494 



NATURE 



\ April 23, X874 



logical anatomy, On the Development of Contagious Molluscum. 

 — The Architecture of Ants forms the subject of a communi- 

 cation from Prof. Maggi, wh(5 has been studying the habits of 

 Foriiiita Jidiginosa Lat. — M. Tessori furnishes a geometrical de- 

 monstration of the error of representations given in many treatises 

 on physics, as to deviation of the plane of oscillation of the 

 pendulum. — In the department of moral and political science, 

 Prof. Bucellati has a paper on central military prisons. 



Archives ties Scimres Physiques el JVaturelles, March 15. — This 

 number commences with a resumi of spectroscopic observations 

 of the sun, made at Geneva, by M. Emile Gautier during the 

 last three years. The results of this work (carried on under 

 much less favourable climatic conditions than in Italy), are 

 mainly a confirmation of those got by other observers. The 

 protuberantial phenomena are classed under three heads ; erup- 

 tions, exhalations, and detached formations ; all of which the 

 author illustrates with drawings. Like P. Secchi he «'as often 

 struck by the fact (which has been doubted), that when a 

 protuberance is observed near a pole, there is generally one 

 symmetrical with it, at the other end of the corresponding solar 

 diameter, and near the opposite pole. The decrease in the 

 number and dimensions of protuberances appeared during these 

 years (from 1869) to precede and exceed that of the spots. M. 

 Gautier adheres to the hypothesis of spots being formed by scorial 

 matters resulting from cooling of the surface by radiation. — 

 In the next paper M. Humbert gives a useful summary of 

 what has hitherto been done by the Chailctiger expedition. — 

 The Bulletin Siii-iitifique, which follows, is larger than usual. 

 Among other notes in it, we find an account of some instructive 

 researches by Dr. Macaluso, on polarisation of electiodes, by 

 chlorine and hydrogen. There is also a notice of an important 

 geological map of the Austro-Hungarian Empire, recently com- 

 pleted by M. de Ilauer, whose name it bears. The publication, 

 directed by Ileidenhain from 1S50 till I S63, represents at least 

 twenty years' labour (under considerable difficulties), of a large 

 number of eminent geologists. Each plate is accompanied with 

 detailed explanations. We further note a resume of some recent 

 researches on the minute structure of the eye ; and another paper 

 on physiological antagonism of poisons, in which are described 

 some observations by MM. Martin-Damourette, Rossbach and 

 Frbhlich, and others, with regard to the effects of physo- 

 stigmine, the active principle of Calabar bean, and atropine. 



SOCIETIES AND ACADEMIES 

 London 



Mathematical Society, April 9. — Prof. Cayley, vice-presi- 

 dent, in the chair. — Mi. G. H. Darwin read a paper On Probable 

 Error in Statistics. He stated that he had been at v.-ork at a 

 statistical inquiry, and was desirous of forming some idea of what 

 degree of accuracy he had a right to expect from the collection 

 of a given number of cases, ffe put the problem into the fol- 

 lowing form : — A bag is known to contain a very large number 

 of black balls and white balls, mixed at hazard ; on drawing a 

 large handfull of n balls, I find / are white and the rest black. 



What is the probable error in asserting that ^ of all the balls 



in the bag, are white ? n and /, though large numbers, are sup- 

 posed to be small compared to the number of balls in the bag. 

 Mr. Darwin then made some further remarks On the Combina- 

 tion of Statistics. The question he considered was the following : 

 — If X and Y are measurements or estimations of quantities such 

 that the errors are distributed according to the exponential 



law, what is the " probable error " of XY and — in terms of 



Ihe moduli e and r' of X and Y respectively? M. J. W. L. 

 Glaisher made some remarks on the papers, drawing the author's 

 attention to the fact that the two questions had been treated of 

 by Laplace and De Morgan. — Mr. Menifield then gave a sketch 

 of his paper entitled Determination of the Form of the Dome of 

 Uniform Stress. He remarked that the general question of the 

 equilibrium-figure of a thin dome is indeterminate, even when the 

 law of thickness or density is given, and it thus differs from the 

 question of the arch, by requiring the assumption of a further 

 condition in order to render its form determinable. If the two 

 following conditions are introduced simultaneously into the 

 general equation^, he stated that a very remarkable simplifica- 

 tion occurs in the analysis : — (i) that the thrust along a meridian 



hall equal the thrust along the parallel per unit of area at every 

 point ; (2) that the normal thickness shall vary in such a manner 

 that the area under compression shall be proportional to the 

 thrust. These seem to be the conditions necessary to the econo- 

 mical use of building materials of homogeneous character, for the 

 maximum stretch is evidently least when the stress is equally 

 distributed through the whole of the material. The form obtained 

 bears a general resemblance to the upper half of a claret bottle, 

 and the dome evidently required a heavy lantern. — Mr. A.J. 

