Table of contents

Addendum to 1921 Proc Phys. Soc.33 207

A Discussion on this subject held on May 28th, 1920.

The Paper treats of the conditions under which interference fringes, produced by reflection of light from the two surfaces of a "thick plate," are visible to an observer. The treatment lays stress on the physical significance of the term "location" as applied to interference fringes, and the dependence of the observed phenomena on the conditions of observation. For a broad source of light a formula is obtained which is equivalent to that derived by Michelson. For a point source of light at infinity, it is shown that the fringes obtainable are equally visible at all distances from the plate.

The Paper mainly consists of an investigation of the form of the fringe system observable at infinity, or in the focal plane of a telescope, when a broad source is employed with a Michelson interferometer, in which the glass paths of the two interfering beams are not equal. The fringes may be elliptical or hyperbolic, with circles and straight lines as special cases. In the recently developed method of using the instrument for optical testing, the fringes due to a point source at infinity are employed. It is shown that the form of the fringes in this case is unaffected by lack of compensation, but that the visibility of the fringes is conditioned by the nature of the fringe system due to a broad source.

The action of the relay depends on the fact that no arc can be maintained between mercury electrodes in hydrogen. One lead is brought to mercury contained in a vertical tube within a solenoid. An iron rod, at the upper end of which is a glass cup, floats in the mercury. The cup also contains mercury, and the other lead is connected to an iron rod which dips into this. When no current flows in the solenoid, the rim of the cup is about 1 cm. above the level of the main body of mercury. When the relay current (about 0.03 ampere) is running the iron rod is sucked down until the rim of the cup is submerged by about 0.5 cm. The space above the mercury contains hydrogen. The relay can be used to break quite large currents (20 amperes) without much spark.

The relation existing between the log-log scale and the log scale in slide rules at present on the market is dealt with, and it is shown that if this relation is made that of the common logarithm the properties of characteristics and mantissæ enable the range of the non-recurring log-log scale to be indefinitely extended. In addition an equally divided scale is arranged to give ae^x and log_eax, where a is a number on the log scale, and scales for all the circular and hyperbolic functions are arranged on the back of the slide so as to read on the log scale. All such functions as eⁿ sin x and log n cosh x are, therefore, obtained with a single setting of the slide and cursor. Other minor modifications are made, and a cursor for magnifying and subdividing the divisions is described.

In this work the Y-arrangement of carbons due to Forrest was used. This facilitated accurate measurement of crater area. The carbons used were solid special electra of diameter 6 mm. For currents up to 10 amperes the crater area was directly proportional to total current, thus maintaining a constant current density. This was 0.746 ampere per square millimetre.

A simple method of producing a bright source of sodium radiation is described. An electric discharge tube of quartz, having a pool of sodium-potassium alloy as one electrode, and an iron rod as the other electrode, is utilised. The sodium vapour is proeduced by gently heating the lower part of the tube, containing the alloy, over a ring gas burner concentric with the tube. When an electric discharge is passed, a bright yellow light is emitted. This light consists almost entirely of the D lines. Any gases present in the tube are absorbed by the alloy while the discharge is passing. No continuous pumping is necessary to keep the tube exhausted, and the experiment works best when the temperature of the sodium vapour is 250°C.

Various elements were deposited in a pure condition on the cathode in an electric discharge tube. To obtain a clean surface of the element, the latter was distilled in vacuum. An electric discharge was passed through nitrogen gas contained in the tube. Measurements were made to compare the amount of gas absorbed by the element in the tube with the quantity of electricity passing in the circuit. Potassium, sodium, mercury, cadmium, antimony, magnesium, calcium, zinc, tin, phosphorus, sulphur and iodine were tested in this way. The rates of absorption were very great with the last three elements. Hydrogen gas was also used in the tube, and absorption occurred with phosphorus, sulphur and iodine. The absorption of the gases is due principally to chemical action, and is attributed to the nitrogen and hydrogen assuming active modifications on the passage of an electric discharge, the gases being at low pressure.

The Paper contains the results of an investigation of the Zeeman effect for Neon lines. The departures from Runge's Rule - that the magnetic separation of the lines are aliquot parts of the separation of the normal triplet - are discussed. It is concluded that such discrepancies are due to variations of the ratio e/m.

The author, following Vallauri, gives an approximate treatment of the conditions which gives rise to retroaction between the grid and anode circuits of a triode valve, and describes an arrangement of circuits whereby the property can easily be demonstrated to a large audience.

Steady voltages were applied between the hot and cold electrodes of a thermionic tube, for intervals of time which could be varied from 0.00001 second to a minute or longer. The mean current during the interval was measured by the Wheatstone bridge, using a null ballistic method.

Two types of thermionic tube were employed, one at a comparatively high gas pressure, the other at a far higher degree of exhaustion. It is found that on applying the voltage the initial rise of current to its maximum is followed by a fall, the rate of which diminishes with time. In the tube at the high gas-pressure the effect is considerable, and the final value of current may be less than half the initial value. In the case of the tubes at lower gas pressure the fall, though sensible, is far less pronounced, say, three or four per cent.

An experiment is described showing that whatever the change of conditions causing the observed fall may prove to be, this fall is not attributable merely to the high temperature of the filament, but is conditional on the thermionic current being permitted to flow.

The results point to the practical conclusion that in order to avoid phase difference between current and applied voltage, and consequent distortion, at telephonic frequencies, of signals transmitted through a thermionic tube, the vacuum should be as high as possible.

The Paper, which is mainly mathematical, is a further development of the system described by the author in the previous Papers of the same title presented to the Society; formulae for skew rays are put into a shape as far as possible similar to those applying to rays in one plane.

In this Paper a generalised formula for the refraction of light through a prism is obtained, and the particular cases pertaining to practical methods of refractometry deduced from it. The sensitivity of various methods for various prism angles and refractive indices is shown in a series of curves, as is also the liability to error due to errors in auxiliary constants.

Two fine platinum wires were stretched parallel to each other in a hole in a copper block, and were heated electrically in a Wheatstone bridge arrangement. The changes caused by rotation were investigated with hydrogen, air and carbon dioxide surrounding the wires. It was found that both for the same current, and for the same temperature of the wires, the inclinometer filled with carbon dioxide was much more sensitive than one filled with air. The shape of the curves obtained suggests that the temperature gradient in the region traversed by the wires is nearly uniform, the difference of temperature of the layers of gas in which the wires happen to be being sensibly proportional to the vertical distance between them.

A diminished image of a slit, on which the filament of a half-watt lamp is focussed, is projected by means of a microscope objective on the photographic plate or other object of which the absorption is to be measured. A second similar objective focusses an image of the slit, magnified up to its original size, on a second slit behind which is mounted a sensitive thermopile of the author's own design connected to an improved D'Arsonval galvanometer. By suitable gearing to an electromotor the photographic plate is given a slow motion at right angles to the beam of light, and at the same time a drum of photographic paper, on which the spot from the galvanometer is focussed, is caused to rotate at a suitable rate. A record is thus obtained of the density of the plate at different parts encountered by the beam of light. The arrangement is dead beat and so quick in response that intensity curves of close spectrum lines, Zeeman triplets, &c., are accurately recorded.

A new method of using the quadrant electrometer for the measurement of electrical power is described. It involves the use of a potential divider across the supply circuit, and a standard non-inductive resistance in series with the load. An ammeter and a voltmeter are employed to measure the supply voltage and the load current.

An example of its application to determine the power-factor of a condenser is quoted.

It is shown that crystals in the form of powder can be examined by the ionisation method. The powder is pasted on a flat surface and placed on the spectrometer table in the position ordinarily occupied by the face of a single crystal. A bulb current of 1 milliampere is sufficient to give satisfactory records.

Determinations were made of the coefficient of discharge through an orifice 0.1469 cm. in diameter of solutions of glycerine and water, varying in kinematic viscosity from 0.01 to 7. The results are plotted in a manner which combines both purely viscous and purely turbulent flows in one graph. It is shown that the effect of slight viscosity is to increase the coefficient of discharge.

This Paper describes the determination of the coefficient of viscosity of water by a method in which water is forced along glass capillary tubes of about 1.5 to 2.0 mm. bore at rates of flow varying from 1 litre in two years to 1 litre in 24 years. The liquid fills a closed tubular circuit which for purposes of description may be said to be rectangular in shape. Two of the tubes of the rectangle are horizontal, and two vertical. The circulation is caused by a difference of density between the contents of the two vertical tubes. The difference is obtained by having a weak solution of uranine in one vertical tube, and pure water in the other.

