12 



DISPLACEMENT INTERFEROMETRY BY 



suitably placing the former, or modifying its objective L. After complet- 

 ing such preliminary adjustments with the fringes, made very sharp, and the 

 ocular scale equally so, this is to be placed at right angles to the fringes. 

 Let Ae denote their displacement measured in centimeters on the ocular 

 scale and AN (cm.) the displacement of the opaque mirror M of the inter- 

 ferometer. The question is whether Ae and AN are nearly enough propor- 

 tional quantities for practical purposes. A number of such standardizations 



-jn. 



were carried out throughout i cm. of Ae, two of which are shown in detail in 

 figure 5. The fluctuation of data is due to air-currents across the interfer- 

 ometer. It was not easy to obviate these, and it was not thought necessary 

 for the present purposes. Otherwise the data would have been smooth. 

 There is no doubt that a linear relation may be assumed. In curve a the 

 readings of the interferometer micrometer increase, in curve b they decrease. 

 If the means be taken from doublets far apart the ratios are 



(a) AN/Ae = 0.003 10 



(b) AN/ Ae = 0.003 10 



and they happen to coincide. Thus Ae is 323 times as large as AN and cor- 

 respondingly easy to measure. The impossibility of setting the micrometer 

 for AN accurately enough, since it is graduated to only 5Xio~ 5 cm., is 

 completely obviated in Ae. Moreover, as zAN cos i = \ (i being the angle of 

 incidence, 45, and X the mean wave-length), we now have 



0.006 1 Ae cos t = X 



so that the fringe displacement 



Ae = 



6X10- 



= 0.014 cm. 



6.iXio~ 3 Xo.7i 



measured on the ocular micrometer, corresponds to the wave-length of light 

 in the interferometer measurements. This is more than one scale part. 

 There is, however, no difficulty in making the fringes larger and obtaining 

 a much more sensitive apparatus in proportion. The achromatic fringes, 

 moreover, when properly produced, contain a distinctive central black line 

 compatible with the measurement of o.i scale part, as here given; i. e., meas- 

 urement to a few millionths of a centimeter are thus easily feasible under 

 proper surroundings. The apparatus will be used below. 



