June 15. 1893] 



NA TURE 



-y- 



on its axle, and nol by the rolling motion, so that all 

 slipping of the wheel on the paper is done away with. 



The great number of slide-rules is surprising. Mr. 

 Stanley alone has sent more than a dozen. 



Among the Arithmometers is the circular form of Mr. 

 Edmondson, and one of great novelty by Prof Selling, 

 in which \.\\^ carrying x's, performed continuously and with- 

 out jerks. The instrument works in consequence with 

 great smoothness and rapidity. 



The same section contains instruments and models 

 referring to Geometry, such as angle dividers, ellipso- 

 graphs. Gallon's pantograph, and several perspectographs. 

 Pepys writes in his diary, April 30, 1669 :— " This morn- 

 ing I did visit Mr. Oldenburgh, and did see the instrument 

 for perspective made by Dr. Wren, of which I have one 

 making by Browne ; and the sight of this do please me 

 mightily." If this instrument can be found it would be 

 welcome at Munich ; perhaps Mr. Penrose could help in 

 this matter. 



The models for instruction in elementary geometry are 

 very complete, and there are interesting illustrations of 

 polyhedra and space dissection, the subject to which 

 Prof Alexander Herschel has devoted considerable at- 

 tention. No. 150 is a collection of six tables on the 

 " Lines of Beauty," to which Hogarth gave great at- 

 tention ; this exhibit should be of interest to artists. 



Under the head of Algebraical Surfaces we find among 

 familiar models a pair of Prof Henrici's confocal deform- 

 able hyperboloids, constructed of a number of straight 

 sticks, tied together at the crossings. Darboux's appli- 

 cation of these linked bars to the description of spheres 

 and planes, and the mechanical illustration of the 

 motion of a body under no forces, a la Poinsot, 

 noted on p. 327 of the Catalogue, may be instanced 

 here. 



The plaster models of the confocal quadric surfaces 

 designed and carried out by Prof. H. A. Schwarz and 

 E. K. Neovius with mathematical accuracy should now 

 form part of the apparatus of every teacher of solid 

 geometry ; the complete series are obtainable for a 

 moderate price through Brill, of Darmstadt. 



Surfaces of the third, fourth, and higher degree, 

 Kummer's and Steiner's surfaces, minimum and deform- 

 able surfaces, and others too numerous to mention here, 

 are profusely illustrated in the catalogue. 



Prof. Dyck's models of surfaces representing the real 

 and imaginary parts of a function of a complex variable 

 at and near a singular value should be studied by every 

 reader of Mr. Forsyth's new book on the Theory of 

 Functions. Of the curious complexity of even the simplest 

 kinds of essential sitigulariiies a clearer idea is obtained 

 by a glance at these models than by a long study of the 

 analytical expressions. 



The third section is devoted to Applied Mathematics, 

 including Mechanics, Mathematical Physics, and instru- 

 ments required in geodesy and navigation. 



The mechanical models illustrate the parallelogram 

 of forces ; the laws of falling bodies, including an arrange- 

 ment exhibited by Mr. F. R. Barrel! of University College, 

 Bristol ; models of Saint Ven.-.nt's torsion prisms, and 

 so forth. 



Mr. A. B. Kempe has supplied a complete account of 

 his Linkages ; and Prof. Reuleaux's well-known collection 

 of kinematical models is profusely illustrated here. 



In mathematical physics we find apparatus for the 

 illustration of wave motion and sound vibrations, refrac- 

 tion of light, interference, Mr. Boys's bullet photographs, 

 and Mr. Bashforth's chronograph. Prof. Alexander 

 Herschel's models are given under the head of models of 

 rystalline structure. 



Under thermodynamics are found the thermodynamic 

 surfaces of Gibbs and Van der Waals ; and Profs. Oliver 

 Lodge and Fitzgerald exhibit their mechanical illustra- 

 tions of the laws of electrodynamical action. 



