By this method it is easy to compare one flat with another, and thus, if the first be known to be free from error, to determine the errors of the second. But how are we to obtain and verify a standard? The plan usually followed is to bring three surfaces into comparison. The fact that two surfaces can be made to fit another in all azimuths proves that they are spherical and of equal curvatures, but one convex and the other concave, the case of perfect flatness not being excluded. If A and B fit one another, and also A and C, it follows that B and C must be similar. Hence, if B and C also fit one another, all three surfaces must be flat. By an extension of this process the errors of three surfaces which are not flat can be found from a consideration of the interference bands which they present when combined in three pairs.
The free surface of undisturbed water is almost ideally flat, and, as Lord Rayleigh (Nature, 1893, 48, 212) has shown, there is no great difficulty in using it as a standard of comparison. Following the same idea we may construct a parallel plate by superposing a layer of water upon mercury. If desired, the superior reflecting power of the mercury may be compensated by the addition of colouring matter to the water.
Haidinger’s Rings dependent on Obliquity.—It is remarkable that the well-known theoretical investigation, undertaken with the view of explaining Newton’s rings, applies more directly to a different system of rings discovered at a later date.
The results embodied in equations (1) to (8) have application in the first instance to plates whose surfaces are absolutely parallel, though doubtless they may be employed with fair accuracy when the thickness varies but slowly.
We have now to consider t constant and α′ variable in (1). If α′ be small,
δ = 2μt (1 − ½α′2) = 2μt − tα2 / μ
(15);
and since the differences of δ are proportional to α2, the law of formation is the same as for Newton’s rings, where α′ is constant and t proportional to the square of the distance from the point of contact. In order to see these rings distinctly the eye must be focused, not upon the plate, but for infinitely distant objects.
The earliest observation of rings dependent upon obliquity appears to have been made by W. von Haidinger (Pogg. Ann., 1849, 77, p. 219; 1855, 96, p. 453), who employed sodium light reflected from a plate of mica (e.g. 0.2 mm. thick). The transmitted rays are the easier to see in their completeness, though they are necessarily somewhat faint. For this purpose it is sufficient to look through the mica, held close to the eye and perpendicular to the line of vision, at a sheet of white paper or card illuminated by a sodium flame. Although Haidinger omitted to consider the double refraction of the mica and gave formulae not quite correct for even singly refracting plates, he fully appreciated the distinctive character of the rings, contrasting Berührungsringe und Plattenringe. The latter may appropriately be named after him. Their tardy discovery may be attributed to the technical difficulty of obtaining sufficiently parallel plates, unless it be by the use of mica or by the device of pouring water upon mercury. Haidinger’s rings were rediscovered by O. R. Lummer (Wied. Ann., 1884, 23, p. 49), who pointed out the advantages they offer in the examination of plates intended to be parallel.
The illumination depends upon the intensity of the monochromatic source of light, and upon the reflecting power of the surfaces. If R be the intensity of the reflected light we have from (7)