Abstract
LONDON. Royal Society, June 29.—Sir Archibtiil Gcikir, K.C. B., president, in the chair.—Francis Darwin and Miss D. F. M. Pertz: A new method of estimating the aperture of stomata. The apparatus here described under the name of porometer is similar in principle to that devised in 1873 by N. J. C. Müller, but differs from it completely in construction. By a simple arrangement a current of air is drawn through the stomata of a living leaf, its velocity being measured by the tail of a water-column. At a constant pressure the rate of air-flow is necessarily dependent on the size of the stomatal pores, and it is accordingly found that agencies such as darkness or loss of water supply, which are known to diminish stomatal aperture, cause a striking drop in the rate of air-flow as recorded by the porometer. Jn studying the effect of severing the leaf stalk, and thus cutting off the water supply, it has been proved that the first effect of withering is a wide opening of the stomatal pore, confirming F. Darwin in Phil. Trans., B, vol. esc, 1898, p. 548. The porometer has been found of value in attacking the question of the causal relation between stomatal aperture and transpiration. This subject, on which a large number of observations have been made, will be fully treated elsewhere. In the present paper a single experiment is given illustrating the parallelism between the transpiration rate and the condition of the stomata as revealed by the porometer.—S. Chapman: The kinetic theor)' of a gas constituted of spherically symmetrical molecules. This paper may be regarded as a sequel to Maxwell's kinetic theory of a gas the molecules of which repel one another according to the famous fifth-power law (Phil. Trans., 1867). Maxwell's deductions from his hypothesis were found not to agree with fact, but the theory was valuable, because it was the only mathematically rigorous kinetic theory in existence. Wlien he wrote a later paper on the same subject (Phil. Trans., 1879) he was aware of the defects of his assumption, but was prevented by certain analytical difficulties from generalising his theory by adopting a wider hypothesis. In this paper these difficulties have been very largely overcome. With the same rigour as in Maxwell's theory, formulae are deduced for the coefficients of viscosity, diffusion, and thermal conductivity in a simple or compound gas. The molecules are assumed to be spherically symmetrical, but no particular kind of interaction is postulated. The latter, however, is involved in the formulae by the occurrence, as factors, of two definite integrals. Certain relations may be deduced without the evaluation of these factors. The most interesting of these is δ=5/2;/µ Cm where 8 is the thermal conductivity, µ the viscosity, and Cm the specific heat at constant volume. This formula, which was also obtained by Maxwell, has always been regarded as a special consequence of his hypothesis, whereas it only depends on the spherical symmetry of the molecules, and is true for rigid-elastic spheres, among other cases. In general, the formula? can be completed only by the evaluation of the before-mentioned factors. In the paper this is done for the case of rigid-elastic spherical molecules, for centres of force repelling according to the inverse nth power law of distance, and for the case of rigid-elastic spheres surrounded by fields of attractive force. The last case furnishes a rigorous proof of Sutherland's formula for viscosity, and some important corrections to his theory are made. Finally, the formulas obtained are compared with experimental results to test the accuracy of the various laws considered, and to obtain improved data concerning the molecules and other physical constants of gases.—Major P. A. MacMahon: Memoir on the theory of the partitions of numbers. Part vi.—Partitions in space of two dimensions, to which is added an adumbration of the theory of partitions in space of three dimensions. In this part the author considers the partitions of a number, the parts being placed at the nodes of an incomplete lattice in two dimensions. Thus, the lattice being of the nature depicted,....../.........—--------> the parts are in descending order of magnitude in each row and in each column. The enumerating generating function is required. It is found that for a lattice of given specification and a given restriction upon the part magnitude the generating function satisfies a functional equation. From this the functional equation satisfied by the corresponding inner-lattice function, as is defined in part v., is deduced. This investigation then turns upon the determination of the fundamental solutions of this equation and the expression of the generating function by means of them. The complete solution of the problems in hand is thence obtained, and the inner-lattice function is showTn to be expressible in an elegant determinant form. At the end of the paper the subject of three-dimensional partitions is broached. It is shown that the method of lattice functions is again available, and the particular case of partition at the summits of a cube is worked out in detail from this point of view. The further investigation of this interesting question is reserved for a future communication.—W. T. David: Radiation in explosions of coal gas and air.