Table of contents

The theory of an instrument for measuring the rate of flow of a gas is outlined, the effects of variation in the temperature and pressure of the gas being taken into consideration. This theory is tested experimentally for pressures varying from 1,250 to 250 mm. Hg., and for temperatures from 10°C. to 100°C. It is found to be fairly accurate. The results are applied to the measurement of the rate of flow of gas on an aeroplane in the upper atmosphere, where a reduction in temperature and pressure is encountered. It is shown that the instrument reading for a certain N.T.P. volume of gas depends on the altitude, but that this volume can be obtained by using a correction factor.

The instrument, devised for bacteriological use, had to be cheap and moderately robust. It consists of a long horizontal fibre joining the lower ends of two vertical beams, each pivoted very little above its centre of mass. A small weight acting at the middle of the fibre thus causes a considerable depression. This is read off by arranging a slider on a vertical millimetre scale about 2 ft. in front, so that the middle of the fibre and a second short fibre placed just behind it are in line with a "peephole" on the slider. Adjustment is provided for quickly and largely altering the sensitiveness. The deflections are converted to masses by the use of calibrating weights. The apparatus is built up from a "Meccano" set.

The Paper gives a method for the resolution of a curve of the compound exponential form B = Σ₁ⁿa₁exp(-λ₁t) into its components, the values of a and λ for the n different exponential terms being found from 2n values of B equidistant along the axis of t. A method is also given for finding the most probable values of these constants from any number (>2n) of observed values of B taken at irregular intervals of t.

Two formulæ are established for the computation of the self-inductance of single layer flat coils, one for the case when the inner and outer radii are not very different and the other for the case of small inner radius. The two formulæ are shown to be consistent and capable of including all possible cases. From the formula a table is calculated which enables the inductance to be expressed in the form L = Qn²r³, in which n is the number of turns per cm., r the outer radius and Q is a tabulated function of the ratio of the inner and outer radii. Some applications of the table are given.

A method of obtaining experimentally the current at break in a magneto is described. A condenser is connected across the secondary winding to reduce the voltage below that to cause sparking at the safety gap. The peak voltage due solely to interruption of the current at any speed is found. The interrupted direct current necessary to give the same peak voltage is also found by using a calibrating circuit. The magnitude of this current is equal to that broken in the magneto. The influence of the secondary condenser on the primary current at high speeds is discussed.

When the pressure in a galvanic cell is suddenly varied, the current in the external circuit is altered, an increase in pressure increasing the current, and vice versa. When the pressure in the neighbourhood of the zinc electrode is suddenly increased, and that in the neighbourhood of the copper electrode is diminished at the same time, an increase in current takes place, and vice versa.

An expression is obtained for the amount of flux received from a perfectly diffusing circular luminous disc (i.e., one radiating according to the cosine law) by a second parallel and coaxial disc. This is obtained from Sumpner's theory of the whitened globe, and also from first principles. The following applications of the theory are made: (I.) It is shown that the surface traced out by the edges of coaxial discs which receive equal amounts of flux from a radiating disc is an hyperboloid of revolution about the common axis of the discs. (II.) The amount of flux received from a radiating disc by the walls of a cylinder infinitely long in one direction is found.

A simple method of testing diode valves for passing no reverse current at voltages up to 20,000 is described. The anode of a standard valve, known to pass no reverse current, is connected to that of the valve under test, and the filaments are joined to the terminals of a high-tension alternating voltage supply. A low-reading electrostatic voltmeter, with parallel condenser, is arranged to indicate if the valve under examination passes reverse current.

A description of a method of using a diode valve to measure the decrement of a highly damped oscillation is given. This consists in arranging the valve connections of the circuit so that the first positive peak is obtained. The valve connections are then reversed, and the first negative peak is found. This method is applied to the measurement of the highly damped oscillations which occur after the primary current is broken in a magneto.

The light from the photophone transmitter described by the author in a previous communication (Vol. XXXI., p. 242) is concentrated on a narrow slit, an image of which is produced by means of an auxiliary lens on a strip of cinematograph film, the slit image being transverse to the film. The variation in intensity of the light when sound waves are received by the instrument are recorded as variations in the density of the film after development. For reproduction of the sounds, light from an illuminated slit is focussed on the film, behind which a selenium cell, connected to a telephone circuit, is placed. As the film moves, the intensity of the light reaching the cell varies in accordance with the density of the film, and the corresponding sound is heard in the telephone.

Two valve-maintained oscillating circuits, one of which is provided with an adjustable subsidiary condenser of small capacity, each cause oscillations in a third resonating circuit. The third circuit has its condenser plates connected through a crystal detector and galvanometer. When the maintained circuits are in unison a very small change in the capacity of the subsidiary condenser causes the galvanometer needle to move through a large angle. The method provides a means of observing small changes of frequency previously studied by the method of beats.

