590 SCIENTIFIC THOUGHT. 



information that we seem to possess ; it resembles the 

 knowledge which an economist may possess of the 

 statistics of a society or of the properties of the 

 " mean " man. If such be the case, the theory of 

 large numbers and the calculus of probabilities must 

 be applicable and useful in dealing with those 

 phenomena which, through their minuteness and great 

 number, elude our detailed examination. 



The first to introduce this conception of treat- 

 ing a very large assemblage of moving things by the 

 method of averages was Joule, 1 who, adopting Daniel 

 Bernoulli's conception, calculated the average velocity 

 which a particle of hydrogen gas must possess in 

 order to explain the total effect which shows itself 

 as a definite gas pressure at a definite temperature. 

 His result was that this average speed must be 6055 

 feet per second in order to be equal to the pressure 

 of one atmosphere at the zero temperature of the 

 Centigrade scale. The speed of the particles, however, 

 cannot be assumed to be equal, owing to continual 

 encounters ; and we are indebted to Clausius and 

 27. Clerk-Maxwell for introducing the more refined statis- 



Clausius 



me thds f the theory of probabilities. They 

 calculated the mean free path, and showed that 

 former calculations of the average speed were in the 

 main correct. The kinetic theory of gases afforded an 

 opportunity of brilliantly applying the conceptions of 

 averages or means and of the differences of frequencies 

 as the measure of the probability of certain occurrences. 

 In this case as was first shown by Joule's figures we 



1 See supra, vol. i. p. 434, and vol. ii. p. 110. 



