152 



NATURE 



[June 15, 1893 



this and other countries, to publishing-hiuses and mechanical 

 workshops, with the wish that, through their hearty cooperation, 

 the project may be furthered. We add the plan and more 

 minute information, for the successful realisation of the 

 exhibition. 



The exhibition lasts from September I to 30, 1893, inclusive, 

 and comprises models, drawings, apparatus, and instruments 

 used in pure and applied mathematics either for purposes of in- 

 struction or investigation.' 



The Deutsche Mathemaliker-Vereinigung will take charge 

 (free of cost) of the fitting of the rooms, the providing of tables, 

 putting in of partitions, &c. , as well as the unpacking and re- 

 packing of all articles intended for the exhibition. Moreover, 

 the society will assume control of the articles while on 

 exhibition, and will take particular care to preserve them, and 

 will carry an insurance against fire. However, it can assume 

 no respon-ibility against injury or loss. 



Exhibitors who desire their various displays to be exhibited 

 under closed cases must provide them at their own expense. 



The expense of shipment to Munich, and, if desired, insur- 

 ance, must be borne by the exhibitor. For the return the same 

 inducements are held out as last year, viz. free freight over the 

 chief German lines. 



A comprehensive detailed catalogue of the mathematical ex- 

 hibition, according to the announcement made last year, has 

 appeared. - 



The first part (142 pages) contain-! a number of essays, of 

 general nature, having reference to problems, results, and 

 methods of presenting geometrical concepts. 



The second part (300 pages) contains, according to the 

 suggestion given below, the enumeration and exact descrip- 

 tion of the articles intended for the Niirnberg exhibition, and 

 gives, with numerous illustrations, a comprehensive view of the 

 general plan of the undertaking, and a statement of what has 

 already been accomplished. 



The catalogue will also give the plan of the preparations of 

 the present year ; a detailed supplement will be added, in which 

 we hope to perfect the non- completed parts of last year's cata- 

 logue. 



As far as possible all technical explanations of the articles 

 will be undertaken by the committee. 



The committee will attend to all sales and buyings (which are 

 ID view by various mathematical institutes of our Hochschulen), 

 and give all desired information. 



During the exhibition the sold articles must not be removed 

 from the exhibition rooms, except with special permission of the 

 committee. 



The intention to participate in the exhibition may be given by 

 the use of the " Exhibition Announcement" until July I. 



Addiess: " Herrn Prof. Dr. Walther Dyck, 

 Munchen, Polytechnicum." 



At the same time all papers and scientific notices for the cata- 

 logue respecting woodcuts (cliches) for illustration must be sent 

 to the same address. 



The editors reserve the right of all abbreviation and change in 

 the notes of Part II. of the catalogue that uniformity may 

 require. 



All articles proposed for exhibition must be forwarded from 

 August 15 to 31 under the address: " Mathematische Ausstel- 

 lung in Miinchen (Polytechnicum) zu Handen Herrn Prof. Dr. 

 W. Dyck." 



The return of all articles will be effected within two weeks 

 after the close of the exhibition. 



In order to more minutely define the extent of the exhibition, 

 we give, in accordance with the arrangement of the catalogue 

 which has already appeared, the following division of groups : — 



I. — Analysis. 



Calculating apparatus (calculating machines, slide rules) ; 

 apparatus for the solution of equations and construction of 

 functional relations ; models and drawings in algebra and theory 

 of functions ; curvometers, planimeters ; other instiuments for 

 mechanical integration. 



' From the field of applied mathematics only those models, apparatus, 

 &c., will be accepted whose chief interest lies in the field of pure mathe- 

 matics. 



2 The catalogue can be obtained direct from Prof. W. Dyck (Munchen, 

 Polytechnicum) at the price of M. 9.80 (including postage). 



II.— Geometry. 



Drawing apparatus ; models for elementary instructio.i in 

 plane and solid geometry, trigonometry, and descriptive 

 geometry ; polyhedra (division of surfaces and spaces in poly- 

 gons and polyhedra) ; analysis situs; plane curves; algebiaic 

 surfaces ; transcendental surfaces ; curves in space and develop- 

 able surfaces ; models in line geometry ; irodels to illustrate 

 theory of curvature ; singularities of curves and surfaces. 



Ill — Applied Mathematics. 

 Mechanics. 

 Models used in elementary instruction ; apparatus and moilels 

 for the demonstration of the laws and principles of dynamics 

 (equilibrium and movement of a material point ; Poinsot mo ion 

 of a rigid body ; apparatus for representing precession and nu 

 tation ; dynamical tops; gyroscopes; models and arti les 

 showing the effect of tension, compression, flexion and torsum 

 of solids ; representation of various phenomena in hydro-dyna- 

 mics) ; ittodels and appartitus in kinematics with regard to lli<ir 

 application in practice. 



Malhematical Physics. 

 Apparatus and models to illustrate the laws of the propagation 

 of waves ; models for the explanation of crystal structure; 

 models to illustrate the optical, elastic, and electric propertitsof 

 crystals; drawings and models in thermodynamics; models 

 and apparatus for the mechanical illustration of eUctro- 

 dynamic phenomena. 



Various Technical Applications. 



It is to be understood that exhibitors mu>t declare thiir 

 willingness to submit to the present rules and further dispositions 

 ordered by the committee for the interest of the exhibition. 



For all further information please address the undersigned 

 delegate of the committee. Prof. Dr. Walther Dyck. 



RELATIONS BETWEEN THE SURFACE-TEN- 

 SION AND RELATIVE CONTAMINATION 

 OF WATER SURFACES. 



IN a recent paper (Nature, vol. xlvi., p. 419) ' 

 have suggested a method for measuring the rel;iti>-e 

 contamination of an anomalous water-surface in my 

 adjustable trough without fearing an error caused by in- 

 complete separation of the surfaces by the partition. It 

 consists in observing not the displacement of the par- 

 tition itself, but that of a floating wire laid across the sur- 

 face, which follows every motion of the superficial water 

 particles. 



By this method I have now tried to find a relation be- 

 tween the relative contamination and the decrease of 

 tension which begins at that relative contamination, w hich 

 we will call unit. 



The surface-tension was measured by the separating 

 weight of a ring of thin wire, which had a circumference 

 of 1 14 mm. and was cleaned by ignition, so that it could 

 be afterwards entirely moistened with water. The ring 

 was attached to a balance with a sliding weight. In this 

 manner the normal surface-tension of water was detei;- 

 mined to be 80 mg. per cm. at a temperature of 15° C. 

 The values obtained by experimenters on this subject 

 differing considerably from each other, I shall express the 

 tensions not in absolute measure, but in fractions of the 

 normal surface-tension of water taken as unit. Thus, I 

 found the surface-tension of a saturated solution of cam- 

 phor 072, and that of a strong solution of soap 0-37. 



On several occasions, when fast working was required, 

 the tension was not observed directly with the wire-ring, 

 but with the small balance used in my former experiments, 

 the tension corresponding to each separating weight 

 being previously determined by comparison with the large 

 balance. 



The observations were made as follows :— A slight trace 

 of oil was communicated to the surface of the trough by 



NO. 1233. VOL. 48] 



