smallest portion of matter which we can subject to experiment consists of millions of molecules,” Maxwell later noted. “We cannot, therefore, ascertain the actual motion of any one of these molecules; so that we are obliged to … adopt the statistical method of dealing with large groups of molecules.”20 That statistical method, he showed, could indeed reveal “uniformities” in molecular behavior. “Those uniformities which we observe in our experiments with quantities of matter containing millions of millions of molecules are uniformities of the same kind as those explained by Laplace and wondered at by Buckle,” Maxwell declared.21

The essential feature of Maxwell’s work was showing that the properties of gases made sense not if gas molecules all flew around at a similar “average” velocity, as Clausius had surmised, but only if they moved at all sorts of speeds, most near the average, but some substantially faster or slower, and a few very fast or slow. As the molecules bounced off one another, some gained velocity; others slowed down. In subsequent collisions, a fast molecule might be either slowed down or speeded up. A few would enjoy consecutive runs of very good (or very bad) luck and end up moving extremely rapidly (or slowly), while most would get a mix of bounces and tend toward the overall average velocity of all the molecules in the box.

Just as Quetelet’s average man was fictitious, and key insights into society came from analyzing the spread of features around the average, understanding gases meant figuring out the range and distribution of molecular velocities around the average. And that distribution, Maxwell calculated, matched the bell-shaped curve describing the range of measurement errors.

As Maxwell refined his ideas during the 1860s, he showed that when the velocities reached the bell-shaped distribution, no further net change was likely. (The Austrian physicist Ludwig Boltzmann further elaborated on and strengthened Maxwell’s results.) Any specific molecule might speed up or slow down, but the odds were strong that other molecules would change in speed to compensate. Thus the overall range and distribution of velocities would stay the same. When a gas reached that state—in which



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement