Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1944"
TL;DR: In this paper, a combinatory formula for the number of ways of arranging a mixture of any number of kinds of molecules on a lattice, the values of N i and X ij being specified, where N i denotes the number number of molecules of type i, z denotes the numbers of sites which are neighbours of one site, and zX ij denotes the pairs of neighbouring sites occupied one by a molecule of type n and the other by a molecular type j. Each molecule of n is assumed to occupy r i sites, where r i is any integer with different
Abstract: A combinatory formula is obtained for g ( N i , X ij ), the number of ways of arranging a mixture of any number of kinds of molecules on a lattice, the values of N i and X ij being specified, where N i denotes the number of molecules of type i, z denotes the number of sites which are neighbours of one site, and zX ij denotes the number of pairs of neighbouring sites occupied one by a molecule of type i . the other by a molecule of type j . Each molecule of type i is assumed to occupy r i sites, where r i is any integer with different values for different types of molecules. This formula is used to derive the thermodynamic properties of mixtures of molecules occupying various numbers of sites, assuming that the intermolecular energy can be regarded as a sum of terms, each pair of neighbours contributing one term. For binary mixtures the formulae obtained are very similar to those previously obtained for ‘regular’ solutions where each molecule occupies one site. A rather simple formula is obtained for the critical temperature and the composition of the critical mixture. The degree of accuracy of the treatment is the same as Chang’s use of Bethe’s first approximation and as the ‘quasi-chemical’ method of approach. A brief investigation of a higher approximation for a binary regular mixture on a close-packed lattice indicates that the errors due to the approximation used are unlikely ever to be serious.
224 citations
TL;DR: In this article, the authors adopt the shortened vector and matrix notation introduced by Aitken (I) to evaluate the effect of selection on the means, variances and covariances of a multivariate population.
Abstract: It is a well-known fact that Karl Pearson's formulae expressing the effect of selection on the means, variances and covariances of a multivariate population hold when the variates are such as to be normally distributed both before and after selection. It is not, however, generally known that the formulae are true under much more general conditions, and in view of a recent controversy it has been thought desirable to establish precisely what these conditions are. In dealing with the problem we shall adopt the shortened vector and matrix notation introduced by Aitken (I). This notation is reproduced below with but slight modifications.
218 citations
TL;DR: In this article, a method is developed which makes it possible to determine the exponents m and n in the force law for a given element from measurements of the sublimation energy, the compressibility, the thermal expansion coefficient, and the dependence of these quantities on pressure and temperature.
Abstract: The problem of the thermodynamics of crystal lattices has been treated by rigorous methods recently in a series of papers by Born and collaborators. In particular, Bradburn succeeded in deriving the equation of state for a solid cubic crystal, consisting of identical atoms, under the assumption that the mutual potential energy of a pair of atoms satisfies a law of the form $\phi $ = - ar$^{-m}$ + br$^{-n}$. In the present paper a method is developed which makes it possible to determine the exponents m and n in the force law for a given element from measurements of the sublimation energy, the compressibility, the thermal expansion coefficient, and the dependence of these quantities on pressure and temperature. The method is applied to a large number of elements, and it is shown that the compression and the thermal expansion of these substances, as predicted by the theory, are in satisfactory agreement with the measured values of these quantities up to very high pressure and up to temperatures near the melting-point. The question whether melting is caused by the mechanical instability of the lattice is also investigated, and a certain rule connecting the two phenomena is found which is closely related to Lindemann's law.
77 citations
TL;DR: In this paper, it was shown that lattice sums may in general be replaced by the corresponding infinite series, and that the distribution of frequencies follows with sufficient accuracy Born's law for cyclic crystals.
Abstract: In the physical theory of crystals great formal difficulties are encountered when the exact shape of the crystal is to be taken into account Certain methods of approximation have therefore been developed and successfully used by several authors However, as the validity of these methods was recently questioned by Sir C V Raman, a more rigorous examination of the problem had to be undertaken It is found that the old procedure is fully justified provided the number of boundary particles is small compared with the total number of particles in the crystal In particular, it is shown that lattice sums may in general be replaced by the corresponding infinite series, and that the distribution of frequencies follows with sufficient accuracy Born's law for cyclic crystals Upper bounds are obtained for the errors caused by these approximations
65 citations
TL;DR: In this article, the frictional behavior between mild steel surfaces lubricated with solutions in white oil of long-chain halides, acids, α-substituted acids, esters, cyanide, thiocyanate and a nitro derivative has been investigated under high loads at low speeds.
