50 MOLECULAR MOTION AND ITS ENERGY 26 



velocity of the molecule being zero. We shall rather obtain 

 a value differing from zero in determining the mean of the 

 absolute values of the molecular speed without reference to 

 direction, in all those cases in which one of the three com- 

 ponents is zero. 



Maxwell's law must therefore be differently expressed 

 than it is in 24, when it has reference not to the com- 

 ponents of the velocity, but to the actual speed itself. We 

 can then explain the law as follows : 



There is a most probable value of the speed which occurs 

 more frequently than any other. Other values of the speed, 

 whether greater or less, occur the oftener or are the more 

 probable the nearer they approach to equality with the most 

 probable. Infinitely great as well as infinitely small values 

 of the speed have infinitely small probability. Molecules at 

 rest, therefore, are infinitely seldom to be met with. 



The connection between the two different forms of the 

 law may be clearly illustrated by a comparison employed by 

 Maxwell l in a lecture. 



If practised marksmen shoot at a target, the hits are most 

 crowded together near the centre, and there are but few 

 shots near the edge ; the marks are approximately repre- 

 sented by the figure on page 51. In this case, too, the distri- 

 bution of the hits follows the same law which Maxwell has 

 found for the molecules of gas, viz. the law of errors ; for 

 a shot at the target is an attempt to hit the centre, just as a 

 measurement is an attempt to hit the true value of the 

 measured magnitude. Small deviations from the centre are 

 therefore more probable than large ones in target practice 

 also. The shots can deviate to right or left, above or below, 

 and thus both horizontally and vertically. We have therefore 

 in this case two components of deviation to distinguish, a 

 horizontal and a vertical ; and for each component the value 

 zero is the most probable, since if we draw a series of 

 parallel lines, say vertically, on the target, that one which 

 passes through the centre passes also through more shot- 

 marks than any other. But what is true for the components 



1 ' On the Dynamical Evidence of the Molecular Constitution of Bodies,' 

 J. Chem. Soc. xiii. 1875, p. 438 ; Nature, xi. p. 357 ; Scientific Papers, ii. p. 418. 



