30 



is, as indicated above, that of averages, whereby, dis- 

 regarding the circumstances of each particular case, we 

 calculate the average size, the average velocity, the 

 average direction, &c. of a large number of instances. 

 But although this method is based upon experience, 

 and leads to results which may be accepted as sub- 

 stantially true ; although it may be applicable to any 

 finite interval of time, or over any finite area of space 

 (that is, for all practical purposes of life) there is no 

 evidence to show that it is so when the dimensions of 

 interval or of area are indefinitely diminished. The 

 truth is that the simplicity of nature which we at present 

 grasp is really the result of infinite complexity ; and 

 that below the uniformity there underlies a diversity 

 whose depths we have not yet probed, and whose secret 

 places are still beyond our reach. 



The present is not an occasion for multiplying illus- 

 trations, but I can hardly omit a passing allusion to one 

 all important instance of the application of the statistical 

 method. Without its aid social life, or the History of 

 Life and Death, could not be conceived at all, or only in 

 the most superficial manner. Without it we could never 

 attain to any clear ideas of the condition of the Poor, 

 we could never hope for any solid amelioration of their 

 condition or prospects. Without its aid, sanitary 

 measures, and even medicine, would be powerless. 

 Without it, the politician, and the philanthropist, would 

 alike be wandering over a trackless desert. 

 Mathema- It is, however, not so much from the side of Science 



and other^ ^ ^^ large as from that of Mathematics itself, that I desire 

 subjects. to speak. 1 wish from the latter point of view to indi- 

 cate connexions between Mathematics and other subjects, 

 to prove that hers is not after all such a far-off* region, 

 nor so undecipherable an alphabet, and to show that even 