 Ellis gave an explanation of his theory that ordinary (commuta- 

 tive) algebra is the calculus of similar triangles upon one plane. 

 Taking two fixed points O and I, any third point A determines 

 a triangle, so that if B be a fourth point, it is immediately 

 possible to find a fifth point C, such that the triangle BOC shall 

 be similar to the triangle I O A, and have the angles thus named 

 turned in the same direction. Marking this operation by <7, as being 

 determined by the position of the point A, and terming it 

 a cliiiaiit, he showed that clinants obey every law of commuta- 

 tive algebra, so that it was possible to consider any and every 

 existing algebraical expression as a clinant, and hence as deter- 

 mining a point in a plane. Clinants thus embraced not only the 

 integers and fractions of ordinary arithmetical algebra, but in- 

 cominensurables, negatives, and imaginaries. Hence also if x 

 and J be any clinants, and f {x y) = o, if .r be determined by 

 taking X anywhere, a corresponding point Y would be deter- 

 mined. Hence arose a complete calculus of the correspondence 

 of points in a plane, which Mr. Ellis calls stigmatic geometry, 

 and which he showed comprehended under one set of equa- 

 tions and greatly generalised, not only the algebraical geometries 

 of Descartes and Pliicker, but the homographic geometry of 

 Chasles, and from a single general principle gave a perfect geo- 

 metrical representation of all the imaginary cases as part of one 

 conception with the real cases. The actual algebraical work, 

 though having the old form and obeying the old laws of opera- 

 tion, is greatly simplified by the clinant signification attached to 

 the symbols, and in especial the expression and determination of 

 direction is rendered easy and certain. (A more detailed expla- 

 nation will be given, the speaker said, in his "Algebra Identified 

 with Geometry," at the present time in the printer's hands.) — 

 Prof. H. J. S. Smith made a short further communicatiun in re- 

 ference to his former paper On the Higher Singularities of Plane 

 Curves. — A paper by Mr. H. M. Taylor, On Inversion, with 

 special Reference to the Inversion of an Anchor-ring, was taken 

 as read. .Some of the properties given in the paper have been 

 already given by Maxwell (Quart. Journ. Math., vol. ix.) where 

 excellent stereoscopic views of four species of cyclides are given, 

 and by Cayley in the same journal, vol. xii., and in a paper in 

 the Phil. 'Trans, by Casey. The novelty of the paper consisted 

 in the point of view from which the properties of the cyclides 

 are investigated, viz. as the inverse figures of the anchor-ring, 

 many of whose geometrical properties are as easily seen as those 

 of the circle. 



Linnean Society, April 16. — H. Trimen, M.B., in the 

 chair. — A number of papers were read, being Nos. 3-14 of the 

 series of contributions to the botany of H.M.S. Challenger Ex- 

 pedition, as follows : — Notes on Freshwater Alg.-e collected in 

 the boiling springs at Furnas, St. Michael's, Azores, and their 

 neighbourhood, by H. N. Moseley. — Note on the foregoing 

 communication, by Prof. Thiselton Dyer. — Notes on some col- 

 lections made at Furnas, by M. Archer. The diatoms belong 

 to species of most frequent occurrence in fresh water, and appear 

 to be in no way affected by the high temperature. The other 

 Alga; are mostly common species, several of them British, be- 

 longing to the genera Spirogyra, Mesocarpus, Bidhochiele, (Edo- 

 givtiiini, tkz. — Notes on plants collected at St. Vincent, Cape de 

 Verdes, by H. N. Moseley — Enumeration of Alga? collected by 

 Mr. Moseley at the Cape de Verdes, by Dr. G. Dickie. — Enu- 

 meration of the fungi collected during the expedition of H.M.S. 

 Challeir^er, Feb. -May 1S73, by the Rev. M. J. Berkeley. — Note 

 on plants collected at St. Paul's Rock, by H. N. Moseley. The 

 only aerial plant found on the island was a Chloroeocetis. — Enu- 

 meration ot the Algre collected by Mr. Moseley at .St. Paul's 

 Rock, by Dr. G. Dickie. — Notes on plants collected at Eer. 

 nando Noronha, Cape de Verdes, by H. N. Moseley. — Enume- 

 ration of Algce collected by Mr. Moseley at Fernando Noronha, 

 by Dr. G. Dickie. — Enumeration of Algx collected by Mr. 

 Moseley in 30 fathoms of water at Barra Granda, Pernambuco, 

 by Dr. G. Dickie. — Enumeration of Alg.-c collected by Mr. 

 Moseley at Bahia, by Dr. G. Dickie. 



Chemical Society, April 16. — Prof. Odling, F.R.S., presi- 



