10 Sir William Thomson [Jan. 21, 



ceiling, absolutely rigid. Tlie 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 * flying about in their room striking the walls 

 and floor and ceiling and one another, and remaining in a constant 

 average condition of denser crowd just over the floor and less and 

 less dense up to the ceiling. 



In this constant average condition the average velocity of the 

 marbles will be the same all through the crowd, from ceiling to floor, 

 and will be the same in all directions, horizontal, or vertical, or 

 inclined. The continually repeated blows upon any part of the 

 walls or ceiling will in the aggregate be equivalent to a continuous 

 pressure which will be in simple proportion to the average density 

 of the crowd at the place. The diminution of pressure and density 

 from the floor upwards will be precisely the same as that of the 

 density and pressure of our atmosphere calculated on the supposition 

 of equal temperature at all heights, according to the well-known 

 formula and tables for finding heights by the barometer. 



In reality the temperature of the atmosphere is not uniform from 

 the ground upwards, but diminishes at the rate of about 1° C. for 

 every 162 metres of vertical ascent in free air, undistui'bed by moun- 

 tains, according to observations made in balloons by the late Mr. 

 Welsh, of Kew, through a large range of heights. This diminution 

 of temperature upwards in our terrestrial atmosphere is most impor- 

 tant and suggestive in respect to the constitution of the solar 

 atmosphere, and not merely of the atmosphere or outer shell of the 

 sun, but of the whole interior fluid mass with which it is continuous. 

 The two cases have so much in common that there is in each case loss 

 of heat from the outer parts of the atmosphere by radiation into space, 

 and that in consequence circulating currents are produced through the 

 continuous fluid, by which a thorough mixing up and down is 

 constantly performed. In the case of the terrestrial atmosphere the 

 lowest parts receive by contact heat from the solid earth, warmed 

 daily by the sun's radiation. On the average of night and day, as 

 the air does not become warmer on the whole, it must radiate out into 



* 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 consifler 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 trans-? 

 lational to two-fifths vibrational. 



