770 REPORT— 1898. 



on us, and it is pointed out that t^e comparatively small encouragement given by 

 our nation to the development of pure science is wholly incommensurate with 

 the gratitude which it ought to feel for the commercial benefits science has 

 enabled it to reach. This is undoubtedly true, and no one understands better 

 than myself how much commerce is indebted to those whose researches have 

 brought them — it may be fame — but certainly nothing else. The world, however, 

 appears to regard as equitable the division of reward which metes out tardy 

 approbation to the discoverer for devising some new principle, a modicum of the 

 world's goods to the inventor for showing how this principle can be applied, and 

 a shower of wealth on the contractor for putting the principle into practice. At 

 first sight, this appears like the irony of fate, but in fact the world thus only 

 proves that it is human, by prizing the acquisition of what it realises that it 

 stands in need of, and by vahiing the possession of what it is able to comprehend. 



Now, is there not a debt of which those who pursue pure science are in their 

 turn equally forgetful — viz., the debt to the technical worker or to some technical 

 operation for the inception of a new idea ? For purely theoretical investigations 

 are often born of technics, or, as Whewell puts it, ' Art is the parent, not the 

 progeny, of science ; the realisation of principles in practice forms part of the 

 prelude as well as of the sequel of theoretical discovery.' I need not remind you 

 that the whole science of floating bodies is said to have sprung from the solution 

 by Archimedes of JBiero's doubt concernintr the transmutation of metals in the 

 manufacture of his crown. In that case, however, it was the transmutation of 

 gold into silver, and not silver into gold, that troubled the philosopher. 



Again, in the 'History of the Koyal Society at the End of the Eighteenth 

 Century,' Thomson says regarding Newton : ' A desire to know whether there was 

 anything in judicial astrology first put bim upon studying mathematics. He dis- 

 covered the emptiness of that study as soon as he erected a figure; for which 

 purpose he made use of one or two problems in Euclid. . . . He did not then 

 read the rest, looking upon it as a book containing only plain and obvious 

 things.' 



The analytical investigation of the motion of one body round an attracting' 

 centre, when disturbed by the attraction of another, was attacked independently 

 by Clairault, D'Alembert, and Euler, because the construction of lunar tables had 

 such a practical importance, and because large money prizes were ofiered for their 

 accurate determination. 



The gambling table gave us the whole Theory of Probability, Bernoulli's 

 and Euler's theorems, and the first demonstration of the binomial theorem ; while 

 a request made to Montmort to determine the advantage to the banker in the game 

 of ' Pharaon ' started him on the consideration of how counters could be thrown, 

 and so led him to prove the multinomial and various other algebraical theo- 

 rems. Lastly, may not the gambler take some credit to himself for the first 

 suggestion of the method of least squares, and the first discussion of the integra- 

 tion of partial difl'erential equations with finite differences contained in Laplace's 

 famous ' Th(?orie Analytique des Probabilit^s ? ' 



The question asked Rankine by James R. Napier reg.arding tlie horse-power 

 which would be necessary to propel, at a given rate, a vessel which Napier was 

 about to build, resulted in the many theoretical investigations carried out by 

 Rankine on water lines, skin-friction, stream lines, &c. For, as Professor Tait has 

 said, ' Rankine, by his education as a practical engineer, was eminently qualified 

 to recognise the problems of wliich the solution is required in practice; but the 

 large scope of his mind would not allow him to be content with giving merely the 

 solution of those particular eases which most frequently occur in engineering as 

 we now know it. His method invariably is to state the problem in a very 

 general form, find the solution, and apply tliis solution to special cases.' 



Helmholtz studied physiology because he desired to be a doctor, then physics 

 because he found that he needed it for attacking physiological problems, and lastly 

 mathematics as an aid to physical research. Rut I need not remind you that it is 

 his spleadid work in mathematics, physics, and physiology, and not his success in 

 ministering to the sick, that has rendered his name immortal. 



