760 BELL SYSTEM TECHNICAL JOURNAL 



second, made as accurately as possible to be twice as long; or rather, 

 the shortest standard had been constructed with the deliberate aim of 

 making it as nearly as possible just half so long as the second shortest. 

 It was the office of the interferometer to determine how nearly this 

 ideal had been attained; which was fulfilled by means of coincidences, 

 detected as before through the coloured fringes. 



Returning once more to Fig. 5, let M and M' stand for the mirrors 

 of the shortest standard, N and N' for those of the second shortest. 

 N and N' are on a higher level than M and M', and the field of view 

 may therefore be divided into quadrants, in which appear the fringes — 

 if and when there are any — formed by the collaboration of D with the 

 virtual images of M and M' and N and N', respectively. The observer 

 then goes through the following routine: (1) D is made to intersect 

 the images of M and N; (2) D is drawn back till it intersects the image 

 of M'; (3) the shortest standard carrying M and M' is drawn back till 

 the image of M again intersects D; (4) D is drawn back until it 

 intersects the image of M'. The witness of intersection is always the 

 central black fringe, appearing in the required quadrant or quadrants. 

 Now if the distance NN' is exactly twice the distance MM', then when 

 the observer completes the four stages of the routine D will intersect 

 not only the image of M' but that of N'; at the end of stage 4 the 

 central fringe will appear in each of the upper quadrants, just above the 

 point where at the beginning of stage 1 it appeared in each of the lower 

 quadrants. If NN' departs by a fraction of a wave from the doubled 

 value of MM', the central stripe in one of the upper quadrants will 

 lag by a little behind that in the other. From the lag expressed in 

 terms of the fringe-width, one may compute the difiference between the 

 length of the second standard and the doubled length of the first, 

 and so obtain the number of waves comprised in the second. Now 

 the second standard is made as nearly as possible of one-half the length 

 of the third, the third of the fourth, and so on up to the ninth, which 

 is made as nearly as possible one-tenth of the length of the standard 

 metre. From each to the next the comparison is made in the same 

 way. To show the remarkable reliability of Michelson's results I 

 quote the three values which he obtained by three independent meas- 

 urements of twice the number of waves of red cadmium light comprised 

 in the length of the ninth standard: 



310678.48, 310678.65, 310678.68. 



After this point it remained to compare the ninth standard with a 

 metre-rod, and the metre-rod with The Standard Metre. Returning 

 for the last time to Fig. 5, we take M and M' as the mirrors at the 



