DISCOVERT BY NEW MODES OF INTELLECTUAL OPERATION. 607 



new scientific instruments) the power and extent of action 

 of man's mind may be as much enlarged beyond its present 

 condition, as its present state is beyond what it was 

 thousands of years ago. That such new methods are 

 really possible appears to be proved by their invention in 

 the past, as well as by the very rapid way in which cal- 

 culating boys arrive at their conclusions. 



Openings for extending the range of man's intellectual 

 influence appear to lie in investigations of the physical 

 conditions of mental action 1 also in the invention of in- 

 struments for combining, dividing, multiplying, and per- 

 mutating ideas ; for drawing conclusions (as in Jevons's 

 logical machine) ; or for calculating periodic phenomena 

 and solving differential equations, as in the ' Integrating 

 Machine ' of Professor J. Thomson, 2 and the ' Harmonic 

 Analyser ' of Sir W. Thomson. 3 



CHAPTER LX. 



DISCOVERY BY MEANS OF CALCULATIONS BASED UPON 

 KNOWN TRUTHS. 



AN immense number of discoveries have been made by 

 this method, but as this book is simply a treatise on 

 qualitative research, I will only refer to a few instances. 

 The method is applicable chiefly in the exact sciences, and 

 in those parts of other sciences which are based upon 

 exact and known quantitative conditions. It has been 

 largely used in mathematics, the mechanics of solids, 



1 See pp. 55-59. 



2 See Proc. Roy. Soc. t vol. xxiv. 1876, pp. 262-275. 

 Ibid. vol. xxvii. 1878, p. 371. 



