Table of contents

The Paper describes work carried out in the laboratory of Prof. Du Bois on the relation between the intensity of magnetisation of various ferro-magnetic materials and the rotation of the plane of polarisation of plane polarised light reflected from a polished surface of the material. The specimens, in the form of circular discs 5 mm. in diameter and 0.5 mm. thick, were soldered to one of the pole pieces of a large electromagnet. Through an aperture in the other pole, monochromatic light, polarised in two nearly coincident planes by means of a Lippich polariser, was incident almost normally on the polished surface of the specimen. The reflected beam passed through an analyser, the rotation of which could be measured, by means of an auxiliary optical system, to a high degree of accuracy.

In the first part of the Paper results are given for a number of materials of known magnetic properties in order to establish the validity of the method, due to Du Bois, of obtaining the value of the saturation intensity from the curve connecting field strength with rotation. The method is then applied to materials of unknown properties. The variation of the Kerr constant with the wavelength of the light was also determined for a number of substances.

The Paper contains the results of the experiments described by the author in Proc. Phys. Soc. Lond., XXI., p. 374, 1908; XXIV., p. 40, 1911; and XXVII., p. 56, 1914, collected and recalculated in accordance with a theoretical correction recently communicated by Dr. Griffiths (Proc. Phys. Soc., XXVIII., p. 255, 1916).

It is found that in the solutions employed the correction is not considerable, except in the case of the strongest: olutions of KCl (2.7 normal), where it amounts to 6 per cent.

The Paper contains the corrected theory of the method, and the value of the coefficient of diffusion is tabulated at different limiting concentrations and at various temperatures; it concludes with a new method of calculating the coefficient at a definite concentration from the experimental results, which appears to be more accurate and free from questionable assumptions than previous calculations of a similar nature.

One of the authors has for some time been investigating the possibility of using base metal thermocouples at temperatures above the melting point of one of the constituents. For this purpose it was necessary to determine whether any peculiarities in the thermo-electric behaviour of metals occur at fusion. In the case of lead, tin, zinc and cadmium there is no perceptible break in the continuity of the curves obtained. In couples containing bismuth, however, several cases were noted in which the E.M.F. remained constant for a wide range of temperature after the fusion of the bismuth. This occurs with silver, aluminium, iron or nichrom as the other element. Useful applications of this property are discussed. No attempt was made to construct a thermo-electric diagram from the results, as it would be impossible to obtain correct values of dE/dt at all parts of the curves, many of which show small flexures, without making more accurate measurements in the region of such flexures than was practicable.

The Paper describes a further development of the work done by the author and Mr. Takamine on the distribution of the satellites of the mercury lines. The apparatus employed was a Fabry-Perot interferometer crossed with an echelon or Lummer-Gehreke plate. An account of the theory governing the interpretation of crossed spectra is given.

It is shown that much of the discord between the results of various observers of these satellites is due to the unsatisfactory nature of the principal line as a datum from which to define their positions, and that if the distances be measured from one of the distinct satellites, good agreement is obtained.

If these separations be expressed as differences of wave-number, instead of wave-length, a remarkable symmetry in their distribution becomes apparent. For example, among the satellites of the green line, 5,461, can be found three groups of symmetrical triplets, of which the wave-number differences are in the simple ratios 1: 3: 12.

Similar results are obtained for other lines, the principal component of λ4,359 being shown for the first time to consist of a triplet, of which the middle component is relatively weak.

A similarity in the distribution of the satellites exists for all the lines examined, and certain wave-number intervals are common to all.

It is observed that the intervals given by lc/3, mc/4, and nc/5, where c=0.71, and l, m, and n are whole numbers, are found among the satellites of the eight lines quoted for l=1 to 4, m=1 to 7, and n=1 to 7.

The possible origin of satellites is discussed in the light of the Zeeman and Stark effects, the magnetic or electric fields being electronic in origin, and many of the results are shown to be consistent with Voigt's theory of the vibrations of electrons in an isotropic, quasi elastic, electric field. The suggested explanations can only be tentative as yet, pending further development of our knowledge of the theory of the Zeeman effect, and the extension of Sir J. J. Thomson's work on positive rays to a larger number of substances.