—Dr. T. E. Stanton: The mechanical viscosity of fluids. The paper deals with the experimental determination of the ratio of the shearing stress to the rate of change of distortion in fluids which are in sinuous or eddying motion. Thus in a fluid in eddying motion flowing through a parallel pipe of circular cross-section, if F is the mean shearing stress on any cylindrical surface of radius r concentric with the pipe, and -0 the average velocity in the axial direction of the fluid in this surface, then writing F = /—'-'- the object of the experiments was ar the determination of fi' as a function of the dimensions of the pipe and the velocity of flow. This ratio has been called by Osborne Reynolds “ mechanical viscosity,” to distinguish it from the corresponding ratio when the field is in steady or laminar motion, which is the ordinary coefficient of viscosity. The fluid chosen for the purpose of the experiments was air flowing at speeds up to 2200 cm. per second through pipes 5-08 and 7-35 cm. diameter. A small Pitot tube of width 0-25 mm., connected to a very sensitive gauge reading to 0-005 mm. of water, has been used for measuring the distribution of velocity, and a second sensitive gauge has been used for measuring the shearing forces. The results of the experiments are as follows:-(1) In pipes artificially roughened so that air friction varied as square of velocity of flow, the value of ft' was found to be proportional to the product of speed of flow v o, and linear dimension of pipe I, by F = CvJ ft - |-^ where C is J \vj jdr t.e. F = kvj - where k is a constant depending on the roughness. (2) In ordinary smooth pipes the corresponding relation was given constant and f (^- J a function of the kinematical coefficient of viscosity V and the above product vcl. (3) In ordinary smooth pipes of different diameters, owing to the existence of a region of viscous flow at the boundaries, exact similarity between the distributions of axial velocity from centre to walls only obtains when the two viscosities (ft and ft') are the same for each pipe.—Dr. G. W. C. Kaye: A silica standard of length. The general properties of fused silica, and in particular its remarkably low coefficient of expansion, render this substance specially suitable for the construction of permanent length-standards of the highest class. The coefficient of expansion of platinum-iridium, which has hitherto been the material almost exclusively employed in the best work, is about 9X10-6 per degree C, while that of silica over the ordinary range is about 0-4X10-”, i.e. one-twentieth of this amount. It is true that the best qualities of invar-M. Guillaume's nickel-steel containing 36 per cent. Ni-have expansion coefficients comparable with that of silica, but experience has shown that while invar is eminently useful for working standards, it is quite unsuitable for primary standards, owing to its large thermal hysteresis. Fused silica, on the contrary, has been found to be practically entirely free from this defect; it enjoys, in the matter of cost, an enormous advantage over platinum-iridium; furthermore, in view of the fact that primary standards are always handled by trained and skilled observers, its comparative fragility is of small consequence. Modern methods of manufacturing and working silica have rendered it possible to construct a silica line-standard metre. The present model, the first of its kind, consists of a silica tube into which are fused at its ends optically-worked plane parallel slabs of silica. These carry the giaduations, and their undersides are platinised. The graduations, defining the metre length, are made by cutting through the platinum film with a ruling diamond. The platinum deposit permits the ruling of very beautiful clean-edged lines. The bar is supported at the Airy points so that the slabs are horizontal. The lines are viewed from above through the slabs, and are thus seen to advantage. The apparent length of the standard is independent of any change of tilt of the cover-slips which are used to protect the platinum films. The thickness and position of the end slabs are so arranged that the image of each reference line lies in the “ neutral plane “ when the bar is immersed in water. The silica metre was annealed at about 450° C, and shrunk a little more than half a micron in the process. It is anticipated that its future secular variation will be negligible so far as practice is concerned.—Ridsdale Ellis: The properties of oil emulsions. Part i.—Electrical charge. The electrical charge^ on the globules and the contact potential at the oil-water interface were obtained from measurements of the migration velocity in an electric field. The apparatus used by Whitney and Blake and by Burton for determining velocity of migration were found not to be accurate, since they did not take into consideration the electrical circulation which takes place, and other factors. To avoid these errors a microscopic method was employed, and corrections for electrical circulation and other effects were introduced into the method of calculating migration velocity. For determining contact potential in presence of electrolytes it was found necessary to modify the apparatus in order to enable the evolution of gas at the electrodes to be avoided, which would otherwise prevent readings being taken. It was found that the magnitude of the contact potential at the oil-water interface is of the same order of magnitude for oils of various kinds, whether very pure or containing large amounts of impurities. Further, the contact potential at the oil-water interface is of the same order of magnitude as that