Michelson and Morley — Wave-length of Sodium Light. 429 



an error less than one part in two millions and probably one 

 in ten millions. But the distance corresponding to 400,000 

 wave-lengths is roughly a decimeter, and this cannot be deter- 

 mined or reproduced more accurately than say to one part in 

 500,000. So it would be necessary to increase this distance. 

 This can be done by using the same instrument together with 

 a comparer. 



The intermediate standard decimeter Im (fig. 2) is put in place 

 of the mirror b. It consists of a prism of glass one decimeter 

 long with one end I plane, and the other slightly convex, so 

 that when it touches the plane to, Newton's rings appear, and 

 these serve to control any change in the distance Im, which has 

 been previously determined in wave-lengths. 



The end I is now adjusted so that colored fringes appear in 

 white light. These can be measured to within one-twentieth 

 of a wave-length, and probably to within one-fiftieth. The 

 piece Im is then moved forward till the fringes again appear 

 at to ; then the ref ractometer is moved in the same direction 

 till the fringes appear again at I, and so on till the whole meter 

 has been stepped off. Supposing that in this operation, the 

 error in the setting of the fringes is always in the same direc- 

 tion, the whole error in stepping off the meter would be one 

 part in two millions. By repetition this could of course be 

 reduced. A microscope rigidly attached to the carriage hold- 

 ing the piece Im would serve to compare, and a diamond at- 

 tached to the same piece would be used to produce copies. All 

 measurements would be made with the apparatus surrounded 

 by melting ice, so that no temperature corrections would be 

 required. 



Probably there would be considerable difficulty in actually 

 counting 400,000 wave-lengths, but this can be avoided by first 

 counting the wave-lengths and fractions in a length of one milli- 

 meter and using this to step off a centimeter. This will give 

 the nearest whole number of wave-lengths, and the fractions may 

 be observed directly. The centimeter is then used in the same 

 way to step off a decimeter, which again determines the nearest 

 whole number, the fraction being observed directly as before. 



The fractions are determined as follows: the fringes observed 

 in the refractometer under the conditions above mentioned can 

 readily be shown to be concentric circles. The center has the 

 minimum intensity when the difference in the distances ah ac is 

 an exact number of wave-lengths. The diameters of the con- 

 secutive circles vary as the square roots of the corresponding 

 number of waves. Therefore, if x is the fraction of a wave- 

 length to be determined, and y the diameter of the first dark 

 ring, d being the diameter of the ring corresponding to one 



wave-length, then x — *- 



° d . 