In Apparatus I. the two vertical tubes are at a distance apart, and an allowance has to be made for the difference of temperature. In Apparatus II. a modification of the rectangular circuit is employed, the vertical tubes are close together, and no such corection is necessary.

Applying the temperature correction to the results recorded in this Paper, the value of the co-efficient of viscosity at 18°C. is 0.010624 ± 0.000229 (assuming observations of equal weight) and 0.010569 gm./cm. sec. from Hosking's formula. Thus there is no experimental evidence that at the extremely low rates of shear (0.0017 to 0.0233 radians/sec.) the viscosity of air-free water in glass capillary tubes differs from its value at normal rates of shear (5,000 to 10,000 radians/sec.).

An heterodyne method of measuring frequency by comparison with a calibrated valve oscillator is described. The calibration is performed by means of two valve oscillators capable of giving frequencies of, say, 1,000 - /sec. upwards. The frequency of the oscillators is raised alternately to give a beat note whose pitch is determined by comparison with a fork. Intermediate frequencies are found by interpolation on the calibration curve and a method of checking the capacities of the oscillator condensers is described.

For the measurement of acoustic frequencies the sounds are converted into alternating currents by means of a suitable transmitter.

The Paper describes the development of a robust form of vacuum tube which was used as a detector of electrical oscillations in the "wireless" circuits carried by aeroplanes. Platinum electrodes are avoided being replaced by strips of tinfoil, to which contact may be made by the spring clips holding the tube in position.

It was found that when a discharge is passed through such a tube, the walls are affected in such a way that thenceforth it is much easier to get a discharge to pass. The change produced by the first discharge is annulled by heating the tube above 210°C. Further, if the walls are coated on the inside with a metallic film, this first discharge is unnecessary, and the tube is unaffected by heating, but when the walls are coated with an insulator it is if anything more difficult to pass a discharge. A silica tube behaves like one coated with metal. It seems possible that the change in the tube may be due to the formation of a layer of gas molecules on the walls by the first discharge. The explanation of the behaviour of the silica tube is a difficulty.

This Paper gives an account of experiments on the Diffusivity of saturated solutions of KCl, NaCl and KNO₃ at constant temperatures near 18°C., when the steady state of diffusion has been attained, employing a method similar to that previously used by the author (Proc. Phys. Soc., Vol. XXI., p. 863, 1908; Vol. XXIV., p. 40, 1911; Vol. XXVII., p. 56, 1914; Vol. XXIX., p. 49, 1916).

The solution under investigation is maintained at complete saturation by the presence of salt crystals in the diffusion vessel. The theory takes into account the change in volume of this salt as it dissolves, and an expression is obtained for the coefficient of diffusion at complete saturation, which depends on the rate of change in weight of the diffusion vessel with time. The experimental results are found to agree very closely with the values obtained by extrapolation from the results previously found for less concentrated solutions. By the present Paper the author has thus extended the range of concentration over which he has studied diffusion from very dilute solutions right up to complete saturation.

This Paper is an attempt to demonstrate the actual existence of thermal transpiration currents. Theoretical considerations are first introduced to show that if a radial temperature gradient be maintained over a disc, so that the centre is the hottest part, thermal transpiration currents sweep radially inwards over the surface of the disc, and discharge themselves more or less radially outwards in the upper regions.

To detect these currents a narrow strip of foil is used which is placed perpendicular to the disc, and to one side of the hot region. When at a considerable perpendicullar distance from the disc, and when the gas pressure is sufficiently low to eliminate convection currents, the deflections of the strip of foil are always away from the hot region. When, however, the strip is placed very close to the disc, its deflections over a certain range of gas pressure are towards the hot region. These facts are explained by the tendency of the thermal transpiration currents to drag the strip with them.

The Paper emphasises one of the essential differences between thermal transpiration currents and convection currents - namely, that while the latter clearly depend on gravitation, the former do not. Further emphasis is laid on the differences between the conditions of molar and molecular equilibrium.

