the Nature of Spectra. 83 



translation, v that of rotation, then (neglecting the oscillatory 

 motion) 



h mv 2 



7 2 =a " 



^ mu 



a can be calculated from the ratio of the specific heat at con- 

 stant pressure and volume, and, for the permanent gases, is 

 0*66 nearly; so that the velocity of the rotatory motion, 



v = tWM6 = ux 0-813. 

 Further, let the radius of the molecule be r, the number of 

 rotations executed in unit time #, while v is the velocity cor- 

 responding to the square of the mean velocity of the particles 

 contained in the molecule. If the entire mass of the molecule 

 were situated at the extremity of the molecular diameter 2r, 

 then would v be the periphery-velocity, and the number of the 

 rotations in unit time 



v u. 0-813 



x= 



Zttx 27rr 



As, however, this is not the case, but there are also mass-par- 

 ticles nearer to the centre, the real periphery-velocity must be 

 greater than the mean value v (and the number of rotations, 

 x, therefore greater), yet always of the same order as the value 

 which results from the above formula. An exact determina- 

 tion could only be obtained if the shape of the molecules were 

 perfectly known. 



For ordinary temperatures, with hydrogen m = 1698 metres, 

 with nitrogen 453 metres ; r with the same two gases, accord- 

 ing to Biihlmann's calculation of Regnault's experiments in 

 the way indicated by Yan der Waals, — 20 x 10 -11 metre and 

 17 xlO" 11 metre. 



For hydrogen we have thus, very nearly, 



x = 11 x 10 11 , therefore a billion ; 

 for nitrogen, about 



3-4 x 10 11 . 



To every rotation of the at all events not spherical molecules 

 corresponds a displacement of the sether, or a fundamental vi- 

 bration. Mostly, however, it does not lie within the region 

 of the visible rays ; but probably w r e can observe certain har- 

 monic vibrations, perhaps those which follow one another with 

 from 500 to 1000 times the velocity. That in fact, on the 

 occurrence of band spectra, harmonic vibrations to over the 

 700th are visible has been proved by the calculations of Stoney 

 and Reynolds for the spectrum of chromium oxy chloride ; they 

 have also shown that, with a suitable choice of the constants, 

 rhythmic arrangements in the degrees of brightness of the 



