[Illustration:  FIG. 3]

A very excellent method was devised by the celebrated Rosse, which is frequently used at the present time; and those eminent workers, the Clarks of Cambridge, use a modification of the Rosse method which in their hands is productive of the very highest results.  The device is very simple, consisting of a telescope (a, Fig. 1) in which aberrations have been well corrected, so that the focal plane of the objective is as sharp as possible.  This telescope is first directed to a distant object, preferably a celestial one, and focused for parallel rays.  The surface, b, to be tested is now placed so that the reflected image of the same object, whatever it may be, can be observed by the same telescope.  It is evident that if the surface be a true plane, its action upon the beam of light that comes from the object will be simply to change its direction, but not disturb or change it any other way, hence the reflected image of the object should be seen by the telescope, a, without in any way changing the original focus.  If, however, the supposed plane surface proves to be convex, the image will not be sharply defined in the telescope until the eyepiece is moved away from the object glass; while if the converse is the case, and the supposed plane is concave, the eyepiece must now be moved toward the objective in order to obtain a sharp image, and the amount of convexity or concavity may be known by the change in the focal plane.  If the surface has periodic or irregular errors, no sharp image can be obtained, no matter how much the eyepiece may be moved in or out.

[Illustration:  FIG. 4]

This test may be made still more delicate by using the observing telescope, a, at as low an angle as possible, thereby bringing out with still greater effect any error that may exist in the surface under examination, and is the plan generally used by Alvan Clark & Sons.  Another and very excellent method is that illustrated in Fig. 2, in which a second telescope, b, is introduced.  In place of the eyepiece of this second telescope, a diaphragm is introduced in which a number of small holes are drilled, as in Fig. 2, x, or a slit is cut similar to the slit used in a spectroscope as shown at y, same figure.  The telescope, a, is now focused very accurately on a celestial or other very distant object, and the focus marked.  The object glass of the telescope, b, is now placed against and “square” with the object glass of telescope a, and on looking through telescope a an image of the diaphragm with its holes or the slit is seen.  This diaphragm must now be moved until a sharp image is seen in telescope a.  The two telescopes are now mounted as in Fig. 2, and the plate to be tested placed in front of the two telescopes as at c.  It is evident, as in the former case, that if the surface is a true plane, the reflected image of the holes or slit thrown upon it by the telescope, b, will be seen sharply defined in the telescope, a.