550 



NATURE 



[January 22, 1920 



microscopists would be likely to go to the trouble of 

 working in invisible light and of passing through a 

 long apprenticeship in mastering the difficulties, ap- 

 paratus of this description would necessarily be ex- 

 tremely costly, as the whole expense of designing and 

 of constructing special tools would fall on a small 

 number of outfits, or possibly on only a single one. 

 And there would still be the grave drawback that the 

 vast majority of objects would be opaque to extreme 

 ultra-violet rays, and yield only black-and-white outline 

 pictures. 



The so-called ultra-microscope does not represent 

 any advance in resolving power at all, but most 

 decidedly the reverse. It is highly valuable for the 

 detection of very minute particles and of their move- 

 ments, which it achieves simply by intense dark- 

 ground illumination, but the structure of the particles 

 remains unrevealed, and only that would amount to 

 an advance in resolving power. The seeing of these 

 minute particles is, in fact, of precisely the same kind 

 as the seeing of stars subtending less than oooi second 

 of arc at night with the naked eye, the resolving power 

 of which is of the order of 60 seconds. 



PARIS ACADEMY OF SCIENCES. 

 Bonaparte and Loutreuil Foundations. 



OF the 72,500 fran;s placed at the disposal of the 

 Academy by Prince Bonaparte, it is proposed to 

 allocate 30,000 francs as follows : — ■ 



5000 francs to Charles Alluaud, travelling naturalist 

 to the National Natural History Museum, for a geo- 

 logical and botanical expedition in the Moroccan Grand 

 .\tlas Chain. 



2000 francs to A. Boutaric, for the construction of 

 an apparatus for recording nocturnal radiation. 



1000 francs to Emile Brumpt, for continuing his 

 work on parasitic haemoglobinuria or piroplasmos of 

 cattle. 



3000 francs to E. Faurd-Frcmiet, for undertaking a 

 series of studies on histogenesis and certain surgical 

 applications. 



3000 francs to A. Guilliermond, for pursuing his 

 researches on lower organisms and on mitochondria. 



3000 francs to Joseph Martinet, for continuing his 

 researches on the isatins capable of serving as raw 

 material for the synthesis of indigo colouring matters. 



3000 francs to A. Vayssieres, for the continuation of 

 his researches of the marine molluscs, family 

 Cypraeideae. 



10,000 francs to the F^d^ration frangaise des 

 Soci^tes de Sciences naturelles, for the publication of 

 a fauna of France. 



The committee appointed to allocate the Loutreuil 

 foundations recommend the following grants : — 



(i) To establishments named bv the founder : 



10,000 francs to the National Museum of Natural 

 History, for the reorganisation of its librarv. 



7500 francs to the Paris Observatory, at the request 

 of the Central Council of the Observatories, for pur- 

 chasing an instrument. 



(2) Grants applied for direct : 



6000 francs to the Socl^t^ G^ologique du Nord, to 

 enable it to take up work interrupted bv the war. 



10,000 francs to I'Ecole des hautes Etudes indus- 

 trielles et commerciales de Lille, for restoring the 

 material of its chemical laboratorv. 



20,000 francs to the Observatory of Ksara (near 

 Beyrout). This laboratory was practically destroyed 

 by the Turks and Germans. The grant is towards its 

 restoration. 



8000 francs to Henri Deslandres, for the studv of 

 the radial movements of the solar vapours and the 

 thickness of the gaseous atmosphere of the sun. 



NO. 2621, VOL. 104] 



7500 francs to Maurice Hamy, to carry out certain 

 improvements in astronomical apparatus of precision. 



3500 francs to F61ix Boquet, for the publication of 

 Kepler tables. 



1000 francs to G. Raymond, for the continuation 

 of his actinometric experiments. 



10,000 francs to Charles Marie, for exceptional 

 expenses connected with the publication of the 

 "Tables annuelles de constants et donn6es num^riques 

 de chimie, de physique et de technologic." 



10,000 francs to the F6d6ration frangaise des 

 Soci(§t6s de Sciences naturelles, for the publication of 

 a French fauna. 



2000 francs to P. Lesne, for his researches on the 

 insects of peat-bogs. 



2000 francs to A. Paillot, for his researches on the 

 microbial diseases of insects. 



2000 francs to Just Aumiot, for the methodical study 

 of the varieties of potato. 



5000 francs to Albert Peyron and Gabriel Petit, for 

 the experimental study of cancer in the larger 

 mammals. 



3000 francs to Th. Nogier, for completing the instal- 

 lation of the radio-physiological laboratory of the 

 Bacteriological Institute of Lyons. 



THE MATHEMATICAL ASSOCIATION. 



'T' HE annual meeting of the Mathematical Associa- 

 -•■ tion was held in the London Day Training Col- 

 lege, Southampton Row, on January 7 and 8, under 

 the presidency of Prof. E. T. Whittaker. .At the 

 advanced section on the evening of January 7 the 

 president gave a lecture on "A Survey of the 

 Numerical Methods of Solving Equations." He 

 described in some detail "iterative processes" for 

 approximating to the roots and graphical methpds of 

 circumscribing the regions on the Argand plane, in 

 which the various roots lay. The Lobachefsky-GraefTe 

 method of approximating to the roots of equations and 

 power series was described in considerable detail. In 

 the animated discussion to which this lecture gave rise 

 it was clearly seen that a wider knowledge of practical 

 computative processes is a desideratum in all branches 

 of mathematical work, which has been practically 

 neglected hitherto in the schools and universities. It 

 was also felt that such practical numerical work was 

 the best possible introduction to the formal study of 

 function theory, many of the ideas underlying which 

 are usually presented in an entirely abstract way, 

 whereas they present themselves naturally and of 

 necessity in less general forms in the science of com- 

 putation. 



Next day, at the general section. Mr. C. Godfrey, 

 of the Royal Naval College, Osborne, surveyed 

 the whole question of the modern teaching of 

 geometry in schools. He strongly favoured a pre- 

 liminary course of practical instrumental work, to be 

 followed by a more formal course in which "logic" 

 is not too prominent. He advocated the entire post- 

 ponement of a really rigorous course of abstract geo- 

 metry until the post-school stage. Prof. T. P. Nunn 

 strongly supported the general tenor of Mr. Godfrey's 

 views, and urged the earlier teaching of "ratio and 

 proportion " as a practical instrument for solving 

 many problems, such as map-drawing, villa construc- 

 tion, etc. 



Prof. E. H. Neville, of University College, Reading, 

 next read a paper on " Convention and Duplexity in 

 Elementary Mathematics," in which he protested 

 against the usual "positive-sign" convention with 

 regard to vectors. Miss H. M. Cook dealt with "The 

 Place of Common Logarithms in Mathematical 

 Training," and Prof. W. P. Milne strongly urged 