At any given filament voltage or current the principal parameters of a triode are: -

1. The co-ordinates of the mid-point of the straight part of the lumped characteristic.

2. The voltage factor g.

3. The differential coefficient di_a/de_a or h_a.

4. The differential coefficient di_a/de_g or h_g.

Methods of determining these quantities are described.

The audio-frequency oscillations were generated by means of a tuning fork, which was maintained in vibration by a triode valve. The alternating-current voltage from the plate circuit of this valve was applied through a transformer to the plate circuit of a feeble radio-frequency oscillator. The radio-frequency oscillations were in this way separated into alternate semi-period trains of waves. The input energy to amplifier was controlled by a sliding coil inductance. The radiating coil of this was loosely coupled through an auxiliary coil with the oscillating coil of the radio-frequency generator and the receiving coil was connected to the tuned receiving circuit of the amplifier The receiving coil of this inductance was adjusted so that the intensity of the rectified oscillations, as received through the amplifier by the telephone, was the same as that of a standard source of sound of the fork frequency. The latter standard was furnished by applying a small alternating-current voltage from the fork alternator circuit to the receiving telephone. The voltage amplification under these conditions is the ratio of the mutual inductances of the sliding coils (1) without the amplifier and (2) with the amplifier. A method of calibrating the mutual inductance and also methods of eliminating strong radiation are detailed in the Paper.

The measurement of amplification at audible frequencies which is described is a mutual inductance method, the alternating voltage applied between the filament and grid of the first valve being varied by quickly changing the connections to an air-core transformer having two secondaries at right angles, which secondaries are capable of rotation so as to give any desired ratio of the mutual inductances between the primary and the respective secondaries. The source of alternating voltage is a triode circuit having such capacity and inductance in the oscillatory portion as to give currents of a sonic frequency. The standard intensity of note is such as to enable signals to be read with comfort, and is obtained by adjustment of the source of alternating current. The first note is obtained when the telephone is in the anode circuit of an auxiliary valve, and the second when the telephone is transferred to the anode circuit of the last valve of the amplifying set, changes also being made in the applied alternating voltage, and in the connections between the valve circuits. All of these changes are brought about by a six-brush switch in a fraction of a second, so that readings are quickly obtained.

The method is compared with a modification of the shunted telephone method, and very good agreement is obtained when the amplifying values are comparatively low. For values of a high order such as 200, it is shown that the two methods are not likely to give the same results, the method described in the Paper being the better one.

In the measurement of amplification of a radio-frequency amplifier an undamped train of oscillations is broken up into groups of sonic frequency by shunting intermittently the condenser in the oscillatory circuit by an inductance of low resistance. A sonic train of oscillations is thus produced.

The receiving circuit is very similar to that used for audible frequency amplification, but the measurement of the amplifying power is made by quickly varying the current at the source, and not by a change of mutual inductance, between the two circuits.

The Paper is an investigation of the possible deviation of the light from a star near the sun due to the temperature changes in the atmosphere produced by the passage of the moon's shadow across the earth during an eclipse. It is shown that while the actual displacements from this cause vary widely for slight differences in the assumed conditions, they are always negligibly small compared with the effects observed at the last solar eclipse.

In calculating functions from Taylor expansions or otherwise, the results obtained by summing any finite number of terms will differ to a greater or less extent from the true results. It is shown in the Paper that by suitable modifications of the coefficients the results obtained, even when comparatively few terms of the expansion are taken, can be made to approximate very closely to the true results for all values of the variable between selected limits.

In the Paper tests on cylindrical bars of magnet steel 1 in. diameter and 10 in. long are described. The tests were conducted using a slight modification of Ewing's double permeameter method. Instead of employing pinching screws in the yokes, the bars and yokes were ground accurately to 1/1,000th in., and arranged to make a good push fit. The method is compared with that in which use is made of differential coils for measuring the value of the magnetising force in situ, as developed at the National Physical Laboratory. It is shown that tests with the latter method can be conducted more speedily and accurately than with the double permeameter method. The variation in the magnetising force along the bar and the leakage between the pairs of bars in the permeameter is treated. A formula is developed, by means of which, with the aid of experimental data given in the Paper, a correction can be applied to allow for leakage effects. A B-H curve and hysteresis loop are given for a certain sample of magnet steel; also the details of the permeameter.

