332 SCIENTIFIC THOUGHT. 



19. The mathematical formula is the point through which 



Focalising -^ " 



matjiemati. ^^^ ^^^ light gained by science passes in order to be of 

 cai formula!, ^^gg ^^ practicc ; it is also the point in which all know- 

 ledge gained by practice, experiment, and observation must 

 be concentrated before it can be scientifically grasped. 

 The more distinct and marked the point, the more con- 

 centrated will be the light coming from it, the more un- 

 mistakable the insight conveyed. All scientific thought, 

 from the simple gravitation formula of Newton, through 

 the more complicated formulae of physics and of chem- 

 istry, the vaguer so-called laws of organic and animated 

 nature, down to the uncertain statements of psychology 

 and the data of our social and historical knowledge, alike 

 partakes of this characteristic, that it is an attempt to 

 gather up the scattered rays of light, the diffused know- 

 ledge, in a focus, from whence it can be again spread out 

 and analysed, according to the abstract processes of the 

 thinking mind. But only where this can be done with 

 mathematical precision and accuracy is the image sharp 

 and well defined, and the deductions clear and unmis- 

 takable. As we descend from the mechanical, through 

 the physical, chemical, and biological, to the mental, 

 moral, and social sciences, the process of focalisation 

 becomes less and less perfect, the sharp point, the 



most all the present difference be- provement of the steam-engine to 



tween the best steam-engine and 

 the worst is some 5 or 6 per cent" 

 (Lodge). Prof. Unwin sums up by 

 saying: "Since 1845 purely scien- 

 titic men, scientific experimenters 



the exclusion of either of the 

 others. . . . Representing perhaps 

 rather the scientific than the prac- 

 tical interest, I do not think that 

 the mathematical and plij'sical re- 



and practical engineers have all ^ searches of which I have tried to 



been engaged in the study of the 

 steam-engine. I do not believe 

 that any one of the three can 

 claim all the credit for the im- 



give an account have had no in- 

 fluence on the practical business of 

 the engineer." 



