98 



THE INTERFEROMETRY OF 



ellipses from wave-lengths X to X'. Then if e' is the thickness of the half- 

 silvered plate H, and R the angle of refraction within it, 



(2) 



If e = o, 



(3) W.= 



which may be called the corresponding air displacement. Hence 



5N-5N a 



(4) B= ^ ^ 



ze Vx 7 ~ vv 



Here 8N=dN a =N-N'-(N a -N' a )=N-N a -(N'-N' a ) 



so that the difference of the corresponding positions of micrometer for a 

 given Fraunhofer line, with and without the plate, are to be found. The 

 method is quite accurate, as will be seen below. More than two constants 

 A and B may be taken, if desirable. 



To return to equation (i), remembering that 2.B/X 2 is small, it is seen that 

 the percentage accuracy of ju i and A/V are about equal. Now AN, for a 

 plate 5 to 6 mm. thick and ordinary glass, is about 0.3 cm. This may be 

 measured within io~ 4 cm. or 3 parts in io 4 of AN or one or two units in the 

 fourth place of n, the index of refraction of the glass. A much more serious 

 consideration is the consistent measurement of the thickness of plate e, which 

 must be given to io~ 4 cm. if the same accuracy is wanted. Naturally this 

 presupposes optic plate. Hence the data below will be inaccurate as to abso- 

 lute values from this cause. The plates used frequently showed increases of 

 thickness of several icf 3 cm. within a decimeter of length. Absolute values 

 are, however, without interest in this paper. 



To show that less than io~ 4 cm. is guaranteed on the micrometer in the 

 placing of elliptic centers at the sodium line, the pairs of results given in 

 table 22, made at different times and with entirely independent adjustments, 

 may be cited. The screw-pitch was 0.025 cm - an d the drum divided into 

 50 parts with a vernier to o.i part. 



TABLE 22. 



x Ellipses long horizontally, xx Circles. / Ellipses long vertically. 



The total difference is less than io~ 4 cm. and probably due to the width 

 of the Fraunhofer lines with deficiency of light at the ends of the spectrum. 



