Chapter 29 of 41
Discussion of Errors.
Experimental Determination of the Velocity of Light Made at the U.S. Naval Academy, Annapolis · Albert A. (Albert Abraham) Michelson
The value of V depends on three quantities D, n, and φ. 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.