The present Paper arises out of two previous Papers by the author on the pressure of light ("Proc." Phys. Soc., XXV., p. 324, 1913, and XXVIII., p. 259, 1916), and consists of an experimental investigation of the nature of certain peculiar movements of strips of thin metal foil surrounded by rarefied gases, and exposed to radiation. The experiments deal chiefly with phenomena at gas pressures below 1 cm. of mercury, and it is shown that the apparently diverse results obtained can be connected by a theory based on the work of a previous Paper ("Proc." Phys. Soc., XXXI., p. 278, 1919).

The author concludes that, at the highest rarefactions, the pressures on the strips arise from the fact that, if differences of temperature exist in an enclosure, the pressure of the gas is not uniform, but varies approximately as the square root of the latter's absolute temperature. The simple conditions that exist at low gas pressures are complicated, at the higher pressures, by gas currents which differ fundamentally from convection currents, but which are closely connected with the phenomena of thermal transpiration.

The Paper describes a method of showing that absorption of nitrogen takes place in the discharge tube when sodium and potassium are used as the electrodes. The amount of gas absorbed for different quantities of electricity passing in the circuit is measured and is less than that absorbed by the sodium-potassium alloy. It shows also that when the alloy is used the amount of gas absorbed increases with temperature.

The instrument consists of two fine platinum wires mounted close together, and forming two of the arms of a Wheatstone bridge. These are heated by the current in the bridge. When a stream of gas moves in a direction perpendicular to the wires but parallel to the plane containing them, the leading wire is cooled, while the second wire, being shielded by the first, is not cooled as much, and may actually be heated on account of the air flowing past it being warmed by the first wire. A deflection of the galvanometer is obtained, therefore, which is reversed if the flow of gas is in the reverse direction. For low rates of flow of gas, the instrument is much more sensitive than the non-directional hot-wire anemometer. An explanation of the increased sensitivity is advanced.

Previous Micro-balances. - Brief reference is made to the instruments of Angström, Salvioni, Nernst, and especially to the all-quartz balance of Steele and Grant.

The Author's Micro-balance. - The instrument devised by the author, and here described, is also wholly of quartz. The knife-edge support is, however, replaced by a suspension consisting of a pair of quartz fibres. A magnetic arrestment is employed. Balance is obtained either (a) by an "air-weight," the upward displacement on a bulb being varied by varying the gas pressure within the enclosing case; or (b) by a "magnetic weight," involving the use of a measured electric current. The range of weighings depends on the size of beam: with one 5 cm. in length the maximum load is between 100 and 200 mg., and the setting can be made to within 10^-7 mg.

The Stromberg Suspension. - Improvements in the construction devised by Dr. Stromberg are described, which obviate the formidable difficulties of manipulation that have hitherto discouraged workers from employing the instrument.

Investigations with the fibre-suspended Micro-balance. - A brief description is given of the following researches already carried out: - (1) The influence of temperature upon weight. This is an an extension of the work of Poynting and Phillips on this subject; (2) the volatility of silica; and (3) the susceptibility of diamagnetic bodies.

It is proposed to conduct investigations on the pressure of light, on the measurement of absolute temperature (based on an equation of Knudsen's), and on the loss of mass accompanying loss of energy.

The Paper gives a short account of a theory of the Crookes Radiometer worked out by Sutherland in 1896, but unfortunately since much neglected. The theory as it stands will not explain many radiometric phenomena, but it is shown that when modifications, depending on the modern knowledge of thermal surface conditions, are made, such explanations become possible.

Radiometer action, especially at the higher gas pressures, would appear to depend essentially on the formation of gas currents near the radiometer vane. These currents are distinct from convection currents, but are closely connected with the phenomena of thermal transpiration.

The present work is the natural outcome of previous work by the author (Proc. Phys. Soc., Vol. XXXII.).

Measurements are described of the hysteresis-losses in silicon iron sheet and wires in very low alternating magnetic fields at low and telephonic frequencies using an alternating current method described in a former Paper. The equations giving the hysteresis losses as a function of B_max are deduced in the case of the sheet material at low frequencies for ranges of H_max from 0.0002 to 0.02.

Comparisons are made between sheet material and wires of different diameters, and curves are given showing the great improvement in the permeability of wires when they are annealed.

The behaviour of the material is studied, both by ballistic tests and at telephonic frequencies, as regards the alternating field when direct current fields of various values are applied at the same time.

Equations for tracing rays in an axial plane through an optical system have the normal refraction terms separated from those representing aberrations. By expressing the latter as a fraction with the first order aberration as the numerator and a correcting factor, which may take various forms, as the denominator, rays may be traced exactly through the system using a short table of cosines in terms of sines in place of the extensive tables, giving sines in terms of angles generally employed. A considerable saving of time is effected in the calculations, and the estimation, without calculation, of the aberrations of other rays is facilitated.

