March 17, 1898] 



NATURE 



477 



temperature and field was not constant, but diminished as time 

 went on. In order to eliminate this effect as far as possible the 

 subsequent measurements were made in the following order : — 

 (i) The change of magnetisation accompanying a certain 

 increase of tension, and the magnetisation at the mean tension 

 (at 10° C. and 55° C.)- 



(2) The magnetic contraction at the mean tension (at 10° C. 

 and 55° C). 



(3) The measurements of (i) repeated. 



(4) The magnetic contraction at 10° C. Values of the expres- 

 sion deduced from KirchhofFs theory were calculated from (i) 

 and (3) for both temperatures, and the mean compared with the 

 observed contraction (2). The results are shown (for 10° C. ) in 

 the accompanying diagram. The calculated contraction is much 



M. CjO^. T&np. /o'C. 



<0A3 



less than the observed, and the difference is approximately pro- 

 portional to the sixth power of the magnetisation. A similar 

 result was obtained by comparing the mean observed contraction 

 at 10° C. (2) and (4), with the calculated value deduced from 

 (3). All the quantities measured showed a diminution as time 

 went on, especially the influence of tension on magnetisation at 

 low fields. The calculated values of the contraction deduced from 

 (i) are indicated in the diagram by the points + + + . . .; those 

 deduced from (3) by the points 0... At the field 275 

 C.G.S. the magnetic contraction was about 16 per cent, less 

 than it was four months earlier. 



Physical Society, March 11.— Mr. Shelford Bidwell, 

 President, in the chair. — Prof. J. D. Everett gave a com- 

 munication on dynamical illustrations of certain optical phe- 

 nomena. The first part of the paper deals with the 

 properties of a series of equal particles attached at equal 

 intervals to an uniform stretched elastic weightless string. 

 Their free simple-harmonic modes of wave-motion are first in- 

 vestigated. The highest frequency occurs when the wave- 

 length is double that of the common distance a. As the wave- 

 length increases from 2a to infinity, or diminishes from 2a to a, 

 the frequency tends to zero. To every wave-length Aj between 

 2a and infinity, there corresponds a wave-length \^ between 2a 

 and a, such that a/Aj + a/\^ = i. The frequency is the same 

 forAj as for A,. Further examination shows that the difference 

 of wave-length between these two solutions is only apparent, 

 and that, so far as the movements of the particles are concerned, 

 waves of length Aj travelling in one direction, are identical 

 with waves of length Ag travelling in the opposite direction. 

 The same is true if a/Aj -I- a/Aj, instead of being unity, is equal 

 to any integer. On the other hand, if the difference between 

 a/A, and a/Aj is an integer, the two sets of waves travel in the 

 same direction. Any simple-harmonic wave-motion of the 

 system of particles may thus be regarded as having any one of 

 an infinite number of wave-lengths. When one particle of the 

 system is constrained to a S.H. motion, of frequency not ex- 

 ceeding that which corresponds to A = 2a, the whole system 

 will ultimately vibrate in equal waves. When the frequency of 

 the constrained particle exceeds that due to A = 2a, the ulti- 

 mate state will be S.H. motion with exact opposition of phase 

 between successive particles. The simultaneous displacements 

 of the particles at any instant, as we travel away from the con- 

 strained particle in either direction, form a diminishing geo- 

 metrical progression with signs alternately plus and minus. 



NO. I481, VOL. 57] 



Expressions are investigated for the constraining force and for 

 the ratio of the energy of the system (consisting of an unlimited 

 number of particles) to the energy of the constrained particle. 

 The second part of the paper deals with pendulums, (i) Sym- 

 pathetic pendulums, such as two equal pendulums suspended 

 from the same support. (2) Double pendulums, i.e. one 

 simple pendulum suspended from another. In each case the 

 investigation consists in seeking a mode of vibration in which 

 the two bobs have either identical or opposite phases, so that 

 their displacements are in a constant ratio, positive or negative. 