NO. 1233, VOL. 48] 



Some interesting apparatus are described and illus- 

 trated in the last section on geodetic, nautical, and mete- 

 orological instruments, including General Strachey's 

 apparatus for the determination of the height and velocity 

 of the clouds. 



It would be impossible to give within reasonable limits 

 a detailed account of all the novel and interesting objects 

 described in this catalogue ; but it is hoped that the 

 present short sketch will show that the catalogue itself, 

 apart from the exhibition, is a valuable work of reference, 

 which should be in the hands of all interested in mathe- 

 matical and mathematicophysical science. 



It is expected that the postponement of the meeting to 

 the coming September will give time for the collection of 

 other objects of interest, which can be described and 

 catalogued in an appendix. 



A fresh manifesto has been issued by the German 

 Mathematical Association inviting further contributions. 

 Intending exhibitors in this country requiring infor- 

 mation and advice, and instructions concerning packing 

 and transport of instruments, are requested to communi- 

 cate with : — 



Prof. O. Henrici, Central Institution, Exhibition Road, 

 W. ;.or Prof A. G. Greenhill, Artillery College, Woolwich. 



At the meeting of the Deutsche Mathematiker-Vereinigung 

 at Halle, it was concluded lo arrange for an exhibition of 

 models, drawing?, apparaluf, and instruments, used in pure and 

 applied mathematics, for the occasion of the proposed conference 

 in Niirnberg in the autumn of 1892. 



The proposal enjoyed, from the beginning, the support of the 

 Royal Bavarian Government, by which, through special material 

 assistance, as by increased funds which the Imperial Ministry 

 of the Interior liberally provided, the undertaking was assured. 



The proposal of the undertaking was received with universal 

 interest in scientific circles, and so the plan of the exhibition 

 seems to lie a natural one. A large number of mathematical, 

 physical, mechanical, and geodetic institutes of our own uni- 

 versities and technic high schools, and those outside of Germany, 

 placed the models in the institutes, as well as those of historical 

 interest, lo the disposal of the project. Announcements of 

 participation were received from museums, private collections, 

 and individual men of science, at home and abroad. 



Besides Germany, America, France, Iialy, Austria-Hungary, 

 Holland, Norway, Russia, and Switzerland joined in the 

 project, and especially in Great Britain a committee was com- 

 posed, with Profs. Lord Kelvin, Greenhill, and Henrici at ihe 

 head, lo send to the exhibition the most prominent articles from 

 the Government, as well as from private collections. Practically 

 all the more important mechanical workshops that are particu- 

 larly engaged in the production of mathematical apparatus and 

 instruments, and also publishing-houses interested, agreed to 

 share in the scheme. 



All initial steps were taken and preparations made. An ex- 

 tensive catalogue was compiled, through the cooperation of 

 numerous men of science, with a minute description and 

 numerous illustrations of the particular objects, together with a 

 series of comprehensive sketches of its contents ; this shows to 

 what extent the various preparations were made: 



The condition of the public health of Germany made the 

 postponement of the meeting of the Deutsche Mathematiker- 

 Vereinigung, and consequently the exhibition, which was almost 

 in readiness, inevitable. The directors of the Deutsche 

 Mathematiker-Vereinigung, however, at once concluded to 

 realise their project in 1893. 



In Munich, the place selected for the next meeting of the 

 Deutsche Mathematiker-Vereinigung, the extensive rooms of the 

 Polytechnichavealready been kindly placed at the disposal of the 

 directors. On account of the proponions that the exhibition 

 has assumed, is will last longer than at first proposed. It will 

 be open from September I lo 30, as the session of the Mathe- 

 matical Society, which lasts from September 4 to 10, will be 

 immediately followed by that of the Society of Nalural Science 

 in Niirnberg, from September II lo 15. 



In this case, too, we rejoice in ihe support of the Royal 

 Government, and hearty assurances of intentions to participate 

 in the exhibition have been given by various scientific circles. 



Again, therefore, and with confidence, do we turn to our 

 fellow scientific men, to the various mathematical institutes in 



