528 



NATURE 



[June 15, 191 1 



The Proceedings of the Royal Society of Edinburgh, 

 xxxi., 3, contains three papers by Dr. T. Muir, F.R.S., 

 dealing with the historical development of certain deter- 

 minants up to i860. The papers refer respectively to 

 " Wronskians," "Recurrent Determinants," and "The 



s common special Forms." 



In two notes contributed to the Aiii dei Lined, xx., 

 5, 7, Dr. U. Cisotti works out in extenso the solution of 

 the problem of discontinuous stream-line motion of a jet 

 wliich is divided in two by impact on a fixed plane, the 

 jet being of finite breadth and bounded by free stream 

 linos. 



It is .innounccd that after the close of the present 

 volume the Annals of Mathematics, hitherto published in 

 October, January, April, and July, under the auspices of 

 Harvard University, will be transferred to Princeton 

 University, New Jersey, to which address editorial and 

 other communications are in future to be sent. 



l.v the Bulletin of the American Mathematical Society 

 for May Prof. Florian Cajori publishes a paper in which 

 it is claimed that the now familiar " Horner's method " 

 of solving an algebraic equation had been previously given 

 ' ■• Paolo Ruffini in an Italian paper. The methods 



lopted by Ruflini and Homer seem to have been identical 

 10 a very great extent ; the main differences which Cajori 

 mentions are that Horner explained a special procedure for 

 separating a pair of nearly equal roots, and, further, that 

 he contemplated the application of his method to trans- 

 cendental equations. It need hardly be pointed out that 

 the solutions of such equations as tanjc = .\-, which can be 

 expanded by Taylor's theorem, constitute some of the most 

 useful and well-known applications of Horner's method. 



We have received a copy of Mr, W. J. Lyons 's paper 

 read before the Royal Dublin Society recently on a method 

 of exact determination of the continuous change in abso- 

 lute density of a substance in passing through its fusion 

 st.ige. The apparatus consists of a dilatometer bulb, from 

 the lower end of which a capillary issues, and is bent first 

 upwards and then horizontally. This tube and the lower 

 part of the bulb are filled with mercury. The upper part 

 of the bulb contains the sMbstance the expansion of which 

 is to be determined, and the magnitude of the expansion 

 ■- calculated from the motion of the mercury meniscus in 

 rlie capillary tube. Experiments on wax show that the 

 fusion lasts over a considerable range of temperature, and 

 that in the neighbourhood the volume on cooling is, at 

 the same temperature, greater than on heating. As the 

 apparatus only differs from Pettersson's of 1881 in the 

 absence of taps for the admission of the substance, it is 

 to be regretted that Pettersson's name is not mentioned 

 in the paper. 



The address given by Prof. Planck to the Soci^t^ 

 fran^aise de Physique on April 21, and reproduced in the 

 May number of the Journal de Physique, constitutes cne 

 of the clearest expositions we have seen for some time of 

 the present difficulties of the attempt to express the rela- 

 tion between energy and temperature. The doctrine of the 

 equlpartltion of energy amongst the various degrees of 

 freedom of a molecule, deduced by Boltzmann and Gibbs, 

 has led to serious difficulties owing to the smallness of 

 observed specific heats as compared with the calculated 

 values. Planck's own theory, that energy exists in 

 multiples of a certain atomic quantity, leads to difficulties 

 with regard to absorption of energy, and, as we pointed 

 out in these columns on March 16 (p. 90), he has now 

 modified it so that only emission takes place by the step 



NO. 2172, VOL. 86] 



by step process, absorption being continuous and energy 

 content of a body no longer an integral multiple of t! 

 atomic energy. Whether this change gives us a satist.i' - 

 tory theory only time can show. 



The Builder for June 9 contains an illustrated article, by 

 Mr. Percy J. Waldram, on the need for horizontal tie- 

 rods in arched timber roofs. Generally, the introduction 

 of such rods is owing to the designer assuming that the 

 joints are flexible, and constructing a force-diagram based 

 on this assumption. Actually, the stiffness of the joints 

 as constructed in practice renders the fitting of tie-rod* 

 quite unnecessary in a properly designed arched roof. The 

 author cites the case of the fine arched hammer-beam roof 

 of Eltham Parish Hall, which has no tie-bars, and gives 

 account of an interesting experiment carried out on on^ 

 truss, which was mounted on pipe rollers on the ground 

 and loaded with bricks laid on a platform slung from the 

 truss. With a span of 42 feet and a load of 7 tons the 

 calculated outward spread was 063 inch. Upon the first 

 application of the load, the spread was found to be slightly 

 more than i inch, owing partly to the tightening up of the 

 joints. On removing the load, the truss came back 

 075 inch, and in each of the two reimpositions of the 

 load, at intervals of two days, the spread was found to b^ 

 0-75 inch. The object of the test was attained, inasmuch 

 as the district surveyor withdrew his requisition for ti^- 

 rods. 



The report of the Indian Association for the Cultiva- 

 tion of Science for the year 1909 has now been received. 

 The association's chief work seems to be the arrange- 

 ment of lectures on scientific subjects. During the year 

 about 280 lectures on various branches of physics and 

 chemistry were delivered, and in addition upwards of a 

 hundred practical demonstrations were arranged. The 

 chemical laboratory conducted by the association has been 

 remodelled, and it is hoped soon to inaugurate a research 

 department. The report also contains a set of meteor- 

 ological observations taken at Calcutta during 1909. 



In a review of Prof. Leduc's book on biological aspects 

 of osmotic phenomena in Nature of May 25 (p. 410) the 

 writer gave examples of the need of proof-reading, and 

 stated that there were errors in the title of a book by 

 Rhumbler. He inferred, unfortunately without verifica- 

 tion, that the strange words " organismischer " and 

 " anorganismischer " were typographical errors, but Prof. 

 Leduc writes to point out that they are the words 

 Rhumbler used in his title. The reviewer regrets that he 

 was guilty of the kind of carelessness for which he re- 

 proached Prof. Leduc, but he is afraid that his remark as 

 to misprints remains true. 



OUR ASTRONOMICAL COLUMN. 



A Remarkable Meteoric Phenomenon. — In No. 4503 of 

 the Astronomische Nachrichten Dr. Max Wolf describes a 

 curious phenomenon observed on May 22, at about 

 iih. 49m. (Konigstuhl M.T.), at Heidelberg. A faint 

 meteor, pursuing a 4° path obliquely from east to west, 

 passed over the star y Aquilae with great velocity ; its 

 breadth was about 15', and it left a faint trail, which dis- 

 appeared immediately. But although this trail was only 

 momentarilv visible,' the star remained invisible for at 

 least 35 seconds, its light apparently cut off by the 

 material left behind by the evanescent meteor. 



The Different Quality of the Light Reflected from 

 Different Parts of the Moon's Surface. — The results 

 obtained bv Herren A. Miethe and B. Seegert in photo- 

 graphing 'the moon's surface through colour-selective 

 screens are further described in No. 4502 of the Astro- 

 nomische Nachrichten, and illustrated by a two-colour 



