M.
June 21
3
81
133.46
0.265
133.19
0.10
1.500
-0.192
257.38
33.330
0.99627
299760
P.M.
June 21
3
82
133.46
0.265
133.20
0.05
1.500
-0.204
257.37
33.330
0.99627
299740
P.M.
June 21
3
82
133.46
0.265
133.20
0.08
1.517
-0.204
257.38
33.330
0.99627
299750
P.M.
June 21
3
81
133.46
0.265
133.19
0.08
1.500
-0.192
257.38
33.330
0.99627
299760
P.M.
June 23
3
89
133.43
0.265
133.16
0.08
1.542
-0.288
257.32
33.345
0.99627
299910
P.M.
June 23
3
89
133.42
0.265
133.15
0.06
1.550
-0.288
257.33
33.345
0.99627
299920
P.M.
June 23
3
90
133.43
0.265
133.17
0.09
1.550
-0.300
257.32
33.345
0.99627
299890
P.M.
June 23
3
90
133.43
0.265
133.16
0.07
1.533
-0.300
257.30
33.345
0.99627
299860
P.M.
June 23
3
90
133.42
0.265
133.16
0.07
1.517
-0.300
257.29
33.345
0.99627
299880
P.M.
June 24
3
72
133.47
0.265
133.20
0.15
1.517
-0.084
257.50
33.319
0.99627
299720
A.M.
June 24
3
73
133.44
0.265
133.17
0.04
1.517
-0.096
257.49
33.319
0.99627
299840
A.M.
June 24
3
74
133.42
0.265
133.16
0.11
1.517
-0.108
257.48
33.319
0.99627
299850
A.M.
June 24
3
75
133.42
0.265
133.16
0.06
1.517
-0.120
257.47
33.319
0.99627
299850
A.M.
June 24
3
76
133.44
0.265
133.18
0.10
1.517
-0.132
257.45
33.319
0.99627
299780
A.M.
June 26
2
86
133.42
0.265
133.15
0.05
1.508
-0.252
257.33
33.339
0.99627
299890
P.M.
June 26
2
86
133.44
0.265
133.17
0.08
1.508
-0.252
257.33
33.339
0.99627
299840
P.M.
June 27
3
73
133.49
0.265
133.22
0.11
1.483
-0.096
257.46
33.328
0.99627
299780
A.M.
June 27
3
74
133.47
0.265
133.20
0.06
1.483
-0.108
257.44
33.328
0.99627
299810
A.M.
June 27
3
75
133.47
0.265
133.21
0.09
1.483
-0.120
257.43
33.328
0.99627
299760
A.M.
June 27
3
75
133.45
0.265
133.19
0.09
1.467
-0.120
257.42
33.328
0.99627
299810
A.M.
June 27
3
76
133.47
0.265
133.20
0.08
1.483
-0.132
257.42
33.328
0.99627
299790
A.M.
June 27
3
76
133.45
0.265
133.19
0.10
1.483
-0.132
257.42
33.328
0.99627
299810
A.M.
June 30
2
85
35.32
135.00
99.68
0.05
1.500
-0.240
193.00
33.274
0.99645
299820
P.M. Mirror inverted.
June 30
2
86
35.34
135.00
99.67
0.06
1.508
-0.252
193.00
33.274
0.99645
299850
P.M. Mirror inverted.
June 30
2
86
35.34
135.00
99.66
0.10
1.508
-0.252
193.00
33.274
0.99645
299870
P.M. Mirror inverted.
June 30
2
86
35.34
135.00
99.66
0.09
1.517
-0.252
193.00
33.274
0.99645
299870
P.M. Mirror inverted.
July 1
2
83
02.17
135.145
132.98
0.07
1.500
-0.216
257.35
33.282
0.99627
299810
P.M. Mirror inverted.
July 1
2
84
02.15
135.145
133.00
0.09
1.500
-0.228
257.34
33.282
0.99627
299740
P.M. Mirror inverted.
July 1
2
86
02.14
135.145
133.01
0.06
1.467
-0.252
257.28
33.311
0.99627
299810
P.M. Mirror inverted.
July 1
2
86
02.14
135.145
133.00
0.08
1.467
-0.252
257.28
33.311
0.99627
299940
P.M. Mirror inverted.
July 2
3
86
99.85
0.400
99.45
0.05
1.450
-0.252
192.95
33.205
0.99606
299950
P.M. Mirror erect.
July 2
3
86
66.74
0.400
66.34
0.03
1.450
-0.252
128.63
33.205
0.99586
299800
P.M. Mirror erect.
July 2
3
86
50.16
0.400
47.96
0.07
1.467
-0.252
96.48
33.205
0.99580
299810
P.M. Mirror erect.
July 2
3
85
33.57
0.400
33.17
0.06
1.450
-0.240
64.32
33.205
0.99574
299870
P.M. Mirror erect.
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 p 3.26 Probable error 5
Discussion of Errors.
The value of V depends on three quant.i.ties D, n, and f. These will now be considered in detail.
The Distance.
The distance between the two mirrors may be in error, either by an erroneous determination of the length of the steel tape used, or by a mistake in the measurement of the distance by the tape.
The first may be caused by an error in the copy of the standard yard, or in the comparison between the standard and the tape. An error in this copy, of .00036 inch, which, for such a copy, would be considered large, would produce an error of only .00001 in the final result. Supposing that the bisections of the divisions are correct to .0005 inch, which is a liberal estimate, the error caused by supposing the error in each yard to be in the same direction would be only .000014; or the total error of the tape, if both errors were in the same direction, would be 000024 of the whole length.
The calculated probable error of the five measurements of the distance was .000015; hence the total error due to D would be at most .00004. The tape has been sent to Professor Rogers, of Cambridge, for comparison, to confirm the result.
The Speed of Rotation.
This quant.i.ty depends on three conditions. It is affected, first, by an error in the rate of the standard; second, by an error in the count of the sound beats between the forks; and third, by a false estimate of the moment when the image of the revolving mirror is at rest, at which moment the deflection is measured.
The calculated probable error of the rate is .000016. If this rate should be questioned, the fork can be again rated and a simple correction applied. The fork is carefully kept at the Stevens Inst.i.tute, Hoboken, and comparisons were made with two other forks, in case it was lost or injured.
In counting the sound beats, experiments were tried to find if the vibrations of the standard were affected by the other fork, but no such effect could be detected. In each case the number of beats was counted correctly to .02, or less than .0001 part, and in the great number of comparisons made this source of error could be neglected.
The error due to an incorrect estimate of the exact time when the images of the revolving mirror came to rest was eliminated by making the measurement sometimes when the speed was slowly increasing, and sometimes when slowly decreasing. Further, this error would form part of the probable error deduced from the results of observations.
We may then conclude that the error, in the measurement of _n_, was less than .00002.
The Deflection.
