of Sodium as the Standard of Length. 465 



the experiment was tried with metallic sodium in an exhausted 

 tube provided with aluminium electrodes. It was found pos- 

 sible to increase this number to more than 200,000. Now it 

 is very easy to estimate tenths or even twentieths of a wave- 

 length, which implies that it is possible to find the number of 

 wave-lengths in a given fixed distance between two planes with 

 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 decimetre, 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 decimetre Im (fig. 2) is put in 

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

 decimetre long with one end I plane, and the other slightly 

 convex, so that when it touches the plane m, 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 coloured 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 m ; then the refractometer is moved in the same direction 

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

 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 metre 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 millimetre, and using this to step off" a centimetre. This 

 will give the nearest whole number of wave-lengths, and the 

 fractions may be observed directly. The centimetre is then 

 used in the same way to step off a decimetre, which again 

 determines the nearest whole number, the fraction being ob- 

 served directly as before. 



The fractions are determined as follows : the fringes ob- 

 served in the refractometer under the conditions above 



Phil. Mag. S. 5. Vol. 24. No. 151. Dec. 1887. 2 I 



