266 M. R. Biihlmann on the Alteration produced by Heat 



In fluor-spar alone the index of refraction diminishes with 

 increase of temperature, as is the case with liquids and gases. 



An explanation and solution of this peculiar contradiction is 

 subsequently attempted. 



The method adopted by Fizeau to determine the numbers he 

 obtained is the following : — 



The substance is cut into plates whose parallel surfaces are 

 about 1 to 10 millims. apart. A pencil of homogeneous light 

 falling perpendicularly upon the plate gives rise to two reflected 

 rays (repeated reflexion being neglected) which produce pheno- 

 mena of interference. Since most surfaces which the mecha- 

 nical optician endeavours to grind flat are almost invariably 

 more or less convex, the interference-fringes have usually a cir- 

 cular form. The difference of path of the two luminous rays is 

 caused by the fact that the first is reflected directly at the front 

 surface of the glass, while the second, entering the glass and 

 being reflected at the back surface of the plate, has to pass back- 

 wards again through the thickness of the glass to reenter the air. 

 "We have accordingly here to consider the difference of the velo- 

 city with which the paths in the air and in the glass are tra- 

 versed, and the difference of phase suffered through the reflexion. 

 "When the plate is warmed, the fringes are of course moved ; and 

 this motion is measured. This motion is owing to two causes : 

 (1) an expansion of the plate perpendicular to its surfaces, and 

 a consequent alteration in its thickness and consequently of the 

 path ; (2) an alteration in the index of refraction itself, whereby 

 the velocity is altered with which the ray traverses the altered 

 path. If the thickness of the plate at a given temperature is 

 known, we can deduce the alteration in the index from the num- 

 ber of the displaced fringes. 



The chief difficulty in applying this otherwise so excellent 

 method lies in the impossibility of determining the coefficient of 

 expansion with perfect accuracy. For the exact description of 

 the experimental arrangement and of the formulae by help of which 

 the results are derived from the experiments, we must refer to 

 the interesting original paper. 



A further investigation in this field is furnished by a second 

 research of the two English physicists, Gladstone and Dale *, 

 which consists partly of fresh determinations of the indices of 

 refraction at different temperatures, but is chiefly concerned in 

 discussing the relation between index of refraction and density, 

 the difference of refractive power in liquids of homologous series, 

 and the effect of the introduction of new radicals. This inves- 

 tigation offers an extraordinary amount of new observations, 



* " Researches on the Refraction, Dispersion, and ^Sensitiveness of 

 Liquids," Philosophical Transactions, 1863, vol. clviii. pp. 318-343. 



