The Galerkin method for the approximate solution of elasticity problems (see e.g. Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression. The two methods are not always equivalent, and the conditions for equivalence are given in Duncan's lucid presentation of the method (Refs. 2 and 3, which unfortunately have been out of print for some time). These conditions, however, are generally omitted from discussions of the Galerkin method, and it is the purpose of this note to re-emphasise them in a slightly different form.

The general problem of the flow through screens has been widely studied, but certain difficulties have arisen in the comparison of screens of various solidities. A theoretical treatment and some experimental work on the flow through screens of low solidity are described below.

Certain elastic systems may not only vibrate freely at proper (non-zero) natural frequencies, but may also move as rigid bodies. Such systems have “rigid body” modes which behave like principal modes corresponding to zero natural frequencies. These modes may be disregarded in the series representation of static distortions of such systems but must be taken into account in the representation of forced vibrations.

This note is concerned with the series representation of receptances of certain simple systems of this type, namely strings, bars, shafts and beams. These systems were discussed in reference 1, but there the rigid body modes were omitted. As the matter appears to raise some points of interest, a discussion of it seems to be called for. A similar analysis to that presented here may be applied to other unsupported, or partially supported systems, such as an unsupported plate.

In a note by Goodey on the combined use of the WKB solution and Rayleigh's principle to estimate the lowest eigenvalue of a second-order linear differential equation, a numerical error concealed an interesting aspect of the result. The exact value λ = 2·062 corresponds to 0·6564π; and not 0·654π as stated. The approximate value 0·6559π is therefore lower than the exact value.

The possibility of approximate evaluation of the integral in a variational expression affecting the direction of approach to the exact value was pointed out by the author in a recent paper on the application of quadrature by differentiation. The application of the method described there to the example considered by Goodey may be of some interest as it gives the eigenvalue to within 1/2 per cent by the solution of a quadratic equation.

In some recent tests we have successfully used the smoke from smouldering paper to indicate the flow of air in the vortices above slender wings at speeds in the region of 200 f.p.s. Smokes of this kind are particularly suitable for the production of the large volume flows required because in certain conditions they do not lose density by condensation in long supply tubes.

Before assessing future developments of agricultural aircraft, it is interesting to study the trends of the industry over the past five years.

In England, after a promising start, which it is now apparent was occasioned by a heavier-than-normal attack of pest and disease, it soon became evident that large scale operations could not be undertaken profitably due to low fleet utilisation and numerous operational problems which arose from the use of existing fixed-wing aircraft. The major operational problems which hampered large scale operations were shortage of acceptable landing strips, small fields and a high incidence of obstacles.

The stability of a uniform cantilever beam subjected to an articulated tip load has been analysed as an equilibrium problem of static elastic stability. It was found there that the articulation of the connecting rod applying the tip load introduced additional component forces during the process of beam deformation.

This note is concerned with the correlation and presentation of information on heat transfer under conditions of turbulent forced convection for the flow of gases in tubes. Discussion will be confined to the region where thermal entrance effects are absent and, furthermore, it will be assumed that the flow velocity is sufficiently low for compressibility effects to be neglected.

The subject matter will be discussed in general terms only and it is not intended to produce quantitative conclusions, which may, however, be found in reference 11.