415. ON METHODS FOR DETECTING SMALL OPTICAL RETARDATIONS, AND ON THE THEORY OF FOUCAULT'S TEST. [Philosophical Magazine, Vol. xxxm. pp. 161—178, 1917.] As was, I think, first emphasized by Foucault, the standard of accuracy necessary in optical surfaces is a certain fraction of the wave-length (A,) of the light employed. For glass surfaces refracting at nearly perpendicular incidence the error of linear retardation is about the half of that of the surface; but in the case of perpendicular reflexion the error of retardation is the double of that of the surface. The admissible error of retardation varies according to circumstances. In the case of lenses and mirrors affected with " spherical aberration," an error of £\ begins to influence the illumination at the geometrical focus, and so to deteriorate the image. For many purposes an error less than this is without importance. The subject is discussed in former papers*. But for other purposes, especially when measurements are in question, a higher standard must be insisted on. It is well known that the parts of the surfaces actually utilized in interferometers, such as those of Michelson 'and of Fabry and Perot, should be accurate to -fa\ to -fa\, .and that a still higher degree of accuracy would be advantageous. Even under difficult conditions interference-bands may be displayed in which a local departure from ideal straightness amounting to ?V of the band period can be detected on simple inspection. I may instance some recent observations in which the rays passing a fine vertical slit backed by a common paraffin-flame fell upon the object-glass of a 3-inch telescope placed some 20 feet away at the further end of a dark room. No collimator was needed. The object-glass was provided with a cardboard cap, pierced by two vertical slits, each -^ inch wide, and so placed that the distance between the inner edges was T% inch. The parallelism of the three slits could be tested with a plumb-line. To observe the bands formed at the focus of the object-glass, a high magnifying-power * Phil Mag. Vol. vm. pp. 403, 477 (1879); Scientific. Papers, Vol. i. p. 415, §§ 3, 4. wall in air.