MATHEMATICS 



various members of a set of alternative events. 

 The value and continuous use of such investiga- 

 tions as the foundation of all actuarial work is 

 familiar to everybody. Less familiar, perhaps, are 

 the contributions which investigations of the same 

 kind have made to the consideration of such matters 

 as heredity and the variations in the generations 

 of a species from its mean type. I wish to say at 

 the outset that of all the modern developments of 

 Mathematics which are now taking place, there is 

 none more fertile and more rapidly expanding in 

 scope than the so-called ' Theory of Probability.' 

 In Physics we have the whole kinetic theory of 

 gases, and the newer Quantum Theory built, in 

 the first instance, entirely upon this as a secure 

 foundation. In the hands of Planck, it has recently 

 come to absorb the whole body of thought 

 which, with the engineer, the physicist, and the 

 physical chemist, previously clustered round the 

 word ' Entropy.' The Entropy of a system is 

 merely determined by the probability of the 

 setting-up of that system as against all others 

 which are formally possible. 



The Theory of Probability is, of course, built 

 up by the gradual solution of more and more 

 complex problems, whose humble starting-point 

 deals with such things as the chance of throwing 

 four sixes in, say, ten throws with dice, or in fact 

 any problem of a simple nature in which we require 



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