320 Intelligence and Miscellaneous Articles. 



If /5 is the angle under which the rays fall upon the back of the 

 drop, and n the refraction-exponent (from air into the liquid), then 



tan/3 





But tan "/3 must be also equal to - if complete polarization is to enter; 



from this we find 



fc=v/2= 1*414..., 



"We must now select a liquid whose refraction-exponent is as distant 

 as possible from V2, consequently oil of cassia for instance, or 

 sulphide of carbon — of which the first is more suitable for producing 

 a rainbow, since, not to mention that its smell is less unpleasant, 

 it more readily scatters in fine drops, which remain longer floating 

 in the air. Calculation gives as the intensity-ratio of the light 

 whose undulations take place perpendicular to, and of that whose 

 undulations are in, the plane of incidence, for the red rays (n = 

 1-5945) 6-3, and for the violet rays (n= 1*7025) 2-8. 



In fact, when oil of cassia is scattered in sunlight before a dark 

 background by a current of air driven through a fine glass tube at 

 right angles above another tube which dips in the liquid, a splendid 

 rainbow is seen, the light of which cannot at any intensity be com- 

 pletely extinguished by the Nicol. — Poggendorif's Annalen, 1877, 

 No. 1, vol. clx. pp. 123-125. 



ON THE NATURE OF GAS MOLECULES. 

 BY LUDWIG BOLTZMANN, OF GRAZ. 

 Since the assumption that gas molecules behave as aggregates of 

 material points (atoms) led to results not in accordance with ex- 

 perience, it has been dropped by the author, and the hypothesis is 

 adopted that we are permitted, in calculating the push-action of 

 the molecules, to regard as approximately rigid the aggregate which 

 we designate as a single gas molecule, and which may consist of 

 various corporeal and probably also sethereal atoms, lie finds, on 

 the basis of his earlier results generalized by Maxwell and "Watson, 

 that then the ratio of the heat-capacities of a gas must be If when 

 its molecules have a spherical form. The ratio of the heat-capaci- 

 ties becomes equal to 1*4 if the molecules have the form of rigid 

 solids of rotation which are not spheres, and 1-J if they are rigid 

 bodies of any other form whatever. These numbers appear to ac- 

 cord at least so far with those found by experiment, that it cannot 

 be said that experiment furnishes any confutation of the theory thus 

 modified. It is also pointed out that the values found experi- 

 mentally for the heat-capacity of gases on this hypothesis are in 

 satisfactory accordance with the heat-capacities of solids. It is 

 self-evident that gas molecules cannot be absolutely rigid bodies ; 

 this is disproved by spectrum-analysis. It may be that the vibra- 

 tions which give rise to gas-spectra are only brief agitations lasting 

 during the collision of two molecules, comparable to the sound- 

 exciting vibrations which ensue when two ivory balls strike one 

 another. — PoggendorfFs Annalen, 1877, No. 1, vol. clx. p. 175-6. 



