September 16, 1922] 



NA TURE 



The order of magnitude of the corresponding number 

 of triplets, of any possible type, is 



(log*) 3 ' 

 and so on generally. Further, we can assign the 

 relative frequencies of pairs or triplets of different 

 types ; there are, for example, about twice as many 

 pairs the difference of which is 6 as there are pairs 

 with the difference 2. All these results have been 

 tested by actual enumeration from the factor tables 

 of the first million numbers ; and a physicist would 

 probably regard them as proved, though we of course 

 know very well that they are not. 



There is a great deal of mathematics the purport of 

 which is quite impossible for any amateur to grasp, 

 and which, however beautiful and important it may be, 

 must always remain the possession of a narrow circle 



of experts. It is the peculiarity of the theory of 

 numbers that much of it could be published broadcast, 

 and would win new readers for the Daily Mail. 

 The positive integers do not lie, like the logical founda- 

 tions of mathematics, in the scarcely visible distance, 

 nor in the uncomfortably tangled foreground, like the 

 immediate data of the physical world, but at a decent 

 middle distance, where the outlines are clear and yet 

 some element of mystery remains. There is no one so 

 blind that he does not see them, and no one so sharp- 

 sighted that his vision does not fail ; they stand there 

 a continual and inevitable challenge to the curiosity 

 of every healthy mind. I have merely directed your 

 attention for a moment to a few of the less immediately 

 conspicuous features of the landscape, in the hope 

 that I may sharpen your curiosity a little, and that 

 some may feel tempted to walk a little nearer and 

 take a closer view. 



The Organisation of Research. 1 



By Principal J. C. Irvine, C.B.E., D.Sc, LL.D., F.R.S. 



r "THE British Association was the product of an age 

 J- rather than the inspiration of any one man, yet 

 of those who first gave practical effect to the movement 

 which has spread scientific learning and has bound its 

 devotees in a goodly fellowship there was no more eager 

 spirit than Sir David Brewster. It is not an ex- 

 aggerated claim that it was he who founded the British 

 Association. One may trace his enlightened action 

 to a desire to combat the apathy and distrust shown 

 by the Government of his day towards scientific work 

 and even scientific workers. Only in the historical sense 

 can I claim any relationship with Brewster. It is my 

 privilege to occupy the Principalship he once held, and 

 I cannot escape from the thought that the daily tasks 

 now mine were once his. 



It is thus inevitable that to-day a name often in my 

 mind should spring once more into recollection, especi- 

 ally as my distinguished predecessor was present at 

 the first Hull meeting in 1853. when he contributed two 

 papers to Section A. Chemists should be among the 

 first to pa)- grateful tribute to Brewster's efforts on 

 behalf of science, and I propose, therefore, to include in 

 my address a review of the position scientific chemistry 

 has won since his day in public and official estimation. 

 Moreover, at the express suggestion of some of our 

 members whose opinions cannot be disregarded, I am 

 induced to add the consideration of the new responsi- 

 bilities chemists have incurred now that so many of 

 Brewster's hopes have been realised. These were 

 recently submitted by me to another audience and, 

 through the medium of an article in Nature (July 22. 

 p. 131), are possibly known to you already, but I agree 

 with my advisers that their importance warrants 

 further elaboration and wider discussion. 



It would be idle to recall the lowly position of 

 chemistry as an educative force in this country, or to 

 reconstruct the difficulties with which the scientific 

 chemist was confronted during the first thirty years 

 of the nineteenth century. Present difficulties are 



1 From Part I. of the presidential address delivered to Section B 

 (Chemistry) of the British Association at Hull on Sept. 7. 



NO. 2759, VOL. I IO] 



serious enough, and press for all our attention, without 

 dwelling unduly on troubles of the past. But we must 

 at least remember that in the early days of the British 

 Association " schools " of chemistry were in their 

 infancy, and that systematic instruction in the science 

 was difficult to obtain. Another point of fundamental 

 importance which has to be borne in mind is that the 

 masters of the subject were then for the most part 

 solitary workers. 



It is difficult for us, looking back through the years, 

 to realise what it must have meant to search for truth 

 under conditions which were discouraging, if not 

 actually hostile. Yet, although his labours were often 

 thankless and unrewarded, the chemist of the time 

 was probably a riper philosopher and a finer enthusiast 

 than his successor of to-day. He pursued his inquiries 

 amid fewer distractions, and in many ways his lot 

 must have been happy, save when tormented by the 

 thought that a subject so potent as chemistry in 

 developing the intellectual and material welfare of the 

 community should remain neglected to an extent which 

 to us seems incredible. 



Public sympathy was lacking, Government support 

 was negligible or grudgingly bestowed, and there was 

 little or no co-operation between scientific chemistry 

 and industry. As an unaided enthusiast the chemist 

 was left to pursue his way without the stimulus, now 

 happily ours, which comes from the feeling that work 

 is supported by educated and enlightened appreciation. 



Let me quote from one of Faraday's letters now in 

 my possession and, so far as I can trace, unpublished. 

 Writing to a friend immediately before the foundation 

 of the British Association, he relates that a manu- 

 facturer had adopted a process developed in the course 

 of an investigation carried out in the Royal Institution. 

 The letter continues : " He " (the manufacturer) 

 " writes me word that, having repeated our experi- 

 ments, he finds the product very good, and as our in- 

 formation was given openly to the world he, as a matter 

 of compliment, has presented me with some pairs of 

 razors to give away." If ever there was a compliment 