Abstract: The frictional behaviour between mild steel surfaces lubricated with solutions in white oil of long-chain halides, acids, $\alpha $-substituted acids, esters, cyanide, thiocyanate and a nitro derivative has been investigated under high loads at low speeds. In all cases a transition from smooth sliding to stick-slips occurs at a temperature characteristic of the particular solution employed. For each substance the transition temperature increases with the concentration. Each solution builds up, and is in equilibrium with, an adsorbed and oriented film of the polar compound on the surface. Assuming that the transition occurs when the surface concentration of this film decreases to a certain value which, for any one material is independent of temperature, an equation has been deduced relating the concentration, and transition temperature with the heat of adsorption U. All the experimental results are in good agreement with this equation. The values of U show that these long-chain polar compounds are adsorbed by the interaction of their dipoles with the atoms in the metal surface, and not by any chemical reaction. The results also suggest that the esters are similarly oriented at metal and at aqueous surfaces.
63 citations
TL;DR: An approximate titration equation is developed for the reaction between fibrous proteins and acids, in which account is taken of the valency and intrinsic affinities of the acid anions, and of the limited number of adsorption sites available for anions.
Abstract: An approximate titration equation is developed for the reaction between fibrous proteins and acids, in which account is taken of the valency and intrinsic affinities of the acid anions, and of the limited number of adsorption sites available for anions. The transition from soluble to fibrous proteins is traced in order to demonstrate that the main difference between the titration curves of the two types of protein arises from the difference in potential developed during the adsorption of protons.
62 citations
TL;DR: In this paper, it was shown that if a factorial analysis is performed on a set of tests of unequal difficulty, using the matrix of variances and covariances, a spurious factor will tend to be introduced depending mainly on the differences in difficulty.
Abstract: 6. The expected score of an individual on a test consisting of a large number of items is assumed to be given by a formula involving the ability of the individual and also two quantities constant for the test. An expression is then derived for the covariance between two tests measuring different abilities. It appears that if a factorial analysis is performed on a set of tests of unequal difficulty, using the matrix of variances and covariances, a spurious factor will tend to be introduced depending mainly on the differences in difficulty. The effect of this is removed by transforming the variances and covariances to a new set of coefficients. A numerical example of the process is given.In conclusion I should like to thank the Carnegie Trust for the Universities of Scotland for a grant to cover the cost of the setting and printing of mathematical formulae in a paper previously published in the Society's Proceedings (LXI, A, 1943, 273–287).
52 citations
TL;DR: In this article, it was shown that the intensities are modified in a systematic way by extinction, and that, after introducing a correction for extinction, the theory advanced can account for all the data.
Abstract: In a previous paper it was shown that X-ray evidence led to the conclusion that a series of intermediate structures is formed during the dissociation of the alloy Cu 4 FeNi 3 . Attempts to determine these structures failed because they led to X-ray intensities that did not agree with those observed, although their positions were adequately accounted for. In the present paper it is shown that the intensities are modified in a systematic way by extinction, and that, after introducing a correction for extinction, the theory advanced can account for all the data. In the type of structure postulated there is a periodic variation of the lattice parameter. Concentration differences are set up in the alloy at regular intervals, while the coherence of the single-phase lattice remains. The wave-length of the periodicity is of the order of 10 -6 cm. On prolonged annealing at constant temperature the diffraction pattern changes gradually. It is possible to follow the wave-length and the amplitude of the periodic variation as a function of time and temperature over a considerable interval. It has been found that the amplitude is independent of time at a given temperature and that the wave-length increases linearly with the logarithm of time. The values of wave-length and amplitude as a function of time and temperature are reproducible within the limit of error, so that the measurements have a quantitative value. After longer times of annealing the diffraction pattern of t-he periodic state gradually changes into another pattern, which can be explained either by a periodic structure with a range of longer periods or by tetragonal lamellae. The bearing of the present observations on the -kinetics of phase change is discussed.
44 citations
TL;DR: In this article, the glow-arc transition theory of the first leader stroke of a lightning flash is further considered, and shown to be in accord with all the observations available, whereas the recombination theory is not considered.
