xxxi.] LIMITS OF SCIENTIFIC METHOD. 759 



his beautiful mode of determining specific gravities. Yet 

 these great discoveries are the commonplaces of our school 

 books. Step by step we can trace upwards the acquirement 

 of new mental powers. What could be more wonderful 

 than Napier's discovery of logarithms, a new mode of 

 calculation which has multiplied perhaps a hundredfold 

 the working powers of every computer, and has rendered 

 easy calculations which were before impracticable ? Since 

 the time of Newton and Leibnitz worlds of problems have 

 been solved which before were hardly conceived as matters 

 of inquiry. In our own day extended methods of mathe- 

 matical reasoning, such as the system of quaternions, have 

 been brought into existence. What intelligent man will 

 doubt that the recondite speculations of a Cayley, a Syl- 

 vester, or a Clifford may lead to some new development of 

 new mathematical power, at the simplicity of which a 

 future age will wonder, and yet wonder more that to us they 

 were so dark and difficult. May we not repeat the words 

 of Seneca : " Veniet tempus, quo ista quse nunc latent, in 

 lucem dies extrahat, et longioris sevi diligentia : ad inquisi- 

 tionem tantorum sstas una non sufficit. Veniet tempus, 

 quo posted nostri tarn aperta nos uescisse mirentur." 



The Reign of Law in Mental and Social Phenomena. 



After we pass from the so-called physical sciences to 

 those which attempt to investigate mental and social 

 phenomena, the same general conclusions will hold true. 

 No one will be found to deny that there are certain uni- 

 formities of thinking and acting which can be detected 

 in reasoning beings, and so far as we detect such laws 

 we successfully apply scientific method. But those who 

 attempt to establish social or moral sciences soon become 

 aware that they are dealing with subjects of enormous 

 perplexity. Take as an instance the science of political 

 economy. If a science at all, it must be a mathematical 

 science, because it deals with quantities of commodities. 

 But as soon as we attempt to draw out the equations 

 expressing the laws of demand and supply, we discover 

 that they have a complexity entirely surpassing our powers 

 of mathematical treatment. We may lay down the general 

 form of the equations, expressing the demand and supply 



