ON THE NATURE OF LIFE 199 



rather less than 2 inches along each side), there will be 

 100x2-705xl0 19 molecules. Each of the latter is moving, but 

 the velocities are variable within certain limits, and their average 

 is about 1-65X10 6 cm. per second. No molecule can move very 

 far without colliding with some other one. and the average free 

 path of a molecule is about 0-00000182 cm. We may regard 

 them as small, spherical bodies of about 2-17xlO~ 8 cm. in 

 diameter. The average velocity of movement depends on the 

 temperature (or, rather, what we call temperature is the variable 

 velocity of the molecules; the higher the latter the higher is the 

 temperature, and vice versa). 



Evidently the molecules will be moving in every conceivable 

 direction, and so they must collide with each other in all sorts of 

 possible ways. Usually the collisions will take place at some 

 ansjle to the directions of movement; sometimes a rapidly moving 



\ (Z)* * f3*f 



\x 





FIG. 50. DIAGRAM OF CHANCE COLLISIONS BETWEEN MOLECULES 



IN A GAS. 



molecule will overtake a more slowly moving one travelling in 

 the same direction, and sometimes two, which are moving in the 

 same direction, but towards each other, will collide " end on." 

 Being perfectly elastic bodies, no energy will be dissipated in 

 such collisions. After the collision the directions and velocities 

 will be changed in ways that are easily worked out from the 

 well-known theorems of mechanics. The reader may easily 

 construct these results by making use of vector diagrams, such 

 as those of Fig. 50. 



Now by certain mathematical formulae (deduced by Clerk 

 Maxwell and others from the theorems of probability) the relative 

 frequencies with which encounters between pairs of molecules 

 moving in all possible directions, and with all the possible 

 velocities lying between the upper and lower limits, can be 

 calculated. An encounter in any possible way (such as in the 

 Cases 1 to 4 of Fig. 50) is equally likely to occur. But there 



