2© G. H. KNIBBS. 



is involved. The more thoroughly we trace these inter-relations 

 the better shall we understand that the distinction between 

 theoretical and practical is modal, not essential. 



Consider for a moment, even the part played in the modern 

 world by computation. The actuary who deals with questions of 

 value and of money, the navigator, engineer, surveyor, electrician, 

 and often too the chemist, employ logarithms : who, a priori, 

 would have imagined that the curious conception of two points 

 moving on lines — the one on a finite line diminishing its velocity 

 so as always to be proportional to the distance to the terminal 

 toward which it is moving, the other on a line of indefinite length 

 maintaining a uniform velocity, coupled with the conception of 

 the ratio between the untra versed distance on the first line, to the 

 traversed distance on the second — who, I say, would have imagined 

 that conception 1 to have led to the production of the logarithmic 

 tables which have become so indispensable to us, and without 

 which much of our computation would be hopelessly tedious. Or 

 if we may be allowed another illustration, who could have antici- 

 pated that the study of the properties of curves formed by the 

 section of a cone by a plane, could have been so applied as to 

 enable the navigator to guide his craft safely over the expanse of 

 ocean. Apparently these belong to worlds of things wholly 

 unrelated ; yet the opposite is the truth. And so it is all through. 

 We do well to remember that the spirit of the scorner of those 

 great outreachings of the human mind after a fuller and deeper 

 knowledge of the laws of thought and of the phenomena of the 

 worlds, in short after abstract science, would lead us back to 

 barbarism : we are never justified in suppressing our insatiate 

 thirst for knowledge because its practical issue is wholly beyond 

 our ken. But of this more anon. 



One of the most striking facts in modern industrial progress is 

 the daily increasing significance of the part played by chemistry, 

 a science in its turn, dependent, for some of its most conspicuous 



1 Napier's, who did not recognise the exponential character of 

 logarithms. 