The second part of the Paper consists of a mathematical investigation of terms of correction in the theory of large sized concave gratings, which prevent the theoretical resolving power from being realised in practice.

The principal feature of the author's arrangement is the employment of a "slave" clock to do the great part of the work, leaving the master pendulum no function beyond that of controlling the rate of the other. The master pendulum swings freely except for a short period (about one-fifth of a second) every minute, during which it receives an impulse from a small falling wheel electromagnetically released by the slave clock. At the end of its fall the impulse mechanism closes a second circuit and is restored to its initial position. These two electric circuits also energise parts of the mechanism in the slave clock by which the latter is kept in time with the master pendulum. The lagging of correction behind error, with the resulting periodic fluctuation in the rate, is reduced almost to the vanishing point by the introduction of a "negative backlash" in the control mechanism.

The Paper contains a mathematical discuss on of the best working conditions and of the possible magnitude of errors which might arise from various causes.

The author discusses the probable influence of moisture in the atmosphere on the refraction of electromagnetic waves round the earth's surface. The conclusion of Kiebitz that the presence of moisture does not affect the dielectric constant by more than 10 per cent. is shown to be erroneous, being based on the assumption that the Clausius-Mossoti formula, k-1 / k+2 · 1/d=constant, holds when passing from the liquid to the gaseous state. Examples are quoted to show that this law fails in many cases, especially where the dielectric constant is high in the liquid state.

In the absence of more accurate data for ordinary temperatures, the author prefers to assume a value for the dielectric constant of water vapour obtained by extrapolating the results obtained by Baedeker for higher temperatures. The extrapolated value is almost certainly too low.

From this result, and the average conditions of the atmosphere over the ocean with regard to temperature gradient, &c., deduced from meteorological data, it is shown that the lowest layers of the atmosphere (1,000 to 1,500 metres approximately in depth) refract electromagnetic waves towards the earth, so that the greater part of the space waves will reach the receiver, contrary to the conclusion of Kiebitz.

In the calculation of the coefficient of diffusion, by B W Clack, a simple relation is assumed between the density of a solution of a salt and the concentration. This simple relation is only approximately correct, and compromises are made which require justification.

This note -

1. Suggests a method of calculating the coefficient of diffusion which, to a high degree of theoretical accuracy, gives values for the coefficient which are independent of a precise relationship between density and concentration; and

2. Justifies the method of calculation adopted by B W Clack.

In the Philosophical "Transactions" of the Royal Society, Vol. CCXVI., pp. 349 to 392, there is a Paper by one of the authors dealing with the possible existence of a temperature coefficient of the constant of gravitation. It was suggested in the discussion that the effect might be due to an inward displacement of the large lead spheres, at the higher temperatures, due to convection currents.

In the present Paper experiments are described in which this point is tested by micrometric measurements of the positions of the supporting wires. It is shown that, at the higher temperatures, there is a small outward displacement of the spheres, probably due to the expansion of the crosshead from which they are suspended. A slightly higher value has, therefore, to be given to the temperature coefficient of gravitation.

In experiments on the Newtonian Constant ("Phil. Trans.," May, 1916) the author used a torsion balance in a vacuum which varied in different cases from 15 mm. to 0.00001 mm. pressure. Before sealing the vessel the pressure was determined by a McLeod gauge. Values of the pressure after sealing off were deduced, in the case of the higher vacua, from observations of the damping of the torsion system.

The formula employed is due to the late Prof. Poynting, and can be expressed in the form P = 35.6(I/saT)λ where I=moment of inertia of suspended system, s=area of surface (supposed plane) which is experiencing the resistance, a=mean distance of plane from centre of rotation, T=period of oscillation, and λ=the observed logarithmic decrement.

A table and curve are given showing the relation between P and λ.

The apparatus consists essentially of a very simple concave grating spectroscope, of which the slit and grating are situated at opposite diameters of a circle, the spectrum being formed on the arc of this circle. Two independent arms carry fittings on which may be placed either telescope eyepieces or small electric lamps. With the slit of the instrument illuminated by a suitable source, the eyepieces can be set so that any two desired wave-lengths are in the centres of their respective fields of view. The eyepieces are then replaced by the small lamps (the filaments coinciding with the previous positions of the crosslines), and the grating is observed with a small telescope pointed towards the widened slit: the whole of its surface is seen to be illuminated with a mixture of the two colours on which the eyepieces were originally set.

