Dr P. T. Bateman has pointed out that the definition of r(a, a) should be

The rest of the proof is unaffected except that the appropriate change should be made in the proof of Lemma 2. (The proof as it stands is incorrect.)

The formula in the first line of p. 644 should be: G(z) = S(z) + N2z.

A calculation of the binding energy of 8Be is given, based upon the separation of the eight nucleons into two groups of four, using Gaussian functions and a Yukawa central force. The calculation is considerably simplified by the use of an integral identity between the Gaussian potential and the Yukawa potential. The energy is calculated with a Gaussian potential, and the identity used to convert the result to that which would have been obtained by direct use of the Yukawa potential. The results of the variational calculation show that unless the saturation conditions usually adopted in the theory of heavy nuclei are abandoned, there can be no binding, confirming an earlier result of Margenau, obtained with a Gaussian potential. The results do not depend essentially on the range of the force, nor on the central two-body type of force adopted. When the old saturation conditions are abandoned, quite reasonable results are obtained. The magnitude of the energies due to the exchange of single particles and pairs of particles indicates that the force between alpha-particles is not additive. A discussion of the saturation conditions and of the alpha-particle model in the light of the results is given.

The solution for the flow of an incompressible fluid past an infinitely long wedge with a finite sloping edge (a finite wedge) is generalized by the hodograph method. In the flow thus obtained the axis of symmetry and a sloping edge of the wedge are again part of one streamline. It becomes possible to describe the flow of an ideal gas past a finite wedge if the hypothesis is made that the first singularity on this streamline, along the sloping edge, corresponds to the shoulder of the wedge. For a given wedge, with gradually increasing velocity at infinity upstream, the singularity appears at first at subsonic velocity. Beyond a certain critical velocity at infinity the singularity is always associated with the speed of sound. The hypothesis thus implies that put forward by Maccoll(9) and supported by Busemann(l). A qualitative examination shows that the solution reproduces experimentally known features of the flow of compressible fluid past a finite wedge.

In the course of some calculations on the lifetimes of excited states of mercury and potassium(9) and photo-ionization of excited potassium, wave functions were derived for various excited states of these atoms. Tables of these wave functions are presented in this paper.

The Thomas-Fermi method has been applied to molecules with tetrahedral or octahedral symmetry in the approximation in which the nuclei of the outer atoms are smeared out over the surface of a sphere. Solutions are given for the molecules CH4, CF4, CCl4, SiH4, SiF4 and SF6, and using the results presented here it will not be a difficult matter to obtain the solutions for other molecules if they should be required.

A comparison of the results for CH4 with those of Buckingham, Massey and Tibbs shows that whilst for such a light molecule the charge distribution is somewhat poor, the potential is already in good agreement with the results of the Hartree self-consistent field method. For CCl4, however, the approximation of smoothing out all the protons appears to break down. An alternative approximation in which the K and L shell electrons are compressed into the nucleus and the modified nuclear charges smoothed, has been investigated and appears to give more reasonable results.

A discussion of the energy has been given, but the method is not sufficiently accurate to be of value for energetic considerations.

(i) In the penultimate line of § 1, the reference should be to example (iii)

(ii) The right-hand side of equation (31) should be divided by 3.

(iii) Two lines below equation (33), v should be defined as the highest common factor of n, u1, u2,…

(iv) Similarly in the penultimate line of the paper (before the References) the words ‘and of n’ should be added.

A superconducting tangent galvanometer suitable for the measurement of thermoelectric voltages in circuits of resistance about 10−7 ohm is described. The inductance has been kept low by the use of only a single turn in each of the deflecting coils, but a high sensitivity has been attained by reducing the controlling field to about 0·01 gauss. The theory of operation of such a galvanometer in circuits of low resistance is discussed; the actual behaviour of the instrument is in satisfactory agreement with the theory. The galvanometer will detect a current of 10−5 A. corresponding to an e.m.f. of 10−12 V.

The classical theory of partition of numbers is applied to the problem of determining the equilibrium profile of a simple cubic crystal. It is concluded that it may be thermo-dynamically profitable for the surface to be ‘saw-toothed’ rather than flat, the extra entropy associated with such an arrangement compensating for the additional surface energy. For both a two- and a three-dimensional ‘saw-tooth’ the extra entropy varies, to a first approximation, in the same way as the surface energy, i.e. is proportional to or respectively, where N is the number of molecules in a ‘tooth’. For the simple cubic lattice, the entropy associated with the formation of a tooth containing N atoms is estimated to be 3.3 It is also possible to estimate the variation of the ‘equilibrium roughness’ of a crystal with temperature, if its surface energy is known.

J. S. R. Chisholm, Calculation of S-matrix elements

In equation (1b), and should be replaced by and . This results in similar changes in the expression (29) for , and in the line following equation (29) the factor -2 should be omited from the expression

This discussion is concerned with the periodic solutions of the differential equation

where the parameter k is small. The equation arises from an investigation of the forced oscillations of a simple electrical circuit (6) containing a triode. The function f(x) is derived from the current-voltage characteristic of the triode and it has a roughly ⊂-shaped graph, with a flat bottom and some slight asymmetry. For a regenerative circuit, we have f(0) < 0. Van der Pol (5) considered the equation with f (x) = x2 − 1, and he and later writers (1, 2, 4) have built up an extensive theory of triode oscillations for this ideal case. In practice, the graph of f(x) has a much flatter bottom than that of the function x2 − 1, and it was asked by Cartwright ((3), p. 214) whether this flattening would alter the qualitative behaviour of the circuit near resonance. The main part of this paper is an attempt to answer this question.

The motion of a pendulum on a periodically accelerated support has been studied by means of an electronic computing machine. The results have been applied to the problem of calculating the second-order correction to measurements of gravity made at sea with the Vening Meinesz three-pendulum apparatus. It is found that the correction for a single horizontal acceleration under typical conditions is likely to be more than twice that found analytically by Browne. His correction for vertical acceleration is valid for a wide range of frequency of the disturbing motion.