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• W4247492697 abstract "LONDON. Physical Society, November 9.—Prof. A. W. Reinold, F.R.S., Vice-President, in the chair.—Dr. R. A. Lehfeldt read a paper on “Electro-motive force and osmotic pressure.” This paper is an attempt to explain a difficulty in the interpretation of the ordinary logarithmic formula for the E. M. F. between a metal and solution, pointed out by the author at the Dover meeting of the British Association. An expression for the E.M.F. of a concentration cell is obtained thermo-dynamically upon the assumption that the electrolyte is only partially dissociated. A partition is used which is permeable to water but not to the salt or its ions, and the conclusion follows that the E.M.F. depends, not on the osmotic pressure of the metallic ions, but on that of the solution as a whole. A graphical representation is given plotting osmotic pressure against dilution, assuming Boyle's law to hold, and it is shown that the E.M.F. is not proportional to the integral ∫PdV but to the converse integral ∫VdP. Assuming, further that the osmotic pressure changes according to Van der Waals's equation, the E. M. F. is greater than that calculated from Boyle's Law. If the electrolytic solution pressure is calculated from the integral ∫PdV it comes out 1019 atmospheres; but if from the converse integral, the value obtained is about 20,000 atmospheres. A comparison between actual E.M.F.'s and those derived from the equation given by the author should afford, if the formula is correctly deduced from the assumptions made, a measure of how far the osmotic pressure deviates from that indicated by Boyle's law. Experiments upon concentration cells have been made by Helmholtz, Wright and Thomson, Moser, Lussana and Goodwin; but as their work was performed upon cells with migration of ions, the calculation of the osmotic pressure is rendered uncertain by the introduction of the transference ratio. Accordingly the author has measured the E.M.F.'s of cells without migration, using zinc as electrodes and chloride and sulphate of zinc as salts. The E.M.F. was measured by the compensation method, using a post office box through which a current was sent by an accumulator. The accumulator kept up a constant potential difference, and was standardised daily by means of a Clarke cell. The experimental results agree with the calculated over the range centi- to deci-normal, showing that the deviation from the value given by the logarithmic formula is accounted for by the incomplete dissociation of the salts. The osmotic pressures are then calculated from the E.M.F.'s and the values of PV plotted. They show irregularities due to the combined effect of the decreasing dissociation of the salt and the increasing departure from Boyle's Law. Dividing the product PV by Van't Hoff s factor, determined from conductivity, values are obtained showing variations similar to those observed in the behaviour of gases when subjected to high pressure. Mr. Whetham said there was one form of membrane which is quite permeable to water and yet does not allow either salts or the ions to get through. He referred to the free surface of the solution itself. The water being volatile can get out, but the salt cannot. Dr. Donnan said the author seemed to have discovered things well known; for instance, the integral ∫VdP is generally taken as proportional to E M.F. He expressed his interest in the explanation of the difficulty in the logarithmic formula. Dr. Lehfeldt, in reply, said Goodwin had used the integral ∫VdP but had not made any numerical calculations by means of it.—Mr. R. J. Sowter read a paper on “astigmatic lenses.” An. astigmatic lens is one which so acts on rays of light falling on it as to produce, in general, two focal lines in the refracted ray system. A lens derived from a quadric surface is the generai elementary type of astigmatic lens, and in the paper an ellipsoidal lens is selected and considered. The focal lines are parallel to the elliptic axes, and correspond to the lens powers, in these directions. These powers are proportional to the inverse squares of the axes. A curve drawn through all points on a lens where the material thickness is constant may be said to determine a natural aperture for that lens. A method of natura apertures is employed to establish the various relation set out in the paper. An ellipse in the natural aperture for an ellipsoidal lens, a circle for a spherical lens, and an infinitely long rectangle for a cylindrical lens. It is shown that two cylindrical lenses crossed at right angles are equivalent to an ellipsoidal lens, and the power of the combination in any direction is the same as that of the ellipsoidal lens in that direction. It is also shown that two obliquely crossed cylindrical lenses are equivalent to an ellipsoidal lens, or to two cylindrical lenses of definite powers crossed at right angles, or to a cylindrical and a spherical lens; for a spherical lens may be replaced by two equal cylindrical lenses crossed at right angles. Prof. S. P. Thompson said he had never seen the treatment of an ellipsoidal, lens before, although the extreme case of a paraboloidal lens had been considered. The author's method was, as far as he knew, new, and would be very convenient to work with. Mr. A. Campbell then read the following papers: (a) “On a phase-turning apparatus for use with electrostatic voltmeters.” Electrostatic voltmeters are particularly insensitive at the lower parts of their ranges, the divisions closing in very much towards the zero point. When measurements of small direct-current potential differences have to be made, it is an easy matter to add to the voltage to be measured a constant voltage large enough to bring the deflection to an open part of the scale. If the small voltage to be measured is an alternating one, it is necessary that the auxiliary voltage should alternate with the same frequency, and be in phase with it. The apparatus described enables the phase of the auxiliary voltage to be turned until it agrees with the one to be measured. The phase difference referred to is not the time lag but the angle whose cosine is the power factor and may be called the power lag. The method is to get two independent equal voltages, U1 and U2, differing in power phase by π/2, and to add together suitable fractions of these, such as U1 sin φ, UU2 cos φ. The resultant is equal to U1 but with the power phase turned through φ. The unknown small voltage is connected in series with an auxiliary voltage and a voltmeter, and the phase of the latter voltage is turned until the maximum deflection is obtained. (b) “On a method of measuring power in alternating current circuits.” The circuit in which the power is to be measured is connected in series across the supply circuit with a small non-inductive resistance. By means of a transformer the small voltage on this resistance may be transformed into one whose power phase is IT behind the voltage on the resistance. This is added to the voltage on the circuit to be measured, and then reversed and added again. The difference of the squares of these effective resultants is shown to be equal to a constant into the power to be measured. If there is any direct current, it must be measured separately by a Weston voltmeter or other suitable instrument, (c) “Note on obtaining alternating currents and voltages in the same phase for fictitious loads.” When testing instruments for the measurement of large amounts of electrical power or energy, it is usually desirable to do so by means of fictitious loads, or by applying to the instrument under test current and potential difference representing the required load. In order to obtain a fictitious non-inductive load with alternating currents, the potential difference and current should be in the same phase. The current for the instrument under test is got by means of a transformer worked on a hundred volt circuit. The potential difference in the same phase is got by allowing the current to flow through a non-inductive resistance and increasing the voltage at the ends of the resistance to the required amount by means of another transformer.—The Society then adjourned until November 23." @default.
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• W4247492697 doi "https://doi.org/10.1038/063074a0" @default.
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