The hot-wire inclinometer consists essentially of two fine platinum wires (diameter about 0.1 mm.) mounted parallel to one another in a closed chamber at a distance apart equal to about 1 mm. A constant current of from 0.4 to 1.5 ampere (according to the sensitivity desired) is maintained in the wires, which constitute two of the arms of a Wheatstone bridge arranged so that the bridge is balanced in the zero position of the inclinometer. If desired, the bridge may be constituted of two pairs of heated wires as above. The inclinometer wires, in the zero position, may be either vertical or horizontal or inclined at any angle to the horizontal. The indications of the instrument are dependent upon the relative heating or cooling effects experienced by the respective wires when the orientation of the wires with regard to a hozontal plane is altered. The galvanoter deflection occurring with alteration in such orientation serves to indicate the inclination of a definitive radius vector to the horizontal, and calibration curves are given for the cases where the axis of rotation is horizontal, and (a) in the plane of the wires and paralel to the wires, and (b) at right angles to the plane of the wires. The characteristics of the calibration curves are discussed and curves are given showing how the resistances of the respective wires depend upon the orientation of the wires with regard to the horizontal plane referred to. Attention is directed to the finite width of the column of heated gas ascending from the wires, and an empirical formula is deduced expressing the maximum deflection as a function of the bridge current employed.

The method, which was devised to overcome the difficulty of making satisfactory soldered joints between the elements of thermopiles having a large number of closely packed junctions, consists in using a continuous wire of one of the elements and coating those parts of it which have to form the other element with an electrolytic deposit of another metal. If the conductivity of the latter is considerably greater than of the former, and a fairly thick sheath is deposited, a thermo-couple is produced which is not appreciably impaired in efficiency by the short-circuiting effect of the core. Constantan wires coated with either copper or silver sheaths were found to be suitable for most purposes.

The Paper discusses the relative merits of short and long mercury arcs for this work, and points out that the defect of the former is due to the broadening of the spectrum lines consequent on the high vapour pressure within the lamp. It is shown that by attaching a condensing bulb to the lamp, so as to prevent excessive rise of vapour pressure, the short lamp can be made practically as good as the long one as regards sharpness of lines, while still being of much greater intrinsic brightness.

This Paper gives a mathematical analysis of the arrangement, previously described by Eccles, whereby the vibrations of a tuning fork are maintained by means of a triode.

In the simplest case, the prongs of the fork vibrate in the field of a permanent magnet, on the pole-pieces of which are wound coils connected in the grid and anode circuits of the valve respectively. From a consideration of the energy relations of the system, it is shown that for the maintenance of oscillations (a) the grid and anode coils must be wound in opposite directions, (b) there is a certain minimum value of the slope of the grid voltage-anode current characteristic of the valve at its working point.

Following this, the case in which condensers are connected across the two coils is treated on the principle of replacing the dynamical system by its electrical equivalent. In the particular example of similar anode and grid circuits, this system gives rise to three possible oscillations, one with the coils similarly wound and two with the coils oppositely wound. The conditions for maintenance are worked out, and the variation of the obtained frequency in the neighbourhood of the natural frequencies of both the dynamical and electrical systems is illustrated diagrammatically.

Finally, the case in which only one condenser is used is analysed, and a table is given showing the condition of maintenance and the oscillating frequency in the three typical examples.

The relative and absolute amounts of radiation and convection from surfaces heated to about 100°C. in air were measured as follows: steam was passed through the cylinders or spheres, the surface temperature being measured by a thermo-junction. The total amount of heat lost from the surface was determined from the equivalent mass of steam condensed. This was done with the surface (a) "bright," (b) "dead-black." The relative amounts of radiation alone from these two surfaces were then found with the aid of a thermopile. If h₁ is the total heat lost, and r₁ the radiation, per square centimetre per second per 1°C. excess of temperature for the "black" surface; h₂ and r₂ corresponding quantities for the "bright" surface; and c the convection in each case, then if h₁=ah₂, r=br₂, r₂/h₂ = (a - 1)/(b - 1), r₁/h₁ = b(a - 1)/a(b - 1).

The numerical values of the radiation, convection and total heat are then easily calculable, and are given in tables. It is found that the amount of convection per square centimetre is inversely proportional to the square root of the diameter of a cylinder, and to the cube root of the diameter of a sphere.

The Paper consists of an application of the "Principle of Similitude" (Ravleigh, "Nature," Vol. 95, p 66, 1915) to the loss of heat from hot wires, thermometer bulbs, &c. An equation is obtained which dces not involve the dimensions of the bodies and which agrees with the formulæ of King for fine wires and of Hill for thermometer bulbs.