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of these Arts ? And I might even appeal to the 

 common consent which speaks of the mathematical as 

 the pattern form of reasoning and model of a precise 

 style. 



Taking, then, precision and exactness as the charac- 

 teristics which distinguish the mathematical phase of a 

 subject, we are naturally led to expect that the approach 

 to sach a phase will be indicated by increasing application 

 of the principle of measurement, and by the importance 

 which is attached to numerical results. And this very 

 necessary condition for progress may, I think, be fairly 

 described as one of the main features of scientific 

 advance in the present day. 



If it were my purpose, by descending into the arena 

 of special sciences, to show how the most various inves- 

 tigations alike tend to issue in measurement, and to that 

 extent to assume a mathematical phase, I should be em- 

 barrassed by the abundance of instances which might 

 be adduced. I will therefore confine myself to a 

 passing notice of a very few, selecting those which 

 exemplify not only the general tendency, but also 

 the special character of the measurements now par- 

 ticularly required, viz., that of minuteness, and the 

 indirect method by which alone we can at present hope 

 to approach them. An object having a diameter of an 

 80,000th of an inch is perhaps the smallest of which 

 the microscope could give any well-defined representa- 

 tion ; and it is improbable that one of 120,000th of 

 an inch could be singly discerned with the highest 

 powers at our command. But the solar beams and 

 the electric light reveal to us the presence of. bodies 

 far smaller than these. And, in the absence of any 

 means of observing them singly. Professor Tyndall has 

 suggested a scale of these minute objects in terms of 