The "concave grating" employed consists of a Thorpe replica of a Rowland plane grating of 14,475 lines to the inch, mounted with its ruled surface in contact with the surface of a concave mirror of 4 ft. focal length. This forms an admirable substitute for the more expensive concave grating.

The author prefers to state results in terms of the number of oscillations per unit of time.

Observations showed that the smallest change of wave-length which could be recognised by the eye as a change of colour was greater than that which corresponded to a change of period of 10¹² vibrations per second, or to a change of one vibration more or less in 1/10¹² second.

The Paper explains a simple method of arriving at the general differential equation for wave motion. A wave motion consists in the propagation of some form of strain through an elastic dense medium or one having comparable qualities. Corresponding to this strain there is an analogous stress in the medium, and we can express this stress mathematically in two ways, kinetically, as the product of the density, and the time rate of change of the strain, or by md²ϕ/dt² per unit of volume, and also statically as the space increment of the expression edϕ/dr where e is a coefficient of elasticity and r is a vector denoting direction of propagation.

In the experiments carried out, the wire to be tested was fixed at each end between the jaws of screw clamps joined to brass cylinders, through which water could be circulated. Attached to one clamp was a rod passing through a framework, enabling tension to be applied by a nut working on a thread.

Heat was supplied to the centre of the wire by passing a current of electricity through a manganin coil wound on the wire, and the temperature difference between two points on the same side of the centre was ascertained by two platinum coils, also wound on the wire.

The resistances of the coils were determined by means of a Calendar-Griffiths bridge, enabling a temperature difference of 0.01°C. to be read, and making it possible to detect a difference in conductivity of 0.05 per cent. If R₁ is the resistance of the platinum thermometer nearer the heating coil, and r₁ is that of the other platinum coil when both are at the jacket temperature; and if R₂ and r₂ are corresponding values when a temperature difference exists, then it may be shown that the conductivity K is proportional to (R₂/R₁ - r₂/r₁)^-1.

For all the wires used (copper, steel, nickel, aluminium, brass, zinc), stretching produced a slight increase in thermal conductivity. The most satisfactory experiments showed an increase of about 0.5 per cent. for a tension of about 0.7 of the elastic limit.

After the tension was withdrawn the conductivity returned approximately to its original value.

1. To re-state and add further evidence in favour of an electrical theory of cohesion.

2. To provide tentative empirical formulae for the expression of inter-molecular forces.

The author defines cohesion as the net attraction (i.e., balance of attraction over repulsion) between molecules which are relatively chemicaly saturated, at distances not greatly exceeding the molecular diameters, and the following formula is proposed for this attraction: t₂ = Gm²/a^{(2 + 4d₀/d)} where G is the Newtonian constant of gravitation, m the molecular mass, d the molecular interval (centre to centre), and d₀ is the molecular diameter.

The Paper contains the results of measurements made on various samples of radium luminous compound during the last two years. Determinations of the brightness of the compound in powder form and when made up into paint, and also after the application of the paint to instrument dials, were carried out; and curves are given showing the rates of decay of luminosity. The radium contents of the compounds were determined by comparison of their γ-ray activities with that of a preparation of pure radium bromide, which is periodically compared with the British radium standard. The various precautions which have to be observed, and the corrections which have to be applied in making the various determinations are explained, and the considerations which should govern the proportion of radium employed for practical purposes are discussed.

The investigation is carried out on the assumptions that the freepaths of the particles of the gas are long compared with the dimensions of the moving body, and that the motion relative to the body of the particles which rebound from it depends only on its temperature. It is shown that if v, w be the components of velocity perpendicular to the surface of a lamina and parallel thereto the corresponding components of the resistance are (4 + π)(3/2π)^1/2(v/V)p and 3(2/3π)^1/2(w/V)p where V is the standard (root-mean-square) speed of the gas-particles and p is the gas-pressure.