Abstract: The glow-arc transition theory of the first leader stroke of a lightning flash is further considered, and shown to be in accord with all the observations available, whereas the recombination theory is not considered to be. The greatly reduced potentials already indicated to be adequate to cause flashes, of the order of only 1 % of those required in a homogeneous field, and the corona currents from the leader stroke channel, are confirmed by a discussion of the records of the currents in, and electrostatic field changes caused by, the first leader, which further indicates that formulae derived from laboratory studies of corona currents from wires and from pointed conductors can be extrapolated to lightning voltages, i.e. over a range of about 1000 to 1.
35 citations
TL;DR: In this paper, the contribution of particular groups in the dye molecules to the free energy of adsorption is determined, and the influence of the valency of the dye ion is related to the potential on the protein fibre.
Abstract: Equations developed previously for the titration of fibrous proteins with acids are shown to accord with extant data for the adsorption of dyes in the presence of salt. The contribution of particular groups in the dye molecules to the free energy of adsorption is determined, and the influence of the valency of the dye ion is related to the potential on the protein fibre. The effect of temperature on the ionic equilibria is calculated, and estimated experimentally for a simple dye using a rapid ‘null’ method for the attainment of equilibrium.
35 citations
TL;DR: In this paper, the rotational and vibrational constants for the singlet electronic states of N$\{2}$ are tabulated, and it is shown that all correspond to transitions to the $\alpha ^{1}\Pi \u}$ upper level of the Lyman-Birge-Hopfield System.
Abstract: Five new systems due to N$\_{2}$ have been observed in a mildly condensed discharge through nitrogen. Rotational analyses of some of the bands have been made, and it is shown that all correspond to transitions to the $\alpha ^{1}\Pi \_{u}$ upper level of the Lyman-Birge-Hopfield System. An additional progression of the system studied by Van der Ziel, here referred to as the Fifth Positive System, has been found, necessitating a revision of the upper vibrational quantum numbers. Some of Kaplan's systems have also been examined, and the rotational analysis of one shows that it corresponds to a transition to the lower level of the Fifth Positive System. This level very probably lies a little below $\alpha ^{1}\Pi \_{u}$ and must therefore be metastable; it may play an important part in the formation of active nitrogen. The rotational and vibrational constants for the singlet electronic states of N$\_{2}$ are tabulated.
TL;DR: The causes and types of continuous spectra emitted by flames are discussed and their importance stressed in this article, where it is shown that the yellow-green continuous spectrum emitted by some flames containing oxides of nitrogen is probably identical with the spectrum of the air afterglow and is therefore due to a reaction between nitric oxide and atomic oxygen.
Abstract: The causes and types of continuous spectra emitted by flames are discussed and their importance stressed. It is shown that the yellow-green continuous spectrum emitted by some flames containing oxides of nitrogen is probably identical with the spectrum of the air after-glow and is therefore due to a reaction between nitric oxide and atomic oxygen. It thus becomes possible to test for the presence of atomic oxygen in a flame by admitting nitric oxide and observing if a yellow-green emission results. For the carbon monoxide flame there appears to be a high concentration of atomic oxygen, both for the dry and moist flame. The combustion mechanism is discussed in detail using this knowledge. For the hydrogen flame a little atomic oxygen is present, but results do not permit of definite conclusions. For hydrocarbon flames there is no sign of atomic oxygen in the inner cone, and this is taken as strong evidence in favour of a peroxidation rather than a hydroxylation mechanism.
TL;DR: In this article, it has been shown that the external applied stress above the yield is no longer balanced primarily by simple displacement of the atoms but also by a new type of secondary internal stress brought about by the process of plastic flow; and that this secondary stress, being of a permanent nature, can be measured by the residual lattice strains exhibited by the lattice after removal of the external stress.
