of Refraction in Selenium and Bromine. 51 



we have for 4 tie upper limit 



irh TT 



or 



2/i = h. 



Hence the quantity h is half the wave-length within the 

 medium of the limiting transmissible ray. 

 As also 



or 



we have at the limit 





sin^ 





sin 



0u 



t 



\ 



= a 







\ 











x; 



smO= 



= sm ni 



^, 





= 



= sin 



TT 



7, 



= 1; 



Xi 



-ime = 



--\- 







If on fm-ther examination this upper limit should be estab- 

 lished as a physical entity it will modify our ideas of dispersion, 

 which we must then regard as identical with refraction. 



There is a relation between the Eulerian integral T(n) and 



sin ^ , . , . ,1 



—^ which IS worthy or notice, 



n'iT=-6. 

 By a well-known relation, 



r«.ri-7i=^^^. 



smriTT 

 Hence 



V{l + n)T[l-n)=- *"^ 



sm WTT 



If a table of r(l +«) is at hand, it can be used as a practi- 

 cally expeditious method of finding the value denoted by ^*. 

 Also if for n we write 1 — n in the above, we have 



r(i + i-n)(ri-(i-^))=^4^^, 



^ ^v ^ /y sm (tt— wtt) 



or 



1-71 



n 



r(l + n) r(l-n)= ^. ^; 



^ '^ ^ ^ sin(7r— c/) 



* The tables of logarithms by Vassal containiHg" a column of circular 

 measures of arc serve every purpose as far as calculation is concerned. 



E 2 



