52 Messrs C. and M. Barns on Interference of 



useful in Rowland's adjustments as well as on the spectro- 

 meter 



VdO'l _ X sin r 



\-dn j e ~o 2<? b(l — cos? 1 ) —a sin r tan r 



for the case of total interference corresponding to equations 

 (8) and (17). If i=-0' orr=-0, 



FdO'l _ X 1 



L dtoJ r= T fl 2e tan (9 cos 0'" 



G. Comparison of the Equations of Total Interference with 

 Observation. 



The partial interferences corresponding to equations (6) and 

 (7) are usually too fine to be seen unless e is very small. They 

 amount in cases of equations (15) and (16), where £ = '48 cm., 

 to the following small angles : — 



(15) (16) 



i = 0°, d&ldn = ()' -060, dd'/dn = 0'*062 



22°-5, 0'-048, 0' 050 



45°, 0'-057, C/-058 



usually less than four seconds of arc and are therefore lost. 

 The origin of the fine interferences actually seen in the table 

 is thus still open to surmise. With small e and the inter- 

 ferometer they are obvious. 



The total interferences as computed in the above table 

 agree with the observations to much within *1 minute of arc, 

 and these are experimental errors ; particularly so, as it was 

 not possible to use both verniers of the spectrometer. The 

 interesting feature of the experiment and calculation is this, 

 that h6' has about the same value for all incidences i from 0° 

 to 45° and even beyond. The equations do not show this at 

 once owing to the entrance of fi and r. But apart from a 

 and b, equation 17 is nearly 



dd_X \/D 



dn 2e/jL 1 — cos (r— 0)' 



which is independent of r to the extent in which cos (r— 0) 

 is constant. The dependence of dd'/dn on wave-length is 

 borne out. See § 7. 



Finally, dd'/dn is independent of /*, except as it occurs in 

 a and b. 