 In every case there are two such modes, one with a positive 

 and the other with a negative ratio. As regards the sympathetic 

 pendulums : when they are equal in mass and length, the periods 

 for the two modes are approximately equal, and the displace- 

 ment of each pendulum follows the law of a " curve of beats," 

 the excursions are largest for one pendulum when they are 

 smallest for the other. As regards the double pendulum : when 

 the lower mass is much less than the upper, there exist, in like 

 manner, motions following the law of beats, provided that, to 

 start with, one bob is at rest in the zero position, and the other 

 at rest in an extreme position. If the lengths of the two strings 

 are decidedly unequal, one fundamental mode has approximately 

 the period of the upper, and the other the period of the lower 

 pendulum. In the former, the displacements of the two bobs 

 are comparable ; in the latter, the displacement of the upper is 

 small compared with the lower. The bearing of these con- 

 clusions is pointed out, first, on Lord Kelvin's conclusions re- 

 specting a suspended clock ; and, secondly, on Lord Rayleigh's 

 assertion (frequently quoted in connection with anomalous dis- 

 persion) respecting the influence on a heavy pendulum of a much 

 lighter one suspended from it. To obtain the phenomenon of 

 beats in perfection, the upper string must be slightly longer 

 than the lower, and the ratio of difference to stun of lengths 

 must equal the ratio of lower mass to upper. The beats thus 

 obtained explain the experiment described in the second edition 

 of " Rayleigh on Sound," § 62. Sellmeier's application of 

 the beats of double pendulums to explain fluorescence is briefly 

 described. Stokes explains fluorescence by the analogy of the 

 chain of equal particles discussed in the first part of the paper. 

 Forced vibrations quicker than the critical frequency are pro- 

 duced by the action of the vibrating ether on the fluorescent 

 body; and when the body is left to itself, its sub- 

 sequent motion is made up of S.H. components, all of 

 which are below the critical frequency. — Prof. R. A. Lehfeldt 

 then read a paper on the properties of liquid mixtures. 

 In a previous communication {Phil. Mag. 5, vol. xl. p. 398) the 

 author followed out the consequences of a certain thermo- 

 dynamic relation between the composition of a liquid 

 mixture and that of the vapour in equilibrium with it, 

 and the saturation-pressure of the system. More stable com- 

 pounds are now chosen, viz. benzene and toluene mixed with 

 carbon tetrachloride, as types of normal organic compounds ; 

 and benzene and toluene mixed with ethyl alcohol as types of a 

 so-called " associated " liquid. These experiments have been 

 carried out in the Davy-Faraday laboratory. The measure- 

 ments come under two distinct groups : (i) vapour- pressure, (2) 

 composition of vapour. They were made separately, on material 

 from the same source, prepared identically. To measure the 

 vapour-pressure of the mixtures, the " dynamic " method was 

 adopted. An experiment consists in weighing out a mixture, 

 taking its refractive-index by a Pulfrich refractometer, placing it 

 in a boiling tube, and after adjusting temperature and pressure, 

 taking observations at different temperatures on a rising scale, 

 and then on a falling scale. The refractive-index of the residue is 

 again measured ; this is always used for checking the composi- 

 tion of the mixtures. For determining the composition of the 

 vapour over liquid mixtures, the method used is to distil a 

 little of the mixture and analyse the distillate. The apparatus 

 is arranged so that the distillate can be drawn off by a tap, as 

 required. The author criticises the results of Linebarger 

 [/our. Ainer.Chem. Soc, vol. xvii.), and also those of Margules 

 {Wien. Ber., vol. civ.). Linebarger states that the partial 

 pressure of benzene and toluene in mixtures, is simply propor- 

 tional to the molecular percentage present. This conclusion, 

 the author considers, is only roughly true ; the partial pressure of 

 the hydro-carbon vapour is not necessarily linear in mixtures ; 

 hence, the rule proposed by Linebarger for determining the 

 molecular weight is incorrect. — The President proposed votes 

 of thanks to the authors, and the meeting was adjourned until 

 March 25. 



