46b 



NATURE 



[June io, 1920 



which is now on the road to solution. The Chamber 

 of Deputies has taken the matter in hand, and agreed 

 to proposals which now await consent by the Senate. 

 According to an article by M. M. Fourniols pub- 

 lished in the Revue ginerde des Sciences for May 15, 

 the plan is to divide the river into six sections, to be 

 managed separately or preferably by a single body. 

 Concessions are to be for seventy-five years' duration, 

 and will be helped by State loans. Besides the utilisa- 

 tion of water-power, the project embraces the im- 

 provement of navigation, the creation of river ports, 

 and the construction of irrigation works. At present 

 the conditions are not favourable for navigation, but 

 the recently opened canal from Marseilles to Aries 

 opens a new vista of possibilities in cheap river con- 

 nections with the sea. It is proposed to erect a 

 number of power stations between Genissiat, near 

 the Swiss frontier, and Comps, near Tarascon. Genis- 

 siat with 200,000 h.p. will be the largest, and will 

 probably supply power to Paris. Other important 

 stations will be near Lyons, ^'alence, Montelimar, and 

 Mondragon. A for;ii of dam and locks is projected 

 which will interfere as little as possible with 

 navigation. 



In an article in the Revue Scientifique for May 22 

 M. ■ A. de Gramont de Guiche, president of the 

 council of the Institute of Optics of France, describes 

 the arrangements made for the first session of the 

 institute, April to July, of the present year. The 

 institute is divided into three sections: (i) A school 

 of higher studies intended to provide the training 

 requisite for the specialists in the subject; (2) a 

 laboratory for research and practiail instruction ; and 

 (3) a school for the training of the workmen and 

 craftsmen both in glass- and in instrument-making. 

 At the opening of the course on April 12 M. Jobin, 

 one of the members of the council, described in detail 

 the objects of the institute and the steps that were 

 being taken to carry out those objects, and Dr. Dunoyer 

 gave the first lecture of a course on optical instru- 

 ments. Other lecture courses are provided on "The 

 Calculation of Optical Systems," "Spectroscopy," 

 "Glass: Its Nature and its Applications," "The 

 Applications of Polarised Light," "The Microscope," 

 and "The Properties of X- and y-Rays." The fee 

 for the session is 150 francs, and, although no one is 

 excluded, it is pointed out that to profit as much as 

 possible from the course students should have a fair 

 knowledge of mathematics. 



In a paper published in the Mathematical Gazette 

 for 1919-20 Dr. S. Brodetsky, reader in applied mathe- 

 matics in the University of Leeds, brings forward a 

 graphical treatment of differential equations as of 

 special value in certain cases which are not soluble 

 by the usual analytical methods and as of general 

 value for purposes of instruction. There is justice in 

 his view that the average student of mathematics 

 regards the usual methods of solution as a series of 

 tricks which he learns to apply with more or less 

 success to such equations as are presented to him. 

 A graphical treatment cannot fail to be of great value 

 in teaching the meaning of differential equations and 

 NO. 2641, VOL. 105] 



in giving the student confidence in their use. The 

 paper contains numerous examples, and illustrates the 

 meaning of singular solutions, cusp loci, etc. Not 

 the least interesting example is the solution of the 

 equation 



ax y 

 which occurred in discussing the motion of a plane 

 lamina moving in air under the earth's attraction — 

 one of the simple types of aeroplane motion. The 

 equation was insoluble by any of the standard 

 methods, but <'asily solubk' graphically. 



During the war considerable quantities of acetone 

 were prepared by the fermentation of starchy material. 

 Hitherto, however, no investigation of the mechanism 

 of this fermentation has been described, and Messrs. 

 J. Reilly, W. J. Higginbottom, F. R. Henley, and 

 A. C. Thaysen publish in the April issue of the 

 Biochemical Journal an account of a quantitative 

 examination of the process. These authors find that 

 the fermented mash contains varying proportions of 

 acetic and butyric acids, the ratio of the latter to the 

 former increasing with the increase (during fermenta- 

 tion) in the acidity of the mash and reaching a maxi- 

 mum at the stage of greatest acidity. Not until the 

 latter stage is reached are appreciable quantities of 

 acetone and n-butyl alcohol produced. With the pro- 

 duction of "oil" the ratio of butyric to acetic acid 

 diminishes, and finally the mash contains an excess 

 of acetic acid. During the period of the increase of 

 acidity of the mash the rate of gas evolution rises ■ 

 steadilv for some time, then becomes constant; and 

 as the acidity falls the rate of gas evolution rises 

 quickly to a maximum, and then falls rapidly until 

 the end of the fermentation. The gas consists of 

 hydrogen and carbon dioxide in a proportion varying 

 from 3 : I at first to 2:3 at the latter part of the 

 fermentation. It is extremely probable that acetic 

 and butyric acids are not the only acids formed, and 

 evidence is given of the presence of an acid less 

 volatile in steam. Lactic acid results from the type 

 of infection most frequently observed. If the fer- 

 mentation is carried out in the presence of calcium 

 carbonate it proceeds as far as the point of maximum 

 acidity, but the production of acetone and tj-butyl 

 alcohol is almost entirely suppressed. 



In the Wiener Denkschriften (Math.-Naturwiss. Kl.,^ 

 Bd. 96, pp. 671-750, 1919) Dr. A. Defant continues 

 his important researches on tides in landlocked and 

 border seas, bays, and channels. After a theoretical 

 discussion of the influence of friction against the 

 ocean-bed in channels, he deduces an average value 

 of the coefficient of skin friction from a considera- 

 tion of the tides in the Gulf of Suez and in certain 

 lakes which exhibit seiches. He then enters upon a 

 careful detailed study of the tides in the English 

 Channel, using a step-by-step numerical methpd for 

 the solution of the differential equations of the tides 

 between successive cross-sections of the Channel. He 

 thus succeeds in demonstrating the truth of a con- 

 jecture made long ago by Airy to the effect that the 

 complicated tides of the Channel are governed mainly 