An examination of the odd order spectra reflected from the 100 plane of fluorspar, using palladium X-rays, has been made with a view to test the Lewis-Langmuir theory of the motion of valency electrons in compounds. Evidence, in partial confirmation of the theory, has been obtained.

The Paper describes an investigation of the relative intensities of the reflections of monochromatic X-rays by the various crystallographic planes of diamond. The special difficulties due to the small size of available crystals and the modification of the usual method required to obviate them are discussed. An interesting feature of the results is that they lie very closely on smooth curves, which indicates that if the outer electrons of the carbon atom lie at any considerable distance from the centre they must be in motion over a wide range, or for some other reason must contribute little to the reflection.

It is shown that the properties of the carbon atom in diamond are based on a tetrahedral and not a spherical form. The tetrahedra point away from any (111) plane in the case of half the atoms, and towards it in the case of the other half. Consecutive 111 planes are not exactly of the same nature and consequently some slight second order reflection from the tetrahedral plane might be expected. This effect, though slight, has been found.

A theoretical investigation has been made upon the effects of self and intercapacities and of eddy-current losses in mutual inductances for which the coils have a common point. The following are the main conclusions arrived at.

1. Small capacities introduce variations in the effective self and mutual inductances which change as the square of the frequency.

2. Corresponding variations are introduced in the effective resistances of the coils.

3. The mutual inductance is no longer "pure," that is, the secondary E.M.F. is no longer in exact quadrature with the primary current. The primary and secondary circuits behave as if they have a resistance in common which varies as the square of the frequency.

4. Eddy currents produce impurity and changes of effective resistance which are initially of the same nature as those due to capacity.

5. Eddy current and capacity effects may be so combined that the variations of mutual inductance and of impurity cancel simultaneously, so that it is theoretically possible to obtain a "pure" mutual inductance having no variation with frequency over the whole range of audio frequencies.

The conditions of balance of three alternating-current bridges, viz.: -

1. The Heaviside inductance bridge.

2. The Carey-Foster bridge.

3. A modified Campbell frequency bridge

have been worked out on the basis that the mutual inductance is not pure and the mutual and self-inductances are not invariable with frequency. It is shown how combined observations on these bridges may be used to determine the frequency corrections of a given inductometer.

An experimental study has been made upon an inductometer of the Campbell type. The results show that if such an inductometer is used at the higher audio-frequencies for the measurements of the effective resistance of coils or of condensers, the inductometer corrections may in certain cases be larger than the quantities measured.

A method for automatically correcting an inductometer is suggested in order that it may be used for the measurement of power factors of condensers

The Paper is a description of an apparatus for the determination of the specific heats of materials such as cork, charcoal, &c., which are difficult to deal with by the ordinary methods. The calorimeter is a closed cylinder rotating on a horizontal axis. The heating coil and the thermo-elements project into the calorimeter and are maintained stationary. The material under test fills about one-third of the calorimeter and is mixed by being carried round by the fins attached to the internal surface. To ensure equalisation of the temperature, the material is ground to a state of fine sub-division before test.

By reducing the weights of all parts to a minimum a calorimeter of 4 litres capacity has been constructed whose water equivalent is less than 100 grams. The jacket surrounding the calorimeter is made of copper wound with a heating coil. In an experiment the temperature of this jacket is maintained equal to that of the calorimeter, thus eliminating the corrections for heat loss by radiation and convection.

This Paper is an extension of the author's previous work on molecular dimensions and structure derived from the combined data of the kinetic theory of gases and of X-ray crystal measurements (Proc. Roy. Soc., A. Vol. XCVIII., p. 360). The cases previously considered have been confined to molecules built up of atoms all of equal size. In this Paper this limitation is removed, and unequal atoms are contemplated.

The results arrived at cover all cases of diatomic molecules and certain special cases in which the molecules are polyatomic. It will be possible to test their validity when the appropriate viscosity data become available.

The problem is that presented by a number of fine parallel wires at the same height above the ground - treated as a plane surface - all charged to the same potential.

The chief object is to investigate how the potential gradient at ground level depends on the height and spacing of the wires. A second object is to find how the potential gradient varies with the height above the ground. The cases of a finite and an infinite number of wires are considered.