June 18275112.790.265112.520.091.483-0.120257-4328.1580.99614299860P.M.
June 18275112.750.265112.480.101.483-0.120257-4328.1580.99614299970P.M.
June 18275112.760.265112.490.081.483-0.120257-4328.1580.99614299950P.M.
June 20360112.940.265112.670.071.517+0.063257.6528.1720.99614299880A.M.
June 20361112.920.265112.650.091.517+0.048257.6328.1720.99614299910A.M.
June 20262112.940.265112.670.071.517+0.036257.6228.1720.99614299850A.M.
June 20263112.930.265112.660.031.517+0.024257.6128.1720.99614299870A.M.
June 20278133.480.265133.210.131.450-0.156257.3633.3450.99627299840P.M.
June 20279133.490.265133.230.091.500-0.168257.4033.3450.99627299840P.M.
June 20280133.490.265133.220.071.500-0.180257.3933.3450.99627299850P.M.
June 20279133.500.265133.240.131.483-0.168257.3933.3450.99627299840P.M.
June 20279133.490.265133.220.061.483-0.168257.3833.3450.99627299840P.M.
June 20279133.490.265133.220.101.483-0.168257.3833.3450.99627299840P.M.
June 21261133.560.265133.290.121.533+0.048257.6533.3320.99627299890A.M.
June 21262133.580.265133.310.081.533+0.036257.6433.3320.99627299810A.M.
June 21263133.570.265133.310.091.533+0.024257.6333.3320.99627299810A.M.
June 21264133.570.265133.300.111.533+0.012257.6133.3320.99627299820A.M.
June 21265133.560.265133.300.131.5330.000257.6033.3320.99627299800A.M.
June 21380133.480.265133.210.061.533-0.180257.4233.3300.99627299770P.M.
June 21381133.460.265133.190.101.500-0.192257.3833.3300.99627299760P.M.
June 21382133.460.265133.200.051.500-0.204257.3733.3300.99627299740P.M.
June 21382133.460.265133.200.081.517-0.204257.3833.3300.99627299750P.M.
June 21381133.460.265133.190.081.500-0.192257.3833.3300.99627299760P.M.
June 23389133.430.265133.160.081.542-0.288257.3233.3450.99627299910P.M.
June 23389133.420.265133.150.061.550-0.288257.3333.3450.99627299920P.M.
June 23390133.430.265133.170.091.550-0.300257.3233.3450.99627299890P.M.
June 23390133.430.265133.160.071.533-0.300257.3033.3450.99627299860P.M.
June 23390133.420.265133.160.071.517-0.300257.2933.3450.99627299880P.M.
June 24372133.470.265133.200.151.517-0.084257.5033.3190.99627299720A.M.
June 24373133.440.265133.170.041.517-0.096257.4933.3190.99627299840A.M.
June 24374133.420.265133.160.111.517-0.108257.4833.3190.99627299850A.M.
June 24375133.420.265133.160.061.517-0.120257.4733.3190.99627299850A.M.
June 24376133.440.265133.180.101.517-0.132257.4533.3190.99627299780A.M.
June 26286133.420.265133.150.051.508-0.252257.3333.3390.99627299890P.M.
June 26286133.440.265133.170.081.508-0.252257.3333.3390.99627299840P.M.
June 27373133.490.265133.220.111.483-0.096257.4633.3280.99627299780A.M.
June 27374133.470.265133.200.061.483-0.108257.4433.3280.99627299810A.M.
June 27375133.470.265133.210.091.483-0.120257.4333.3280.99627299760A.M.
June 27375133.450.265133.190.091.467-0.120257.4233.3280.99627299810A.M.
June 27376133.470.265133.200.081.483-0.132257.4233.3280.99627299790A.M.
June 27376133.450.265133.190.101.483-0.132257.4233.3280.99627299810A.M.
June 3028535.32135.0099.680.051.500-0.240193.0033.2740.99645299820P.M. Mirror inverted.
June 3028635.34135.0099.670.061.508-0.252193.0033.2740.99645299850P.M. Mirror inverted.
June 3028635.34135.0099.660.101.508-0.252193.0033.2740.99645299870P.M. Mirror inverted.
June 3028635.34135.0099.660.091.517-0.252193.0033.2740.99645299870P.M. Mirror inverted.
July 128302.17135.145132.980.071.500-0.216257.3533.2820.99627299810P.M. Mirror inverted.
July 128402.15135.145133.000.091.500-0.228257.3433.2820.99627299740P.M. Mirror inverted.
July 128602.14135.145133.010.061.467-0.252257.2833.3110.99627299810P.M. Mirror inverted.
July 128602.14135.145133.000.081.467-0.252257.2833.3110.99627299940P.M. Mirror inverted.
July 238699.850.40099.450.051.450-0.252192.9533.2050.99606299950P.M. Mirror erect.
July 238666.740.40066.340.031.450-0.252128.6333.2050.99586299800P.M. Mirror erect.
July 238650.160.40047.960.071.467-0.25296.4833.2050.99580299810P.M. Mirror erect.
July 238533.570.40033.170.061.450-0.24064.3233.2050.99574299870P.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.