Abstract: In previous work, stress-strain curves for the atomic lattice of certain metals have been obtained from X-ray diffraction measurements of the lattice dimensions of test specimens under tension or compression, and it has been shown that when the external yield stress is exceeded, there is a systematic departure from Hooke’s Law. It is pointed out in the present paper that this departure indicates that the external applied stress above the yield is no longer balanced primarily by simple displacement of the atoms but also by a new type of secondary internal stress brought about by the process of plastic flow; and that this secondary stress, being of a permanent nature, can be measured by the residual lattice strains exhibited by the lattice after removal of the external stress. These residual strains are measured in various directions to the stress direction for mild steel subjected to tension, and it is shown that the lattice after tension exhibits a longitudinal compression and a transverse expansion in the ratio of 2:1, which means that the density of the material is thereby kept constant. Comparisons of X-ray and mechanical measurements further show that the hysteresis loop exhibited by the external stress-strain curve of mild steel after overstrain can disappear and the linear elastic relation be recovered without any corresponding change in the internal stress, which is therefore a more fundamental physical property. It is also shown that when the elastic range is extended by overstrain in tension, there is no symmetrical increase in the elastic range in subsequent compression, thus confirming the existence and direction of the secondary internal stress. Finally, the lattice stress-strain curves are also obtained for a 0.4 % C steel (partially pearlitic) and a 0.8 % C steel (pearlitic), and by comparison with the results on pure iron and 0.1 % C steel (annealed) it is shown that the maximum residual internal strain developed by the lattice increases markedly with the fineness to which the crystallites can be broken down by the plastic deformation.
TL;DR: In this paper, a series of marble pebbles, made experimentally by attrition of rectangular blocks by fragments of hard steel, is compared with natural pebble found in nature.
Abstract: This paper may be regarded as the sequel to an earlier one (Rayleigh 1942) and deals with the formation of artificial pebbles under controlled conditions, and their comparison with the pebbles found in nature. As before, symmetrical pebbles having an approximate figure of revolution are chiefly considered. A series of marble pebbles, made experimentally by attrition of rectangular blocks by fragments of hard steel, is shown in comparison with natural pebbles. The series ranges from cylinders with rounded ends, to an approximately spherical figure, and then on to oblate forms ending in a disk with rounded edges. These are closely matched by a series of natural flint pebbles collected from the glacial gravel. Prolate or oblate spheroids, differing widely from the sphere, are not obtained in experiments of this kind, nor are they found in the gravel formation. An alternative way of making pebbles in the laboratory is by ‘pothole’ action. The experimental pothole is a cylindrical vessel containing water with a paddle revolving coaxially with it. The paddle maintains a vortex, which carries the stone round. Either the bottom or the wall of the vessel may be made of abrasive material. When the bottom is abrasive, the pebbles are of such a shape that they lie inside a spheroid of the same polar and equatorial diameter in contrast to the previous case, where they lie outside. When the sides are abrasive, the form tends to the spherical. This effect appears to depend on the well-known tendency of an elongated body to set itself athwart the stream; thus the end tends to rub against the abrasive wall. Spherical pebbles of considerable perfection can be made in this way. As regards concave pebbles, the discussion in the former paper is withdrawn. A new method of experiment is used, depending on the pitting of a small square of sheet glass, revolved in a box with the abrasive. If many broken flints are used, each comparable in size with the glass, the latter is chiefly pitted in the middle, tending to form a concavity. If a single flint only is used, the pittings on the polished surface are uniformly distributed, and there is no tendency to form a concavity. It would seem, therefore, that concavity is produced by the edges being more protected than the middle, the protection being given by pebbles other than the one which is making the wound at the given moment. This action is apart from the rounding of the edges, which ultimately spreads, invading the concavity and producing a general convexity as in ordinary pebbles.
TL;DR: Inhibition by propylene showed that free radical chains occur in the thermal decomposition of acetone as mentioned in this paper, and the mechanism of the chain processes was compared and contrasted with those occurring in other decomposition reactions.
Abstract: Inhibition by propylene shows that free radical chains occur in the thermal decomposition of acetone. Quantitative investigations permit of conclusions about the mechanism of the chain processes, which are compared and contrasted with those occurring in other decomposition reactions.
TL;DR: In this article, the advantages of using the photographic method of detecting nuclear particles to the study of the scattering of the high-energy beams of particles provided by the cyclotron are discussed.
Abstract: The advantages to be derived from a successful application of the photographic method of detecting nuclear particles to the study of the scattering of the high-energy beams of particles provided by the cyclotron are discussed. The design of a 'camera' for this purpose is described. The most important feature of the method lies in the fact that a single plate, exposed to the scattered particles for a few minutes, contains the information required for a complete examination of the variation of the scattered intensity in the angular range from 10 to 170 degrees with the direction of the primary beam. A very great saving is thus effected in the time the cyclotron is occupied in making such experiments as compared with other methods of detection. The theory of the method is discussed in some detail, and tests of the performance of the instrument are described which demonstrate its reliability. It is shown that the angular resolving power of the method is of the order of $\pm $2 degrees, and that its ability to distinguish different groups of scattered and disintegration particles from range distribution curves is superior to that hitherto achieved with counter and other methods of detection.
