382 Of the Kinetic Theory of Gas. 



of the limbs of animals, and would have about as great a range 

 from the swiftest of them to the slowest. On the same 

 immense time-scale the duration of the journeys of the mole- 

 cules of ordinary air would average about one day each, while 

 the encounter which closes each journey may last some 20 

 minutes*. The motions of the limbs of animals are able to 

 accomplish a good deal in a struggle lasting 20 minutes. On 

 the same scale, the ten-thousandth of a second of time grows 

 to be an immense duration, extending to 1900 years. The 

 number of struggles to be encountered by each molecule in 

 the ten-thousandth of a second is accordingly the same as the 

 number of days in the whole Christian Era, from the birth of 

 Christ down to the end of the present century. If something 

 can be done during the 20 minutes that one of the struggles 

 may last, how great a task might be accomplished by such an 

 enormous succession of them. It must be borne in mind, too, 

 that these encounters are not mere repetitions of one another, 

 but that each has its own definite incidents. Moreover, all 

 this is what occurs in the experience of one individual molecule, 

 so that we must multiply it by something like a thousand 



* We may fill in this picture by combining a lengthening of distances 

 with the prolongation of the times. A cubic millimetre, the volume of 

 a small pin's head, if each of its edges were magnified 10 10 times, would 

 become almost as huge as the earth. Under the same circumstances 

 molecules of air would be spaced at intervals averaging ten metres ; and 

 700 metres would have become the mean distance to which they would 

 travel between their encounters. On this great scale it would not be 

 inappropriate to use men or other animals to represent the individual 

 molecules — their hearts beating, their chests heaving, their limbs in 

 vigorous motion to represent the B or internal events. And as to the mo- 

 tions with which the molecules of a gas dart about amongst one another, 

 these as they exist in common air would have become journeys as long 

 and of as various lengths as the streets of a great city, while the widths 

 of the streets may stand for the intervals at which the representatives of 

 the molecules are to be spaced asunder at starting. 



In this model we have applied so much more magnification to time 

 than to space that all the velocities come out 60,000 times slower than in 

 nature. Accordingly our animated molecules must be conceived of as 

 quietly gliding along the journeys they have to make between their 

 encounters; for the mean duration of a journey is to be a da} r , and the 

 average speed must accordingly be only half a metre per minute — on the 

 supposition that our model is to represent what occurs in gas as dense as 

 air and at its temperature and pressure. It thus appears that we must 

 conceive them as requiring on the average about a quarter of an hour to 

 get past each house in the streets along which they have so slowly to 

 make their way. 



A model of this kind is not without its use, if it were only as a means 

 by which we can gain a lively perception of how considerable the events 

 going on within the molecules may be when compared with the motions 

 of translation of the molecules. 



