February 6, 1908] 



NATURE 



331 



looked for once every fourlh or sixth year, tor it is 

 not claimed that inoculation cures " sickness " and 

 increases the frequency with which leguminous crops 

 can be grown. Even a 50 per cent, increase in crop, 

 useful though it would be, would in these circum- 

 stances hardly effect any particular revolution in agri- 

 cultural practice. We are therefore unable to follow the 

 author when he remarks : — " For a few thousand pounds 

 the 21 million acres of poor barren land in this country 

 could be made productive and rendered capable of finding 

 work for and supporting such a population that both the 

 food problem and the unemployed problem would be easy 

 of solution. . . . Waste land reclaimed and made fertile 

 for 6d. an acre! . . ." It would have been better if the 

 author had induced an agricultural friend to revise this 

 estimate. We are told on pp. 8 and 10 that inoculation 

 will be a failure when the soil is too acid and in need 

 of lime, when it is deficient in phosphates and potash, 

 when the physical conditions of the soil are unfavourable, 

 or when drainage is needed. Barren land in England 

 commonly suffers from several or all of these defects. 

 How far would sixpence an acre go in putting them 

 right? 



.\t a time when the farmer needs, and is willing to 

 accept, all the assistance the scientific investigator can 

 give him, the fnct that an enthusiastic worker like Prof. 

 Bottomley has directed fiis attention to agricultural botany 

 is a matter for congratulation, and we can only regret 

 that in this, his first appeal to the practical man, his 

 enthusiasm should have outrun his judgment. However, 

 although we must regard the present production as un- 

 satisfactory, we still look forward to sound work from 

 the author on this subject, and we wish him success in 

 'his work on the numerous and difficult problems connected 

 with soil inoculation. E. J. R. 



yiXTHEMXTlCM. EDUCATION AND 

 RESEARCH. 

 'T'HE annual meeting of the Mathematical Association 

 was held at King's College, London, on Saturday, 

 January 25. The proceedings bear abundant testimony to 

 the great changes which are taking place in the methods 

 of teaching mathematics, and show that these changes 

 are not confined to the subject of elementary geometry. 

 Mr. W. J. Dobbs showed what useful work could be done 

 by means of simple home-made apparatus in the teaching 

 of mechanics, his apparatus consisting merely of spiral 

 springs with cardboard scales attached for illustrating 

 applications of the parallelogram law, and suspended sticks 

 for illustrating the principle of the lever and the balance. 

 He further showed how the solution of problems on 

 accelerated motion could be greatly simplified by the 

 application of direct methods not involving such restric- 

 tions as to units as are necessary in working with 

 " poundals " or "slugs." Mr. C. O. Tuckey made a 

 distinct step in advance in his suggestions as to the 

 methods of introducing the properties of convergent series 

 to students who require these series principally in the study 

 of the calculus, and it is interesting to compare his views 

 with those which prevailed twenty or thirty years ago, 

 when the calculus was regarded as something sacred which 

 should not be handled by students until they had passed 

 ■ through a lengthy period of probation in working with 

 algebraic series. Mr. F. J. W. Whipple's lantern-slides, 

 showing how the convergency of certain trigonometric 

 series could be illustrated by diagrams drawn by mere 

 beginners, were a revelation to those who had approached 

 the subject by the study of pages of long formula?. Mr. 

 \\'. E. Bryan suggested a very original way of introducing 

 similar figures in geometry, a method w'hich, however, 

 may well form a basis of further discussion and criticism. 

 An apparatus for drawing rectangular hyperbolas was 

 shown bv Mr. H. I,. Trachtenberg. 



