394 POPULAR LECTURES AND ADDRESSES. 



up and down, or obliquely, or horizontally, but 

 in no fixed direction ; and by mutually jostling 

 the heap swells up till the ceiling of the room 

 prevents it from swelling any further. Suppose 

 now the floor to become, like the walls and ceiling, 

 absolutely rigid. The workmen may cease their 

 work of hammering, which would now be no more 

 availing to augment the motions of the marbles 

 within, than would be a lamp applied outside to 

 warm the contents of a vessel, if the vessel were 

 made of ideal matter impermeable to heat. The 

 marbles being perfectly elastic will continue for 

 ever l flying about in their room, striking the walls 



1 To justify this statement I must warn the reader that the ideal 

 perfectly elastic balls which we are imagining, must be supposed 

 somehow to have such a structure that each takes only a definite 

 average proportion of its share of the kinetic energy of the whole 

 multitude, so that on the average there is a constant proportion of 

 energy in the translatory motions of the balls ; the other part being 

 the vibratory or rotational motions of the parts of each ball. For 

 simplicity also we suppose the balls to be perfectly smooth and 

 frictionless, so that we shall not be troubled by need to consider 

 them as having any rotatory motions, such as real balls with real 

 frictional collisions would acquire. The ratio of the two kinds of 

 energy for ordinary gases, according to Clausius, to whom is due 

 this essential contribution to the kinetic theory, is of the whole 

 energy, three-fifths translational to two fifths vibrational. 



