a Light-wave as Ultimate Standard of Length. 185 



back till it coincides with the upper mirrors of both A and B 

 if B is just twice A. If not, the fringes and fractions in the 

 difference are noted. 



In the actual experiment the fringes always were adjusted 

 to move to the right (in the observing telescope) when the ref- 

 erence plane was moving from the observer. 



The following table gives the final results from the observa- 

 tions on E in wave-lengths. After the first series was com- 

 pleted all the standards were altered in length and adjustment. 

 Series III was taken by another observer. 



Ser. 

 Ser. 



Ser. 



I 



II 

 HI 



5896-08 

 5896-08 

 5896-09 



6707-98 

 6708-00 

 6708-00 



5460-85 

 5460-85 

 5460-85 



5790-70 

 5790-67 

 5790-68 



4358-42 

 4358-42 

 4358-41 



Mean 5896-083 6707-993 5460-850 5790-683 4358-417 



The arguments for the accuracy of these results are as fol- 

 lows : 



1st. In every step of every series the mean difference between 

 observation and calculation is less than it is when the whole 

 number selected is either greater or less. 



2d. In every step of every series the maximum difference 

 between the greatest and least values of the errors is less than 

 it is when the whole number selected is either greater or less. 



3d. In every step of every series the difference between the 

 errors of the longest and shortest waves, namely, lithium and 

 violet mercury, is less than it is when the whole number is 

 either greater or less. 



1th. In every step of every series the number selected as 

 agreeing most nearly with the results of observation differs 

 less than six tenths of a wave, and usually less than three 

 tenths of a wave from the number found by the comparer. 



5th. In every step the results of the three independent series 

 agree within - 15 of a wave. 



It may be considered reasonably certain therefore that the 

 number of Waves in the distance between the two planes of 

 the standard E is known to within about one part in a million. 

 It is also reasonably certain that the distance may be increased 

 at least eight fold and hence the error reduced to less than one 

 part in eight millions. 



These results have been attained with apparatus having 

 many imperfections and inconveniences. With better appli- 

 ances and with the benefit of the experience gained it is hoped 

 the last trace of uncertainty may be removed and the whole 

 operation of establishing a material standard a meter long 

 whose length in light waves is known to within one part in 

 one million, and perhaps one in ten millions may be accom- 

 plished with ease and certainty. 



