2t; 



Lord Kel 



vm on tne 



th 



successive sets o£ twenty flights : thus I find Si cos 20 to be 

 positive for eighteen out of thirty, and Si sin 20 to be nega- 

 tive for nineteen out of the thirty. 



§ 38. A very interesting test-case is represented in the 

 accompanying diagram, (fig. 6) — a circular boundary of semi- 



circular corrugations. In this case it is obvious from the 

 symmetry that the time-integral of kinetic energy of com- 

 ponent motion parallel to any straight line must, in the 

 long run, be equal to that parallel to any other. But the 

 Boltzmann-Maxwell doctrine asserts, that the time-integrals 

 of the kinetic energies of the two components, radial and 

 transversal, according to polar coordinates, would be equal. 

 To test this, I have taken the case of an infinite number of 

 the semicircular corrugations, so that in the time-integral it 

 is not necessary to include the times between successive 

 impacts of the particle on any one of the semicircles. In 

 this case the geometrical construction would, of course, fail 

 to show the precise point Q at which the free path would 

 cut the diameter AB of the semicircular hollow to which it is 

 approaching ; and I have evaded the difficulty in a manner 

 thoroughly suitable for thermodynamic application such as 

 the kinetic theorv of gases. I arranged to draw lots for 1 