at the. glass-water interface and at the interface between the suspended particles of colloidal metals, lycopodium, quartz, and other substances. From these and other considerations it would appear that the contact potential in neutral solution depends almost wholly on the dielectric constants of the suspended particle and of the medium in which it is suspended. The contact potential at the oil-water and glass-water interface is a maximum in neutral or slightly alkaline solutions. Thus the addition of caustic soda at first increases the contact potential at the oil-water interface, but when the concentration exceeds o-ooi N the contact potential is diminished, rapidly at first, and then slowly. In the glass-water interface the maximum potential appears to be in neutral solution. If hydrochloric acid is added the contact potential is reduced very rapidly for small concentrations, but only slowly for comparatively high concentrations.—Dr. W. H. Young;: A class of parametric integrals and their application in the theory of Fourier series. In this paper the following theorem, inter alia, is proved:-If f[x) and g(x) are two functions the (l+/)th power and (t+) power of which respectively are summable, and if (a, !>“), la, $”), be their Fourier constants, then the series the general term of which is (allan+6nSv) cos n9 is the Fourier series of a continuous function, a simple expression for which is given. From this theorem follows as a corollary that if the series Y-a0 ao + 2,=i (a, an t bn Bn) T f(x)g(x)dn for its sum, and more generally it always has this expression for sum when the summation is performed in the Cesaro manner. The method employed is shown also to lead to results of analogous nature, previously known. It involves the study of certain parametric integrals, and of a theorem in the theory of sets of points stated and proved in the paper, to the effect that if a set of points of positive content be shifted bodily a sufficiently small distance along the straight line on which it is situated, it necessarily coincides with its original position as to a sub-set of points the content of which may be made as near as we please to the content of the set.—Dr. W. H. Young:: A mode of generating Fourier series.—H. R. A. Mallock: Pendulum clocks and their errors. The errors to which pendulum clocks are liable may be divided into three classes, viz.:-(1) those which may affect free pendulums oscillating in vacuo; (2) errors depending on the action of the air or gas in which the oscillation takes place; (3) errors due to the escapement and maintaining mechanism. In good clocks unexplained variations of rate are not uncommon, and may be as large as half a second a day, or even more. At any rate, a clock the rate of which continues constant within 1/200,000 for a year or more is exceptional, and anything which succeeds in securing a constancy of rate better than five parts in a million may be considered an improvement. In discussing the various sources of change of rate, all matters (so far as the author knows) which can alter the period by as much as 10-8 are taken into account. It appears that most of the anomalous changes of rate are due to variation of friction in the escapement and maintaining mechanism, which acts chiefly, but not exclusively, by altering the arc of vibration. A graphic method is given for determining in detail the action of escapements on the period.—Prof. Sydney J. Hickson: Ceratopora, the type of a new family of Alcyonaria. A specimen of a compound tubular coral was obtained by the naturalists of the Blake off Cuba in ioo fathoms of water. This specimen was figured by Agassiz in his account of the expedition, and referred to as “ a supposed Favosites is probably a bryozoan genus allied to Heteropora.” A more detailed examination of the dried corallum shows the presence of long tuberculate spicules, in addition to the crystalline calcareous tubular skeleton, which is formed in a horny matrix. There are no tubulse, and the tubular walls are not perforated. The evidence suggests that this coral is an alcyonarian belonging to the order Caenothecalia, and it is proposed to give it the name Ceratopora nicholsonii.—Dr. W. Watson: Note on the sensibility of the eye to variations of wave-length. The author has compared the width of Edridge-Green's monochromatic patch with the minimum change in wave-length perceptible as a change in hue in the yellow under exactly similar conditions, and finds there is a marked difference. It is also shown that an admixture of white light would not account for the increased sensitiveness when two monochromatic patches are compared.—E. N. de C. Andrade: The distribution of slide in a right six-face subject to pure shear.—Major C. L. Williams: The viability of human carcinoma in animals.—Prof. W. B. Bottomlcy: The structure and physiological significance of the root-nodules of Myrica gale.—H. W. Harvey and W. B. Hardy: Note on the surface electric charges of living cells.—Prof. C. S. Sherrington and Miss S. C. M. Sowton: Reflex inhibition of the knee flexor.—Prof. H. E. Armstrong and Dr. E. F. Armstrong:: The origin of osmotic effects. IV.—Note on thedifferential septa in plants with reference to the translocation of nutritive materials.
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Societies and Academies . Nature 87, 65–68 (1911). https://doi.org/10.1038/087065a0
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DOI: https://doi.org/10.1038/087065a0