Radiant Flux Through Apertures— III

This paper completes our treatment of radiant flux through pairs of apertures. In Part II, we obtained approximate equations for rectangular apertures in parallel planes, with the restriction that two apertures be identical and that one be directly above the other. Here we generalize to the case of any apertures that fit into a rectangular grid. The idea for this generalization originated with Ondracek but it is here expressed in matrix notation, which allows coefficients F_ij to be obtained rather simply.     

Radiant flux through apertures—I

Equations for the calculation of radiant power F through two apertures in series are well known. A characteristic of these formulae is that they give F as a small difference between two large terms. Evidently, the flux through the apertures must decrease as the spacing between them increases; and for large spacing, the inverse-square relation must hold. Instead of exhibiting this behaviour in an obvious manner, however, the traditional equations give the specious impression of an increase in F with increase in spacing. The paper develops an approximate formulae that applies to apertures in the shape of any regular polygon and that shows clearly how the inverse square relation is approached for large separation.     

The role of higher education institutions in national development

Abstract from the report of the International Conference on Education (33rd Session) of the International Bureau of Education. It deals with (i) the role of higher education institutions in national development, (ii) improving and sustaining the competence of educators and (iii) managing the system of education.     

Simplified interflection calculations

The purpose of the paper has been to present simplified methods that will expedite the calculation of ceiling lighting (Type II). Approximate formulas have been given, which allow ordinary slide-rule calculations to be made very easily for the usual range of variables. Only with rooms having very high domance (or perhaps with extraordinarily high floor reflectance) are the complicated equations of the previous paper (1) needed. These approximate formulas can be represented also by alignment charts, Figs. 2 to 5, which further simplify the work.Either the formulas or the charts may be used to investigate the effect of a change in ?₁, ?₂, or ?₃. However, if reflectances are standardized at recommended values, other methods are possible.In particular, one may use graphs (Fig. 6) or a slide-rule (Figs. 7 and 8). The method of calculation chosen for a specific problem will depend on the problem and on the preferences of the designer. The previous equations and tables (3) may always be used; but in most cases, time can be saved by employing the short-cuts given in the present paper.     

Separability in a class of coordinate systems

A study is made of separability conditions for the Helmholtz and Laplace equations. Attention is confined to the most useful case for physical applications; namely,

1.

(a) The coordinate system is either cylindrical or it has rotational symmetry, and     

Interflectance calculations for various luminaires

Previous interflectance tables have dealt principally with three basic types of lighting (Types I, II, and III). The present paper extends the scope of the interflection method by showing how it can be applied to rooms lighted by hanging luminaires. It is found that most cases arising in practice can be covered by six canonic distributions. The effect of mounting height is handled by means of a simple equation.     

Radiation reaction forces and the expanding universe

The expanding universe is described in terms of the known forces of classical physics. It is shown that great clouds of stars are non-conservative systems and that radiation reaction forces play a part in guiding stellar motions. The forces are of importance in unsymmetrical stars and evidence is collected to show that perhaps all stars are possessed of deep seated thermal asymmetries. The forces continually act to increase the mean velocity of the stars and the galaxy is calculated to expand at a rate which closely approximates the observed rate of expansion. From a relation connecting the mean velocity of the stars and their age, it is deduced from the observed motions that the age of the galaxy is about 10¹⁰ years. The deduced rate of expansion of the galaxy agrees well with the observational data and is identical in form and numerical constant with Hubble's relation connecting the velocity of recession and distances of nebulæ.Because of the relative size and spacing of the extra galactic nebulæ and the short time scale it is supposed that the nebulae were formed by fission from a parent-super nebula and this resulted in thermal asymmetries which brought the newly considered forces into action.The resulting expansion was produced by slow evolutionary radiation processes which bear no direct relation to the properties of space or atomic constants.The calculations suggest that in describing the motions of typical stars over long periods of time, radiation reaction forces are as important as the classical gravitational forces.