186 LES PBINCIPES MATHEMATIQTJES DE 



make to tlie principles, the method, or the conclusions of a French 

 philosopher, we may always he sure that it is our own fault if these 

 objections are founded on a misconception of his meaning. To 

 the French philosophers we owe almost entirely those applications 

 of abstract science to the problems of social organisation, which are 

 already beginning to produce important results : the calculus of 

 probabilities, as given by Laplace, is destined to effect perhaps the 

 greatest social changes that the world has yet seen: still, in that 

 very wide field of research, which we call by the general name of 

 political economy, no mathematician had hitherto ventured to 

 intrude ; yet surely no science ever called louder for this aid. 

 Search where we will amid the labyrinth of words which at present 

 is said to constitute our political philosophy, we shall not fail to 

 come across definitions undefined, manj'-headed ambiguities of 

 terms, confusions of consequence and hypothesis, hardy prognos- 

 tications of contingencies that never happen, till the exasperated 

 searcher resigns in despair the " talking theory," and submits, 

 sulkily enough, to the " silent practice." 



It may fairly be doubted whether our science of political economy 

 has made one real step in advance since the famous treatise of 

 Adam Smith ; yet, admirable in itself and wonderful considering the 

 circumstances of its production, as this treatise is, Smith has done 

 little more than clear away obstructions and trace out the founda- 

 tions of the building which is to be : materials enough were ready 

 at hand, but tools were wanting. As in most other sciences, the 

 first investigators are stopped by failure of modes of expression and 

 forms of calculation ; seldom has it happened that a science springs 

 all-armed from the brain of one man as of Newton ; yet if Archi- 

 medes had possessed the Arabic numerals and the Hindoo algebra, 

 the world would not have waited two thousand years for a Newton ; 

 and if Adam Smith had possessed the calcidns, we should not at 

 this day be wearied and perplexed with the prolix circumlocution 

 of Eicard, or the refining complications of Mill. 



The work cited at the head of this article is the first attempt that 

 we are aware of to submit any part of this subject to formal analysis. 

 Its author is a well known and able French mathematician, and his 

 work is no less remarkable for the novelty of its method and the 

 lucidity of its style, than for the nature of the results which he has 

 obtained, and for which he justly claims the character of scientific 

 deductions. "We do not propose in this place to examine the truth of 

 the principles from which he sets out : all that we contend for is that, 

 granting the principles, the conclusions follow inevitably. As the 



