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imagine that a cylinder of hot lime, if it could be made airtight, would still be permeable to carbon dioxide. As a rule the disintegration produced by chemical action would prevent such partitions from being effective for any length of time, but still cases of this kind are possible and must therefore be considered.

The diffusion, which takes place in these cases by the gas particles being handed from one molecule to the other, follows in general the same kind of laws as those which have first been considered. There is, however, one very important difference conditioned by the fact that, the reaction being reversible, there is a definite dissociation pressure for each temperature. When the external pressure is the dissociation pressure, the whole of the superficial layer is turned into the compound, so that the solid cannot transmit a pressure greater than the dissociation pressure. Hence, if we start with a very high pressure on one side of the diaphragm and zero pressure on the other side, the pressure on the low pressure side will rise until it is equal to the dissociation pressure, when no further transference will take place. On the other hand, if the pressure on one side is always kept at zero, whilst that on the other side is capable of taking all values, then the rate of flow through will be a uniform function of the pressure up to the dissociation pressure, at which there will be a discontinuity, and the rate of flow will be independent of the pressure for all higher pressures.

XXVI. An Instrument for Drawing Conics. By J. R. COTTER, M.A., Assistant to the Professor of Experimental Physics, Trinity College, Dublin*.

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APROPOS of Prof. Karl Pearson's article in the Philo

sophical Magazine' for February, I should like to mention that in the year 1894 I designed an instrument for drawing conics which has the advantage of always keeping the drawing-pen parallel to the direction of the curve. The compasses will draw any kind of conic, given the foci and a point on the curve. The accompanying figure is drawn from the actual instrument, but as it is only a rough home-made model it is faulty in construction.

AGBF is a rhombus formed of four equal and freely jointed flat brass rods. The corner A slides freely along the slot of the bar BC. FH is another flat brass bar pivoted

* Communicated by Prof. John Joly, F.R.S.

to the rhombus at G. It is slotted for a portion of its length and slides between the rhombus and BC. A pencil-holder P moves in both slots together.

H

Two pins are driven into the drawing-board at the foci of the required conic and the pencil P brought to a point on the curve. The corner F' of the rhombus is pivoted on one focus and FH turned round to the other focus, which can be fitted into one of the holes in FH. For an ellipse the second focus must be near the end F; for an hyperbola near the end H. Suppose that we wish to draw an ellipse, F and F being the foci. By elementary geometry PFPG, therefore FP+PF-FG, which is a fixed length on the rod. Thus P describes an ellipse. If the second focus were at H, we should have HP-PF'=HG=const., so that P would describe an hyperbola with F' and H as foci.

In either case the line AB bisects the angle FPF' externally (or F'PH internally) so that AB moves as a tangent to the curve. Thus if a drawing-pen were made to slide along AB without turning, but turning freely in the slot of FH, it would always keep tangential to the curve. This property is not possessed by the ingenious instrument described by Prof. Pearson. On the other hand, my instrument is open to the objection that it will only draw a little more than half an ellipse in one position. To describe the other half it must be reversed on the focal pins. Similarly, after drawing one branch of an hyperbola, it must be reversed on the pins to draw the other branch.

It is clear from the figure that perfection of design has, in the model, been sacrificed for the sake of simplicity of construction. Instead of having holes bored in FH the slot should be extended to F and another slot cut between G and H. A sliding focal pin could then be clamped in any position. Also the rhombus should have been shaped at the corners A and B so as always to leave sufficient space between the sides to allow of the pen P sliding right up to the corners, even if the rhombus is nearly closed.

To describe a parabola, F' is made the focus, and FH is moved at right angles to itself, keeping it always parallel to its original direction. Under these circumstances P describes a parabola, and G its directrix. I made no provision in my model for drawing parabolas, but I found that it would describe a very fair parabola if the flat end of F were made to slide along a fixed ruler.

I have not previously published any description of these compasses, as I hoped some time to improve the design and get a good working instrument made.

XXVII. The Charges on lons. By JOHN S. TOWNSEND, F.R.S., Wykeham Professor of Physics, Oxford*.

THE

HE relation between the charges on ions produced in gases by various methods is a matter of some importance, as the theory of electric currents in liquids and gases which is almost universally adopted is founded on the principle that all these small subdivisions of electricity with which the ions are charged are equal to or exact multiples of some charge which is absolutely fixed. The theory is supported by the phenomena which accompany the passage of electricity through liquids, and as is well known the charges on the ions are all exact multiples of the charge on the hydrogen ion in a liquid electrolyte. The theory also holds for gases; and it can be proved that the charge on an ion produced by almost any of the known methods, in a gas, is identical with the charge on the hydrogen ion in a liquid electrolyte.

It is of interest to collect the results upon which this theory is founded, and to show to what degree of accuracy the atomic charge may be considered to be known.

If E is the charge on a hydrogen ion or atom in a liquid electrolyte, N the number of molecules per cubic centimetre

*Communicated by the Author.

of a gas at 15° C. and 760 mm. pressure, then, since a known volume of hydrogen is evolved at the negative electrode when unit quantity of electricity passes through the liquid, the formula

NXE=1.22 × 1010

is established, E being measured in electrostatic units.

If e is the charge on an ion in a gas, u its velocity when acted on by a force of one volt per centimetre, K the rate of diffusion of ions in the gas, it can be shown that

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This formula is derived from the kinetic theory of gases by very simple considerations, it does not involve any assumption as to the distributions of the velocities of translation of the molecules, or the law of force between molecules during a collision. It may therefore be considered very reliable from a theoretical point of view.

The values of K and u have been found experimentally in a large number of cases, so that the values of Nxe may be calculated. The mean values of u for positive and negative ions produced by Röntgen rays in different gases have been found by Prof. Rutherford *. Another set of determinations of the velocities have been made by Prof. Zeleny †, using a different method in which the velocities of the positive and negative ions have been determined separately.

The values of u for ions produced by ultra-violet light have also been determined by Prof. Rutherford‡.

The values of K have been determined by the author for ions produced by Röntgen rays, ultra-violet light, and radioactive substances §.

Taking the values of u given by Prof. Rutherford, the following values of Nxe are obtained, for ions produced by Röntgen rays:

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E. Rutherford, Phil. Mag. November 1897.

† J. Zeleny, Phil. Trans. vol. cxcv. pp. 193-234 (1900).

E. Rutherford, Cambridge Philosophical Society Proc. vol. ix. pt. viii. (1898).

SJ. S. Townsend, Phil. Trans. vol. exciii. (1899) and vol. excv. (1900).

the mean value of K for positive and negative ions being used.

From the values of and K for ions in air produced by ultra-violet light

Ne 1.12 10-10.

The following table of values of Nx ex 1010 may be deduced from Prof. Zeleny's determinations of the velocities:

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The mean values of N xe for the different gases are

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In addition it has been shown that the values of u and K for ions in air are both inversely proportional to the pressure for pressures between 760 and 200 millimetres.

The discrepancy between the above numbers is not greater than the probable experimental errors, and they afford evidence of the equality of the charges. There is also evidence from other investigations which leads us to believe that the above values of Nxe should all be equal. This may be deduced from experiments on the ionization of molecules produced by collision, which are of a much simpler kind than the experiments which are necessary for the determination either of the velocities or the rates of diffusion.

It has been shown that the negative ions produced in gases by the action of Röntgen rays or by collisions are all exactly the same as the ions set free from a zinc plate by the action of ultra-violet light.

In order, therefore, to obtain the most probable value of Nxe we are justified in taking the mean of the above

* J. S. Townsend, Phil. Mag. June 1902.

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