The resistance to the motion of a cylinder or a sphere is found to differ very slightly from the resistance to a lamina occupying the central section. The formulae are applicable to the problem of the damping of the oscillations of a system suspended in a rarefied gas.

The Paper describes a method of avoiding the troublesome double adjustment required in Maxwell's method of comparing inductances. A current detector, whose deflections depend on the component of the current in quadrature with the E.M.F., is employed, which makes it possible to arrange that the condition for no deflection depends chiefly either on the inductances or resistances. In series with the bridge is placed either a non-inductive resistance or a capacity. In the first case the balance depends chiefly on the inductances, and in the second case on the resistances. A few alternate repetitions of the two adjustments suffice to balance the bridge, both for resistances and inductances. As detector a sensitive moving coil galvanometer in conjunction with a commutator, or a Sumpner electrodynamometer, may be employed; the latter proved more satisfactory.

The Paper consists of a mathematical treatment of the subject, the following being some of the conclusions arrived at: The radiation resistance of a loaded antenna, and also the radiation from the antenna, are dependent not only on the wave-length, but on the current values at the top and bottom. The radiation cannot, therefore, be written Σ = AT²l² / λ² where A is constant and T is the R.M.S. current at the base, as is done in most textbooks. Rüdenberg's formula for flat-top or umbrella antennae is valid only for very long wave-lengths, with a capacity at the top of the antenna very large compared with that of the vertical part, and Austin's table of radiation resistances up to ratios of l / λ = 0.4 is based on an unjustifiable extrapolation of Rüdenberg's results.

The Paper also treats of the directions in which the energy is most strongly radiated under different conditions.

The absence of coma from an optical system free from spherical aberration can be established by means of the sine condition, from the refraction of rays which originate at the centre of the object. In actual systems spherical aberration is always present to some extent, and the conditions which have to be secured in practical cases do not involve mathematical freedom from spherical aberration and coma, but rather their confinement within predetermined limits. Previous investigations on this subject have been published by Conrady and by Chalmers; the present Paper shows that the conclusions of both require some qualification. Conrady's conclusion, that the sine ratio for any zone gives the exact magnification, holds only for rays in a secondary plane, and one of the further conditions (a) that the zone is free from spherical aberration, or (b) that the stop is at the principal focus for rays travelling in the negative direction, must also be satisfied. Under these conditions the magnification for rays in a primary plane is (1 + tan θ' d/dθ') times that for the secondary rays, where 2θ' is the angle subtended by the zone at the centre of the image. The conditions assumed by Chalmers involve the satisfaction of a relation between various quantities, including the curvature and astigmatism of the system; his results may in consequence not apply strictly where very large apertures are involved. Analysis of the general problem shows that the primary and secondary comatic displacements can be accurately derived from the properties of thin oblique pencils of rays. If a central incident ray inclined at θ to the axis is met by an oblique ray in the same axial plane at a distance r from its point of origin, and is refracted at an angle θ' with the axis and meets the image plane at a distance r' from the image of its intersection with the oblique ray, the primary comatic displacement of the oblique ray plus the aberrationless first order displacement is proportional to r' sec θ'/sr sec θ, where μs/μ' is the magnification in a primary plane for a small normal object at the point of intersection of the two rays. The corresponding secondary displacement is ρ'/σρ, where the Greek letters have the same meaning for secondary rays as the corresponding Roman letters for primary rays. These two quantities determine the coma exactly whatever the spherical aberration may be. It follows that coma is dependent upon the principal surfaces of a lens. When the object is at infinity the coma is determined by the locus of the point of intersection of a ray, incident parallel to the axis, with its refracted portion.

The results established in the Paper form one of a series of reciprocal relations which exist between the aberrations of an object and those of the effective stop.

The Paper describes various parallax effects observable when objects illuminated by light of different colours are seen through a "pinhole" of smaller diameter than the pupil of the eye. The effects are due to the well-known chromatic aberration of the eye; and it is shown that in most optical instruments of precision the necessary conditions for parallax of this nature are present when observations are made in the blue and violet; and that this results in a serious diminution of the accuracy of such measurements. Several methods of obviating the difficulty are described.