TL;DR: The barometer coefficient of penetrating showers was evaluated from an extended series of observations and was found to be B = − 11.7 + 2.7 % per cm as mentioned in this paper.
Abstract: The barometer coefficient of penetrating showers is evaluated from an extended series of observations and is found to be B = — 11.7 + 2.7 % per cm. Hg. The significance of the correlation coefficient is discussed briefly.
TL;DR: In this paper, an iterative method was proposed to determine the supersonic regime for gas flowing irrotationally through a convergent-divergent nozzle, i.e. that (unique) regime in which the pressure and density of the gas decrease continuously in its passage from end to end.
Abstract: An iterative method outlined by Green & Southwell (1944), but not applied in their paper for the reason that it makes no use of 'relaxation methods', is here applied to determine the supersonic regime for gas flowing irrotationally through a convergent-divergent nozzle, i.e. that (unique) regime in which the pressure and density of the gas decrease continuously in its passage from end to end. Osborne Reynolds's approximate treatment of the problem (1886) assumed the velocity to be distributed uniformly over each cross-section, and in consequence found a unique value for the limiting mass-flow, whether the velocity be subsonic or supersonic downstream of the 'throat' (upstream it is always subsonic). Here, a more exact treatment shows that the supersonic value is very slightly ($0\cdot 045$%) greater than the subsonic value, which Reynolds's theory overestimates by $0\cdot 083$%. The two regimes of course imply two different values of the pressure at exit, and for intermediate pressures (on the assumptions of this paper) there is no solution of the problem. Even in the subsonic regime (when the mass flow is critical) velocities exceeding the local speeds of sound are attained in regions adjoining the nozzle walls near the throat.
TL;DR: In this paper, the authors derived the local field acting on a dipole and replaced the surroundings by a continuum whose dynamic dielectric properties they have taken into account, resulting in larger dielectrics constants and smaller losses than in Onsager's theory.
Abstract: From an investigation of structure it is shown that there exists a large group of dipolar organic solids whose dipoles have two equilibrium positions with opposite dipole direction. To calculate the dielectric properties Onsager's theory has been extended and developed into a systematic approximation which converges above a critical temperature. To derive the local field acting on a dipole we have replaced the surroundings by a continuum whose dynamic dielectric properties we have taken into account. As a result we find larger dielectric constants and smaller dielectric losses than in Onsager's theory. We have also shown that liquids with high viscosity behave similarly to solids, while for liquids with low viscosity there are no such deviations from Onsager's theory.
TL;DR: In this article, the transition effect of penetrating showers is investigated and the effect is found to agree with the theory of Hamilton, Heitler & Peng as extended by Janossy.
Abstract: Observations of the transition effect of penetrating showers are reported and the effect is found to agree with the theory of Hamilton, Heitler & Peng as extended by Janossy. The Z -dependence of the transition effect reported previously by Janossy has not been confirmed.
TL;DR: In this paper, a method was described for determining the orientation of proton tracks in a photographic emulsion with an accuracy of $\pm $ 1 degrees, where ρ is the intensity per unit solid angle of the scattered neutrons in the centre of mass co-ordinate system of the colliding particles.
Abstract: A method is described for determining the orientation of proton tracks in a photographic emulsion with an accuracy of $\pm $ 1 degrees. This technical development increases the range of application of the photographic method to problems in nuclear physics. The method has been applied to an investigation of the scattering of $8\cdot 8$ and $13\cdot 0$ MeV neutrons by protons. If I($\phi $) is the intensity per unit solid angle of the scattered neutrons in the centre of mass co-ordinate system of the colliding particles, the measurements give values of I($\phi $) in the range from $\phi $ = $\pi $ to $\phi $ = $\frac{1}{2}\pi $. When this range in the value of $\phi $ is divided into five equal intervals, the observed numbers of tracks in the different intervals are consistent with the scattering being isotropic in the centre of mass system to within the limits of the statistical error, for the 8$\cdot $8 MeV group of neutrons. There is some evidence for a periodic fluctuation of high order in the angular distribution of the scattered intensity which remains to be confirmed. For the 13 MeV group the ratio of I($\pi $)/I($\frac{1}{2}\pi $) is found to be $0\cdot 67\pm 0\cdot 20$. The neutrons employed in this experiment were produced by bombarding boron with 600 keV deuterons and arise from the reaction B$^{11}$(d, n) C$^{12}$. There is evidence that the excited state of C$^{12}$ at $4\cdot 5$ MeV is complex.
