71\eovij of Befrdction in Gases. 479 



points A and B we oet onliuary refraction with a tempera- 



tare-coetficient less than, and for values of L beyond B a 



ft) 



temperature-coefficient greater than, Gladstone and Dale's 



law indicates. We note that at the point B the variation 



is zero, and aojain for lar o-e values of L the variation becomes 

 ° ^ ft) 



very small. 



The manner in which -^ J 1 — Eigj becomes largely in- 

 dependent of temperature calls for some explanation. It is 

 due to the fact that for large values of 4- the asymptotic 

 expansion tor 1 1 — E-% j is 



jr p' p' 



Since or is proportional to 6, we see that for large values 



// .If IT' \ 



of ^ the expression >, -^1 — E — - is to a o-reat extent 

 independent of temperature, while for small values of 

 —^ the expression varies nearly as 7, 



ft)- o 



Let us now consider whether the dispersion indicated by 

 the formula is dependent on temperature. The change of fju 

 for a given wave-length was measured by counting the 

 number of interference-bands displaced for a known dif- 

 ference of pressure, and the results of Mascart and Lorenz 

 were that the ratio of the number of bands displaced for two 

 given wave-lengths was the same at all temperatures. 



Denoting the frequencies by p and p' , the experiments, so 



far as thev can be trusted, assert that — . is the same at 



all temperatures between say 0° and 100° C. 

 Xow, since /a — 1 is small, we have 



hi 



„_^_i+tHi-^S} 



Now we have just proved that for moderately large 



-alues of 1^, ^ j 1 — E -^[ varies little with temperature, in 



