Mabch 30, 1883.] 



SCIENCE. 



225 



MATHEMATICS. 

 Complexes of the second degree. — Herr Stahl 

 gives a synthetic treatment of certain points in con- 

 nection witli Kummer's sixteen-nodal quartic surface. 

 Tlio processes are new; but, for the most part, the 

 results are well known. — {Journ. reine angew. math., 

 xciii.) T. c. [475 



Rbtation of a liquid ellipsoid. — In two articles 

 Mr. G-reenhill has examined the conditions to be 

 satisfied in order that a liquid ellipsoid may rotate 

 about an axis other than a principal axis, and have 

 a free surface. The axis of rotation, as stated by 

 Kiemann, lies in a principal i^lane of the ellipsoid. 

 The motion is supposed to be set up in the liquid by 

 mechanical processes ; and the pressure at any point 

 is investigated, the liquid being supposed contained 

 in a rigid shell. The conditions are then investigated 

 that are requisite for tlie ellipsoidal shell to be a sur- 

 face of equal pressure, and that a free surface can 

 exist. — [Proc. Cambr. phil. soc, 1882. ) T. c. [476 

 Non-Euclidean geometry. — Dr. Story has shown, 

 in a previous paper, how tlie formulae of a non- 

 Euclidean plane trigonometry could be deduced from 

 those of the Euclidean spherical trigonometry ; viz., 

 by the replacement of each side by a constant multiple 

 of that side, and each angle by a constant multiple of 

 that angle. In the present paper he makes the cor- 

 responding deduction for any non-Euclidean spherical 

 trigonometry, and also gives a number of formulae 

 relating to distances, areas, etc. A new and impor- 

 tant principle is exliibited; viz., the distance (or 

 angle) between any two geometrical elements [points, 

 planes, or straight lines) is, to a constant factor pres, 

 the same, in whatever way it is measured. For exam- 

 ple, tlie formulae show that the distance of a given 

 point from the nearest point in a given plane is pro- 

 portional to the angle between the given plane and 

 the nearest plane through the point (i.e., that which 

 makes the least angle with it) ; the least (or greatest) 

 distance from a point of one of two given straight lines 

 to a point of the other is proportional to the least 

 (or greatest) angle which a plane through one of the 

 straiglit lines makes with a plane through the other; 

 and, if the lines intersect, this is proportional to the 

 angle between the lines, etc. Expressions are given 

 for the circumference and area of any circle, the area 

 of any spherical polygon, the surface and volume of 

 any sphere ; it is also shown that the double plane is 

 identical with a sphere of guasi-infinite radius. A 

 further abstract will be given on the completion of the 

 paper. — [Amer. journ. math., y.) t. c. [477 



PHYSICS. 



Acoaatics. 

 Vibratory movement of bells. — Mathieu has 

 recently studied the vibrations of bells, with a pre- 

 liminary investigation of the vibrations of bent bars, 

 considering the case of an ordinary bell in which the 

 thickness in any meridian increases from summit to 

 base. Between the vibratory movement of a bell and 

 that of a plane plate, the essential difference exists, 

 that, while in the latter the longitudinal or tangential 

 movement and the transverse movement are given 

 by independent equations, in the former, the normal 

 and tangential motions are given by three equations 

 which are not independent. The pitch of the notes 

 of a bell does not change if the thickness varies in 

 the same relation throughout every part: since the 

 terms depending on the square of the thickness may 

 be neglected ; at least, for the graver partials. It is 

 impossible to construct a bell so that it shall vibrate 

 only normally ; and, with a hammer, the tangential 



vibrations are of the same order as the normal vi- 

 brations. A purely tangential motion can be real- 

 ized only with a spherical bell of constant thickness. 

 — {Journ. dephys., Jan.) c. E. C. [47S 



Vibrations of solid bodies in contact -with 

 liquids. — F. Auerbach has investigated the effect 

 of liquid contained in a glass vessel upon tlie pitch of 

 the sound produced when the latter is set into vibra- 

 tion. He reaches tlie following results: ' 1. The 

 geometrical lowering in pitcli (ratio of number of vi- 

 brations), produced by a liquid contained in a cylin- 

 drical glass completely filled by it, is less in proportion 

 as the pitch of the empty glass is higher. 2. The arith- 

 metical lowering of pitch with a cylindrical glass of 

 mean pitch is approximately proportional to the recip- 

 rocal of the square root of the number of vibrations of 

 the empty glass. 3. The lowering of pitch, when 

 tlie glass is completely filled, is not noticeably de- 

 pendent on its height. 4. The geometrical lowering 

 of pitcli produced in cylindrical glasses of different 

 widths is greater in proportion as the glass is nar- 

 rower. 5. The arithmetical lowering of pitch witli 

 cylinders of different widths is inversely as the square 

 root of the width. 6. The arithmetical change of 

 pitch is inversely proportional to the square root of 

 the number of wave-lengths of the sound given by 

 the empty glass contained between the walls and axis 

 of the cylinder. 7. The lowering of pitch is greater 

 as the density of the liquid is greater. 8. It is greater 

 in proportion as the compressibility of the liquid is 

 less. — {Ann. phys. chem., 1882, xiii.) c. K. c. [47^ 



Optics, 

 (P/iotometrt/.) 

 Solar photometry. — M. A. Crova has recently 

 made some comparisons of the relative brilliancy 

 of the sun and of a Carcel lamp. He compared the 

 lighting-power of different wave-lengths in the two- 

 spectra, thereby deducing curves for each. The areas 

 enclosed by these curves then represented the total 

 amount of light given out by each source. He then 

 deduced the factor by which it was necessary to mul- 

 tiply the smaller ordmates in order to render the two 

 areas equal. The ordinate of intersection of the 

 two curves of the same area then furnislied at once 

 the wave-length whose photometric comparison would 

 give the ratio of the total light emitted by the two 

 sources. This wave-length (582) is situated in the 

 yellowish-green, and may be isolated by transmitting 

 the light through a mixture of the solutions of per- 

 chloride of iron and chloride of nickel. The two 

 lights thus obtained were of precisely the same color, 

 and their ratio was at once determined by measure- 

 ment with a Poucault photometer. After making all 

 corrections, this method gives about 60,000 carcels 

 (600,000 candles). — (Comptes rendus, Dec. 18, 1882.) 

 w. H. P. [480 



Electricity. 

 Electric amalgamation. — In the process of ob- 

 taining gold by amalgamation from ores containing 

 arsenic and certain other impurities, the mercury 

 ' sickens,' and fails to take up all the gold present. 

 Mr. Richard Barker has devised a method of amal- 

 gamation which has given very satisfactory results. 

 The inclined table over which the ore is washed 

 contains hollows filled witli mercury; over these, in 

 the water containing the washings, copper wires are 

 introduced, and brought so near that a powerful cur- 

 rent may be passed to the mercury, which seems to 

 gather itself away from the impurities, and to act 

 more energetically upon the ore. — {Iron, Feb. 9.) 

 J. T. [481 



