500 



NA TURE 



[March 23, 1893 



before the American. Metrolo-ical Society, December 30, 1892, 

 by the President, Dr. B. A. Goulcl. 



Bulletin de r Acadeniie Royale de Belgiqite, No. i, 1893. — On 

 Poisson's law of large numbers, by P. Mansion. — On the influence 

 of time upon the mode of formation of the meniscus at the tem- 

 perature of transformation, by P. de Heen. If a sealed glass 

 tube is partly filled with carbonic acid in the liquid state, and 

 then heated slightly above the critical temperature, the meniscus 

 forming the surface of separation gradually disappears until all 

 the liquid is converted into vapour. But for some time after 

 this has taken place the density of the substance above the 

 surface of separation is less than that below, as may be seen by 

 the appearance of a generating line. If the tube is withdrawn 

 from the water bath at 33", the formation of a small cloud is ob- 

 served in the region where the meniscus disappeared, and the 

 latter is gradually reproduced in the same place. The phenome- 

 non is not observed when the tube is inverted, or l<ept at 33° for 

 24 hours, thus allowing the two constituents to mix by diffusion. 

 — Two experimental verifications relating to crystalline refrac- 

 tion by J- Verschafifeh. — Crystallographic note on the axinite 

 of Quenast, by A. Franck. 



SOCIETIES AND ACADEMIES. 

 London. 

 Physical Society, February 24. — Prof. A. W. Riicker, 

 F.R.S., President, in the chair.— Mr. Everett, junr., read a paper 

 on a new and handy focometer, by Prof. J. D. Everett, F.R.S., 

 and exhibited the instrument described. The focometer is con- 

 structed on the principle of the " Lazy tongs," and so arranged 

 that the distance between the object and screen can be varied 

 whilst the lens is automatically kept midway between the two. 

 This gives sharpest definition and the simplest calculation. The 

 lazy tongs has eight cells, formed by eighteen bars 13" x |" x V'. 

 and is capable of being extended to about eight feet, or closed 

 up to abo-it one foot. Brass pins about V' diameter and one and 

 half inches long project upward from each joint in the middle 

 row, and serve as supports for clips carrying the lens, object, and 

 screen. The instrument can be used for any lens whose fjcal 

 length lies between twenty-four inches and one inch or less. 

 Details respecting the most appropriate objects and screens, and 

 practical hints about the working of the instrument are given in 

 the paper. The question of what accuracy is obtainable is also 

 briefly discussed. — Mr. A. Hilger thought the instrument was 

 too flexible to be used for accurate work. — Mr. Blakesley sug- 

 gested that by using a plane mirror close behind the lens the 

 light would be reflected back, and the length of the focometer 

 could be reduced by one-half. — The President thought Prof. 

 Everett never intended the instrument to compete, as regards 

 accuracy, with the elaborate and expensive apparatus now used, 

 but nevertheless the focometer was a very valuable one, es- 

 pecially for students' work, and was particularly well adapted to 

 impress upon them the facts relating to conjugate foci. — A paper 

 on a hydrodynamical proof of the equations of motion of a 

 perforated solid, with applications to the motion of a fine frame- 

 work in circulating liquids, by G. H. Bryan, M,A., was read by 

 Dr. C. V. Burton. The object of the paper, which is a mathe- 

 matical one, is to show how the equations may be deduced 

 directly from the pressure-equation of hydrodynamics, without 

 having recourse to the laborious method of "ignoration "of co- 

 ordinate-. The resultsare applied to determine the motion of a light 

 framework of wires. When the framework has a single aperture 

 it is shown that no force produces motion in its own direction, 

 and no couple produces rotation about its own axis. In the case 

 of a fine massless circular ring the direction of whose axis is 

 taken as the axis of a-, a constant force along the axis of jj' pro- 

 duces uniform rotation about the axis of z, and a constant couple | 

 about the axis of ^' produces uniform translation along the axis : 

 of ;. In conclusion the author states that the results might be ! 

 made to furnish mechanical explanations of certain physical 

 phenomena. The President said the author had done good service 

 by attacking the difficult problem by elementary methods. 

