MATHEMATICS 



to the practical value of a solution of a very special- 

 ised chess problem, in which we are informed that 

 " Black mates in three." But such a comparison 

 would be very unjust. I will give one illustration 

 only, in which this very comprehensive enumera- 

 tion has been of service. Let us turn our thoughts, 

 by an apparently violent transition, to an opalescent 

 liquid, consisting of water with particles of some sub- 

 stance in suspension, the substance being capable of 

 forming, with equal likelihood, agglomerations of 

 one, two, three, or any number of molecules con- 

 sistent with a state of suspension in the liquid. If the 

 maximum number under these conditions is N, the 

 proportion which will form, say, an agglomeration 

 of m particles is, on the whole, from considerations 

 of probability, directly proportional to the number 

 of partitions of the integer m, if the total number of 

 molecules is extremely large. Thus the constitu- 

 tion of the suspended particles can be calculated, 

 and so also, in consequence, as we know the number 

 of any specified size, can such phenomena as the 

 effect of the liquid on light passing through it, 

 which is different for light of different colours or 

 wave-lengths. In fact, a very large number of 

 physical phenomena which such a liquid would 

 shew can be actually predicted as a consequence 

 of the formulas belonging to this apparently quite 

 useless branch of Mathematics. He would be a 

 bold man, therefore, who would say that any 



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