1900.] 



on the Dynamical Theory of Heat and Light. 



381 



anywhere over the whole surface. This, if true, would be an exceed- 

 ingly 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 prelimi- 

 nary 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 



Fig. 3. 



boundary of the table ; the boundary being of any shape whatever, 

 instead of the ordinary rectangular boundary of an ordinary billiard 

 table, and being perfectly elastic. An interesting illustration, easily 

 seen through a large lecture hall, is had by taking a thin wooden board, 

 cut to any chosen shape, with the corner edges of the boundary 

 smoothly rounded, and winding a stout black cord round and round 

 it many times, beginning with one end fixed to any point, I, of the 

 board. If the pressure of the cord on the edges were perfectly 

 frictionless, the cord would, at every turn round the border, place 

 itself so as to fulfil the law of equal angles of incidence and reflection, 

 modified in virtue of the thickness of the board. For stability, it 

 would be necessary to fix points of the cord to the board by staples 

 pushed in over it at sufficiently frequent intervals, care being taken 

 that at no point is the cord disturbed from its proper straight line by 



