Febkuabt 2, 1906.] 



SCIENCE. 



171 



"We are now in position to calculate not 

 only the values of y for various gases, but 

 also their molecular heats, that is, the heat 

 capacities of their gram-molecules, from 

 estimates made of the probable number of 

 their principal degrees of freedom. 



In the case of a monatomic gas we sup- 

 pose the molecules to act either as points 

 or as smooth spheres, for which the only 

 effective degrees of freedom are the three 

 translational ones. For these, therefore, 

 we have 



iS=3, Q,m = 4.943, }' = f = 1.66+. 



I do not know that the molecular heats of 

 the monatomic gases have been measured, 

 but the values of y obtained for mercury 

 vapor, krypton, helium and argon range 

 from 1.666 to 1.64. 



For the diatomic gases, while we still 

 treat the atoms as points or smooth spheres, 

 we notice that 5 coordinates are necessary, 

 being also sufficient, to determine the posi- 

 tion and orientation of the molecule, in 

 view of the fact that its orientation about 

 the line joining the two atoms is indif- 

 ferent. The only other principal degree 

 of freedom which the molecule can possess 

 is the single one which determines the dis- 

 tance between the atoms. If this distance 

 is fixed, we have i^O, and 6 = 5 ; if it is 

 variable, i = 1, and 0^1. From these 

 assumptions we can calculate the constants 

 for comparison with the results of observa- 

 tion. 

 * = 5. /c(iJ + 2)=6 9202. (i? + 2)/i? = 1.400. 



Hydrogen 



Nitrogen : . 



Oxygen 



Nitrous oxide 



Hydrogen bromide.. 



1.402 

 1.405 

 1.402 



When we consider the triatomic mole- 

 cules, we find several of them of the type 

 of which the molecule of water vapor is an 

 example, in which we may suppose that 

 the bivalent atom stands between the other 

 two similar atoms, at the center of gravity 

 of the molecule. If we can conceive the 

 atoms thus placed and take the coordinates 

 not fixed by this assumption as correspond- 

 ing to subsidiary degrees of freedom, we 

 may consider the energy of the molecule as 

 determined by the 5 degrees of freedom 

 which fix the position and orientation of 

 the molecule, and by one additional degree 

 of freedom, determining the distance be- 

 tween either of the univalent atoms and 

 the center of gravity. On these assump- 

 tions we obtain 6 = 7. 



For reasons which I will not stop to give, 

 Staigmiiller considers the molecule of bi- 

 sulphide of carbon to be of a different class, 

 in which the above described symmetry 

 does not obtain, so that we have a ^ 6, and 

 each of the sulphur atoms determined as to 

 its distance from the center by one coor- 

 dinate, so that i = 2, and 6 = 10. 



For the two vapors, phosphorous chlo- 

 ride and arsenious chloride, we may think 

 of the univalent atoms as free to move in 

 planes at right angles to the directions of 

 the valencies of the trivalent atom, each 

 with 2 degrees of freedom, while 6 more 

 are needed to determine the position and 

 orientation of the molecule. We have thus, 

 in these cases, 6^1'&. 



