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Lord Kelvin on the 



of the doctrine as interpreted from previous writings both of 

 Boltzmann and Maxwell, and subsequent writing's of Boltz- 

 mann, and of Rayleigh *, the most recent supporter of the 

 doctrine, is that a single geodetic drawn long enough will not 

 only fulfil Maxwell's condition of passing infinitely near to 

 every point of the surface in all directions, but will pass with 

 equal frequencies in all directions ; and as many times within 

 a certain infinitesimal distance +S of any one point P as of 

 any other point P' anywhere over the whole surface. This, if 

 true, would be an exceedingly interesting theorem. 



§ 35. I have made many efforts to test it for the case in 

 which the closed surface is reduced to a plane with other 

 boundaries than an exact ellipse (for which, as we have seen 



in §§ 30, 31, 32, the investigation fails through the non- 

 fulfilment of Maxwell's preliminary condition). Every such 

 case gives, as we have seen, straight lines drawn across the 

 enclosed area turned on meeting the boundary, according to 

 the law of equal angles of incidence and reflection, which 

 corresponds also to the case of an ideal perfectly smooth 

 non-rotating billiard-ball moving in straight lines except 

 when it strikes the boundary of the table ; the boundary 

 being of any shape whatever, instead of the ordinary rect- 

 angular boundary of an ordinary billiard-table, and being 

 perfectly elastic. An interesting illustration, easily seen 



* Phil. Mag.. January 1900. 