In his' presidential address Prof. G. H. Bryan, F.R.S., 

 de.ilt wilh the uses of mathematics and the training of 

 mathematical teachers. It was necessary that the public 

 should be made aware of the important part w-hich higher 

 mathematical research had played, and w'as destined to 

 play, in practical applications on which the prosperity of 



NO. 1997. VOL. yy] 



a nation depended. As an instance. Prof. Bryan referred 

 to the seemingly unpractical and uninteresting study of 

 the properties of imaginary quantities, without which 

 modern applications of electricity to purposes of commerce, 

 including wireless telegraphy, could never have reached 

 their present developments. In order to overcome the 

 existing lack of public interest in mathematical matters 

 it was important that the university training of every 

 mathematical teacher should afford him some insight inta 

 the research aspect of some one branch of the subject, 

 and the experiments that had already been made in this 

 direction in the university colleges of Wales showed that 

 this ideal was quite capable of attainment. Turning to 

 the teaching of mathematics in elementary schools, Prof. 

 Brvan e.xpressed the opinion that the children of the work- 

 ing man should' learn to measure and calculate correctly 

 in order that they might become more efficient and improve 

 their positions in the labour market. If their teaching 

 was conducted in such a way as merely to stimulate in 

 them a spirit of luxury and discontent as distinct from a 

 desire for self-improvement, the working classes had quite 

 as much cause for complaint as the tax-payers. But in the 

 training of elementary teachers, antiquated and unpractical 

 methods are still prevalent, and are often greatly 

 encouraged by examinational requirements. 



RADIOGRAPHY IN PEARL FISHING. 

 'T'HE products of the sea are commonly wasted to a 

 "^ very deplorable degree by those who gather and use 

 them. In no instance is this waste more marked than 

 in the search for pearls. By the old method, which is 

 still in vogue as a general rule, an enormous number of 

 the so-called oysters are taken from their habitat and 

 destroyed without any thought of economy. It is said 

 that only one pearl is found in 100 oysters, and only 

 I per cent, of the pearls found are of any commercial 

 value. Thus some 10,000 of the precious molluscs are 

 sacrificed for every useful pearl obtained. Among these 

 victims there must be a vast amount of immature pearls 

 or seed, pearls in posse, which might grow and become 

 valuable gems, which are deprived of that possibility by 

 preiTiature destruction. 



In the year 1901 Prof. Raphael Dubois took radiographs 

 of pearls in situ within the shell of Unio prolijera, and' 

 obtained a clear view of their size and situation in spite 

 of the thickness of the shell in which they were encased. 

 He showed these radiographs at the Linnean Society of 

 Lyons, and remarked that the X-rays might receive a 

 novel application if used in the fisheries of Ceylon, and 

 the destruction of a vast number of the prized molluscs 

 might thus be avoided. 



The difficulty of applying the X-rays to many thousands 

 of shells per diem seemed sufficient to deter the ordinary 

 person from such a laborious attempt. However, a few 

 vears later an electrical engineer of New York, Mr. John 

 j. Solomon, who took an interest in the question of 

 pearls, was struck by the same idea of using the X-rays 

 to detect the existence of pearls within the shell of the 

 living animal. He was then unaware of the earlier ex- 

 periments of Prof. Dubois, but promptly set himself about 

 the work from a commercial point of view. 



He found that an exposure necessary to obtain a good 

 picture did not in any way injure the animal, and even 

 an exposure of ten times as long could be applied with- 

 out causing its death from the effect of the rays. The 

 dangers lay rather in the removal of the bivalve from its 

 normal attachment and in the time required for its transit 

 from its bed to the laboratory of the photographer : for 

 the pearl oyster is really a kind of mussel, which holds 

 on to some fixed object by a brush of fibrils {hyssus) 

 growing from its body 



Thus the fundamental principle of Prof. Dubois, to save 

 the life of unremunerative bivalves, bids fair to be carried 

 out by ."Xmerican ingenuity and capital. 



For practical purposes, where many thousands of shells 

 have to be radiographed daily, a completely novel kind of 

 plant had to be devised. This was done, and final success 

 was considered to be well in view, when too clear radio- 

 graphs could be taken on an overage every fifteen seconds. 



