14 REPORT 1878. 



whereby solid figures may be delineated on paper, or what is now termed 

 descriptive geometry. 



Nor perhaps wonld the sciences which concern themselves with 

 reasoning and speech, nor the kindred art of Music, nor even Literature 

 itself, if thoroughly probed, offer fewer points of dependence upon the 

 science of which I am speaking. What, in fact, is Logic but that part 

 of universal reasoning ; Grammar but that part of universal speech ; 

 Harmony and Counterpoint but that part of universal music, " which accu- 

 rately lays down," and demonstrates (so far as demonstration is possible) 

 precise methods appertaining to each 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 characteristics which 

 distinguish the mathematical phase of a subject, we are naturally led to 

 expect that the approach to such 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 investigations alike tend to issue in 

 measurement, and to that extent to assume a mathematical phase, I should 

 be embarrassed 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 particularly 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 representation ; and it is improbable that one of 120,000th of 

 an inch could be singly discerned with the highest powers at our com- 

 mand. 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 the lengths of luminiferous waves. To this 

 he was led, not by any attempt at individual measurement, but by taking 

 account of them in the aggregate, and observing the tints which they 

 scatter laterally when clustered in the form of actinic clouds. The small 

 bodies with which experimental Science has recently come into contact 

 are not confined to gaseous molecules, but comprise also complete organisms ; 

 and the same philosopher has made a profound study of the momentous 

 influence exerted by these minute organisms in the economy of life. And if, 

 in view of their specific effects, whether deleterious or other, on human life, 

 any qualitative classification, or quantitative estimate be ever possible, it 

 seems that it must be effected by some such method as that indicated above. 



