and partly by theory what is the radiating power of a surface in this state. Thus it is not difficult to compute how large an area of the sky Betelgeuse must cover in order that the area multiplied by the radiating power may give the observed brightness of Betelgeuse. The area turns out to be very small. The apparent size of Betelgeuse is that of a half-penny fifty miles away. Using a more scientific measure, the diameter of Betelgeuse predicted by this calculation is 0.051 of a second of arc.

No existing telescope can show so small a disk. Let us consider briefly how a telescope forms an image -- in particular how it reproduces that detail and contrast of light and darkness which betrays that we are looking at a disk or a double star and not a blur emanating from a single point. This optical performance is called resolving power; it is not primarily a matter of magnification but of aperture, and the limit of resolution is determined by the size of aperture of the telescope.

To create a sharply defined image the telescope must not only bring light where there ought to be light, but it must also bring darkness where there ought to be darkness. The latter task is the more difficult. Light-waves tend to spread in all directions , and the telescope cannot prevent individual wavelets from straying on to parts of the picture where they have no business. But it has this one remedy -- for every trespassing wavelet it must send a second wavelet by a slightly longer or shorter route so as to arrive in a phase opposite to the first wavelet and cancel its effect. This is where the utility of a wide aperture arises -- by affording a wider difference of route of the individual wavelets, so that those from one part of the aperture may be retarded relatively to and interfere with those from another part. A small object- glass can furnish light; it takes a big object-glass to furnish darkness in the picture.

Now we may ask ourselves whether the ordinary circular aperture is necessarily the most efficient for giving the wavelets the required path-differences. Any deviation from a symmetrical shape is likely to spoil the definition of the image -- to produce wings and fringes. The image will not so closely resemble the object viewed. But on the other hand we may be able to sharpen up the tell-tale features. It does not matter how widely the image-pattern may differ from the object, provided that we can read the significance of the pattern. If we cannot reproduce a star-disk, let us try whether we can reproduce something distinctive of a star-disk.

A little reflection shows that we ought to improve matters by blocking out the middle of the object-glass, and using only the extreme regions on one side or the other. For these regions the difference of light- path of the waves is greatest, and they are the most efficient in furnishing the dark contrast needed to outline the image properly.

But if the middle of the object-glass is not going to be used, why go to the expense of manufacturing it? We are led to the idea of using two widely separated apertures, each involving a comparatively small lens or mirror. We thus arrive at an instrument after the pattern of a rangefinder.

This instrument will not show us the disk of a star. If we look through it the main impression of the star image is very like what we should have seen with either aperture singly -- a 'spurious disk 'surrounded by diffraction rings. But looking attentively we see that this image is crossed by dark and bright bands which are produced by interference between the light-waves coming from the two apertures. At the centre of the image the waves from the two apertures arrive crest on crest since they have travelled symmetrically along equal paths; accordingly there is a bright band. A very little to one side the asymmetry causes the waves to arrive crest on trough, so that they cancel one another; here there is a dark band. The width of the bands decreases as the separation of the two apertures increases, and for any given separation the actual width is easily calculated.

Each point of the star's disk is giving rise to a diffraction image with a system of bands of this kind, but so long as the disk is small compared with the finest detail of the diffraction image there is no appreciable blurring. If we continually increase the separation of the two apertures and so make the bands narrower, there comes a time when the bright bands for one part of the disk are falling on the dark bands for another part of the disk. The band system then becomes indistinct. It is a matter of mathematical calculation to