74 



NA TURE 



[November 15, 1900 



place in their educational curricula? A glance at the Time 

 Table of any Public School, and of most Grammar Schools, or 

 at a list of scholarships available at Universities, will show that 

 science is the Cinderella in secondary schools, and its presence 

 is more tolerated than encouraged. When science (rationally 

 taught, of course) takes so many hours of a boy's school work as 

 classics, it will be time to suggest that the languages of ancient 

 Greece and Rome are being ousted. Father Cortie's views as to 

 the plan and method of science teaching maybe judged from the 

 final remarks from his paper :— " Our aim in teaching science, as 

 in teaching every other subject to the boys committed to our 

 charge, ought to be chiefly directed to training the mind, and 

 not to the imparting of a number of isolated and disconnected 

 facts. I would advocate in the first place a preliminary course of 

 classical and literary training before joining the science classes, 

 and secondly that in the science course itself the training should 

 be neither wholly didactic, nor yet wholly experimental, or 

 Heuristic, to employ the term so much in fashion at present, but 

 a judicious mixture of both. A cultured mind should be the 

 outcome of our training, in science, as in other subjects. And 

 for true culture, a knowledge of facts, in lieu of knowledge of 

 principles and methods, is worthless." 



SOCIETIES AND ACADEMIES. 



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 interpre- 

 tation 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-dynami- 

 cally 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 in- 

 tegral / VdP. Assuming, further.that the osmotic pressure changes 



accordmg 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 10^^ 



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 pres- 

 sure 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 cal- 

 culation 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 



NO. 1620, VOL. 63] 



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 j VdP 



but had not made any numerical calculations liy 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 general 

 elementary type of astigmatic lens, and in the paper an ellip- 

 soidal lens is selected and considered. The f(jcal 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 

 natural apertures is employed to establish the various relatiot^ 

 set out in the paper. An ellipse is 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 direc- 

 tion 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 cylin- 

 drical 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, Uj and Ug, differing in 



power phase by — , and to add together suitable fractions of these, 



such as Uj sin <p, Uj cos <|). The resultant is equal to Ui, but 

 with the power phase turned through <p. 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 ir 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 measure- 

 ment 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 repre- 

 senting 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 



