January 9, 1914] 



SCIENCE 



47 



were conserved. The important thing then 

 was the application of the laws of proba- 

 bility, and by this means Maxwell was led 

 to show that in a steady state, that is, one 

 independent of the time, the velocities were 

 distributed according to the so-called law 

 of errors. As this law is so important, per- 

 mit me to give the familiar example which 

 illustrates the main points of the discussion. 

 Suppose we have a vertical board into which 

 are driven a large number of horizontal 

 pins regularly arranged in symmetrical 

 diagonal lines. If now we allow shot to fall 

 from a funnel above the middle of the 

 board, a shot striking any pin will fall 

 either to the right or the left. Of course 

 the circumstances will, according to the 

 laws of dynamics, determine in each partic- 

 ular case which way it will fall, but if we 

 know nothing more about them we can only 

 assume that it is equally likely to fall either 

 way. The next time it strikes the same thing 

 is the case, and the question arises what 

 will be the effect of a great number of sim- 

 ilar causes each equally likely to act one 

 way or the other. The answer is simple. 

 Evidently there will be more shot that will 

 fall directly below than toward either side, 

 and the distribution will be symmetrical on 

 both sides, falling off to nothing at great 

 distances. If we should find that the distri- 

 bution was unsymmetrical we should im- 

 mediately infer that there was something 

 unfair about the apparatus, for instance, 

 the pegs were different on one side from 

 the other. 



Let me here diverge for a moment to 

 point out that here is a method which is as 

 applicable to biological phenomena as to 

 dynamics, and that by its means the re- 

 sultant of a large number of causes acting 

 at random may be investigated. The essen- 

 tial of the method is that one of two effects 

 is held to be as likely as the other. If we 

 consider a large number of similar objects, 



say beans or shells, measure their length or 

 some characteristic feature, the different 

 values will in general be distributed accord- 

 ing to the law of errors. If not, our as- 

 sumptions as to what is equally likely are 

 not true. This statistical method is of the 

 greatest use in anthropology and in the 

 study of inheritance, now such an impor- 

 tant part of biological study. It is true 

 that the biologist may object that this 

 method is a purely mathematical one, and 

 is not borrowed from physics. This I shall 

 not stop to discuss, merely pointing out 

 where the same method is applicable to 

 both physical and biological phenomena. 



To return then to the application of sta- 

 tistical methods to dynamics. Besides the 

 law of distribution of velocities. Maxwell 

 was able to show that if molecules of two 

 or more kinds were admitted to the same 

 space then when statistical equilibrium was 

 attained the mean kinetic energy of the 

 different types of molecules would be the 

 same, thus leading to a dynamical explaua- 

 tion of the law of Avogadro, one of the most 

 important of chemical laws. Boltzmann, 

 taking up the subject at this point, pushed 

 the generalization of Maxwell farther, and 

 applied it to individuals each more compli- 

 cated than the simple molecule, and was 

 able to show how a system not in statistical 

 equilibrium tends to approach that condi- 

 tion. Furthermore, he defines a certain 

 function of the state of distribution which 

 continually tends to increase, thus having 

 the same property as the entropy of a sys- 

 tem. Thus for the first time we get an ex- 

 planation of entropy, which dynamics alone 

 failed to give, by means of statistical dy- 

 namics or probability. 



Perhaps the most striking triumph of 

 the statistical method has been its applica- 

 tion to the theory of radiation from a hot 

 body, which has been successfully worked 

 out in the last decade, through the endeav- 



