The value of one turn of the screw was found by comparison with the standard meter for all parts of the screw. This measurement, including the possible error of the copy of the standard meter, I estimate to be correct to .00005 part. The instrument is at the Stevens Institute, where it is to be compared with a millimeter scale made by Professor Rogers, of Cambridge.
The deflection was read to within three or four hundredths of a turn at each observation, and this error appears in the probable error of the result.
The deflection is also affected by the inclination of the plane of rotation to the horizon. This inclination was small, and its secant varies slowly, so that any slight error in this angle would not appreciably affect the result.
The measurement of r is affected in the same way as D, so that we may call the greatest error of this measurement .00004. It would probably be less than this, as the mistakes in the individual measurements would also appear in the probable error of the result.
The measurement of φ was not corrected for temperature. As the corrections would be small they may be applied to the final result. For an increase of 1° F. the correction to be applied to the screw for unit length would be -.0000066. The correction for the brass scale would be +.0000105, or the whole correction for the micrometer would be +.000004. The correction for the steel tape used to measure r would be +.0000066. Hence the correction for tan. φ would be -.000003 t. The average temperature of the experiments is 75°.6 F. 75.6-62.5 = 13.1. -.000003×13.1 = -.00004
Hence φ should be divided by 1.00004, or the final result should be multiplied by 1.00004. This would correspond to a correction of +12 kilometers.
The greatest error, excluding the one just mentioned, would probably be less than .00009 in the measurement of φ.
Summing up the various errors, we find, then, that the total constant error, in the most unfavorable case, where the errors are all in the same direction, would be .00015. Adding to this the probable error of the result, .00002, we have for the limiting value of the error of the final result ±.00017. This corresponds to an error of ±51 kilometers.
The correction for the velocity of light in vacuo is found by multiplying the speed in air by the index of refraction of air, at the temperature of the experiments. The error due to neglecting the barometric height is exceedingly small. This correction, in kilometers, is +80.