TL;DR: In this paper, a general method is set up for modifying the energy-momentum tensor so as to remove the singularities in the flow of energy and momentum into the world-line of a particle without affecting the equations of motion of the particle.
Abstract: A general method is set up for modifying the energy-momentum tensor so as to remove the singularities in the flow of energy and momentum into the world-line of a particle without affecting the equations of motion of the particle. It is shown how the singularities of different order may be removed one by one. In the case of the electromagnetic and meson fields it is shown that the modified tensor leads to a finite integral of energy and momentum over any space-like surface. In other cases the corresponding result may be secured by making a further modification in the tensor.
TL;DR: In this paper, it was shown that if hydrogen made luminous by a powerful discharge is blown out of the electric field by its own expansion, the time in question is under some conditions a thousand times more.
Abstract: The light of a condenser discharge through hydrogen, emitting the Balmer series of lines, persists for much longer than current theories and experimental determinations of the time of relaxation of the hydrogen atom would lead one to anticipate. These determinations indicate a time of the order of 10$^{-8}$ sec. for the intensity to diminish in the ratio e:1. It is shown in the present paper that in fact, if hydrogen made luminous by a powerful discharge is blown out of the electric field by its own expansion, the time in question is under some conditions a thousand times more. The discrepancy is not cleared up, but the aim has been to present the evidence as clearly as possible for criticism.
TL;DR: In this article, the statistical mechanics of some crystalline systems may be reduced to statistical correlations between objects which are the unit cells of a fictitious lattice, where correlations are deduced from postulates according to which some configurations of the cells are incompatible with some other configurations of neighbouring cells; if, on the other hand, configurations of neighbours are compatible with each other, their probabilities are to combine by multiplication.
Abstract: The statistical mechanics of some crystalline systems may be reduced to statistical correlations between objects which are the unit cells of a fictitious lattice. The correlations are deduced from postulates according to which some configurations of the cells are incompatible with some configurations of the neighbouring cells; if, on the other hand, configurations of neighbours are compatible with each other, their probabilities are to combine by multiplication. By these postulates matrices are implicitly defined such that the probability distribution for a chain of cells is found by forming the powers of a matrix. A similar approach to the statistics of a lattice involves infinite matrices. It does not seem practicable to give explicit expressions for these matrices. If appropriate conditions are complied with, the correlations in a chain are accounted for by adjusting the mean probability coefficients of the cells and for the rest regarding the cells as statistically independent. In this case the infinite matrices may be replaced by the outer power of finite matrices. As result an equation is given by means of which the thermodynamical energy may be calculated as function of temperature.
TL;DR: In this paper, it was shown that the large barometer effect of penetrating showers can be understood in terms of an exponential absorption of the primaries giving rise to the showers, which is compatible with the theory of Hamilton, Heitler & Peng when account is taken of fluctuations.
Abstract: It is shown that the large barometer effect of penetrating showers can be understood in terms of an exponential absorption of the primaries giving rise to the showers. A number of other experimental results favour such an assumption. It is shown further that the exponential absorption of the primaries is compatible with the theory of Hamilton, Heitler & Peng when account is taken of fluctuations.
TL;DR: In this article, the authors deduced the relationship between the radius of curvature of a steel strip and the stress in the deposit by means of an equation given by Stoney (1909).
Abstract: In our recent paper (Hume-Rothery & Wyllie 1943) on the structure of electrodeposited chromium, figures were given for the stress in electro-deposits prepared on steel strip. These figures were deduced by means of an equation given by Stoney (1909) for the relation between the radius of curvature of the steel strip and the stress in the deposit. According to Stoney the radius of curvature, R , of a strip of length l is related to the deflexion of the strip, z , by the equation R = l 2/8z. In our work, we assumed that if the strip were held at one end, during electrodeposition, the deflexion was the movement of the free end. Actually, as can be seen from figure 1, if zis the movement of the free end of the rod, then for small deflexions R = l 2/2z If the deflexion is defined as the perpendicular distance from the mid-point of the rod to the chord of the circle joining its two ends, i.e. the distance y in figure 1, then the relation is R = l 2/8 y , which is that given by stoney.