 — Dr. C. V. Burton made a communication on plane and i 

 spherical sound-waves of finite amplitude. The first part of { 

 the paper refers to plane waves. This subject had been con- ! 

 sidered by Riemann, but Lord Rayleigh had criticised that part ! 

 of Riemann's work, where it is held that a state of motion is ' 



NO. I 22 I, VOL. 47] 



possible in which the fluid is divided into two parts by a surface 

 of discontinuity propagating itself with constant velocity, all the 

 fluid on one side of the surface of discontinuity being in one uni- 

 form condition as to density and velocity, and on the other side 

 a second uniform condition in the same respects. After quoting 

 Lord Rayleigh's criticisms the author shows that the same objec- 

 tion applies when the velocity and density on either side of the 

 surface may vary continuously in the direction of propagation, 

 and the velocity of propagation of the surface of discontinuity is 

 also allowed to vary. In each case the assumed motion violates 

 the condition of energy, and can only exist under that special 

 law of pressure for which progressive waves are of accurately 

 permanent type. Inquiry is then made as to what becomes of 

 waves of finite amplitude after discontinuity sets in (which con- 

 dition must always occur with plane waves), in the course of 

 which it is pointed out that the front of an air disturbance 

 produced by a moving source which starts impulsively, travels 

 faster than the source, even if the velocity of the source exceeds 

 that of feeble sounds. A mechanical analogy suggests that a dis- 

 sipative production of heat takes place when discontinuity occurs. 

 In all cases Riemann had assumed that the pressure is a function 

 of density only according to the isothermal oradiabatic law, and 

 thus failed to take account of any heat which may be dissi- 

 patively produced. Part II. of the paper deals with spherical 

 waves, and contains a mathematical investigation into the con- 

 ditions under which the motion remains continuous or becomes 

 discontinuous. The criterion is found in the finiiude or 

 infinitude of a certain integral. It is shown that if viscosity be 

 neglected, then undtr any practically possible law of pressure 

 the motion in spherical sound waves always becomes discon- 

 tinuous. For waves diverging in four dimensions some ca-es 

 occur in which the motion remains continuous. The general 

 question of spherical sound waves of finite amplitude is then 

 treated of, and the paper concludes with a method of finding 

 the differential equation of an infinitesimal spherical disturbance 

 which is superposed on a purely radial steady motion. Prof 

 A. S. Herschel inquired whether the nature of the solution for 

 plane waves of finite amplitude was similar to that for ordinary 

 waves-motion ? In the latter case everything depended on the 

 instantaneous impulses, for these alone determined the nature of 

 the wave. The President said Mr. Boys' experiments on flying 

 bullets might have some bearing on Dr. Burton's paper. 11 the 

 conclusions there stated were correct, then the velocity of the 

 air in front of a bullet should be greater than that of the bullet, 

 even if the latter was travelling faster than ordina;y sound 

 waves. He now asked Mr. Boys if his photographs gave any 

 evidence of this. Mr. Boys said the fact that the ))hoiographs 

 showed disturbances in front of the bullet proved that the dis- 

 turbance travelled faster. In one case where a large bullet was 

 moving at a velocity rather greater than that of ordinary sound 

 in the medium, the front of the disturbance was about half an 

 inch in advance of the bullet. In another in.^tance where the 

 bullet was smaller and the velocity greater, the distance which 

 the disturbance was in advance of the bullet was somewhat less. 

 In all cases, even when the velocity of the bullet was four times 

 that of sound, the character of the effects remained the same. 

 Dr. Burton replied to the points raised. 



March 10.— Prof. A. W. Riicker, F.R.S., President, in the 

 chair. — Dr. C. V. Burton read a paper on the applicability 

 of Lagrange's equations of motion to a general class of pro- 

 blems, with special reference to the motion of a perforated solid 

 in a liquid. The paper shows that to apply Lagrange's equa- 

 tions it is not always necessary that the configuration of the 

 system should be completely determined by the co ordinates, but 

 that under certain conditions one need not consider whether the 

 whole configuration is determined by the nature of the known 

 co-ordinates, nor inquire what is the nature of the ignored co- 

 ordinates. The result, which is arrived at by the aid of the 

 "principle of least action," and the investigation given in 

 Thomson and Tail's " Natural Philosophy," second edition, 

 parti. § 327, is expressed by the following proposition : — If the 

 kinetic energy of a material sy.'<tem can be expressed as a 

 homogeneous quadratic function of certain generalised velocities 

 ^, (p, . . . only, the co-efficients being functions of if/, <^, . . . 

 only, and if this remains always true so long as the only forces 

 and impulses acting are of types corresponding to il*, <^, . . ., 

 the equations of motion for the co-ordinatts ;//, ^, . . . may 

 be written down from this expresssion for the ei.eigy in accord- 



