348 M. R. Ruhlmann on the Alteration 'produced by Heat 



(«, the coefficient of expansion for air, being 0*00367) . Now 

 for £=0° and b = 760 nrillims., according to the same physicists, 

 ftj = 0*000294 is the index of refraction of air, whence the con- 

 stant is found =0*000588. If now n l be the absolute index of 

 refraction for air for t° and b millim. pressure, and n be the re- 

 lative index of refraction of a medium in air of f and b millim. 

 pressure, then the absolute index of refraction N is 



at „ /l+ 0-0005886 



1 V (1 + ^)760 



We might imagine that the temperature of the layers of air 

 next to the prism would be t. A simple calculation shows that 

 it is only necessary to take into account the temperature of the 

 place where the observations are performed, under the hypothesis 

 that the prism is so distant from the object-glass of the telescope 

 that the latter has the temperature of the whole room. 



We may suppose that the glass plates have a temperature /, 

 which is the same as that of the liquid, and that the temperature 

 of the air remains constant through each of the narrow layers 

 parallel to the glass plate, but that the temperatures of the suc- 

 ceeding layers diminish as they recede from the prism, until at 

 a certain distance from the prism their temperature is equal to 

 T, that of the surrounding air. I imagine the air to be divided 

 into such thin layers, parallel to the surface of the prism, that 

 the temperature of these layers may be considered constant. In 

 the layer lying next to the glass let the temperature be t — e^t, 

 in the following one t — e^t, until at last at some distance 

 / — € k t=T. If a ray of light comes out of a liquid and falls at 

 an angle i upon the closing glass plate, it is broken towards the 

 normal at an angle r (fig. 10). Let N be the absolute index of 

 refraction for water at t°, and n that of glass at t° ; let v x , v 2 , v 3 

 be the absolute indices of the refraction of air for the tempera- 

 tures t-\-€ x t, t + egt, &c, and v k that for T°. The relative in- 

 dices of refraction, through which the relation of the angle of 

 refraction to the angle of incidence is determined, are the quo- 

 tients of the absolute indices out of the one into the other me- 

 dium. Consequently r and % depend upon one another accord- 

 ing to the equation 



n . . 

 smr= ~ sin 2. 



Since the bounding surfaces of the air-layers are always as- 

 sumed to be parallel to the parallel surfaces of the glass plates, 

 the angles of refraction out of a preceding medium are the inci- 

 dent angles into the succeeding one ; and consequently, in our 

 equation, 



