By JOHN A. BRASHEAR.

In our study of the exact methods of measurement in use to-day, in the various branches of scientific investigation, we should not forget that it has been a plant of very slow growth, and it is interesting indeed to glance along the pathway of the past to see how step by step our micron of to-day has been evolved from the cubit, the hand's breadth, the span, and, if you please, the barleycorn of our schoolboy days. It would also be a pleasant task to investigate the properties of the gnomon of the Chinese, Egyptians, and Peruvians, the scarphie of Eratosthenes, the astrolabe of Hipparchus, the parallactic rules of Ptolemy, Regimontanus Purbach, and Walther, the sextants and quadrants of Tycho Brahe, and the modifications of these various instruments, the invention and use of which, from century to century, bringing us at last to the telescopic age, or the days of Lippershay, Jannsen, and Galileo.

Critical Methods Of Detecting Errors In Plane Surf 484 6a

FIG. 1.

It would also be a most pleasant task to follow the evolution of our subject in the new era of investigation ushered in by the invention of that marvelous instrument, the telescope, followed closely by the work of Kepler, Scheiner, Cassini, Huyghens, Newton, Digges, Nonius, Vernier, Hall, Dollond, Herschel, Short, Bird, Ramsden, Troughton, Smeaton, Fraunhofer, and a host of others, each of whom has contributed a noble share in the elimination of sources of error, until to-day we are satisfied only with units of measurement of the most exact and refined nature. Although it would be pleasant to review the work of these past masters, it is beyond the scope of the present paper, and even now I can only hope to call your attention to one phase of this important subject. For a number of years I have been practically interested in the subject of the production of plane and curved surfaces particularly for optical purposes, i.e., in the production of such surfaces free if possible from all traces of error, and it will be pleasant to me if I shall be able to add to the interest of this association by giving you some of my own practical experience; and may I trust that it will be an incentive to all engaged in kindred work to do that work well?

Critical Methods Of Detecting Errors In Plane Surf 484 6b

FIG. 2.

In the production of a perfectly plane surface, there are many difficulties to contend with, and it will not be possible in the limits of this paper to discuss the methods of eliminating errors when found; but I must content myself with giving a description of various methods of detecting existing errors in the surfaces that are being worked, whether, for instance, it be an error of concavity, convexity, periodic or local error.

Critical Methods Of Detecting Errors In Plane Surf 484 6c

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.

Critical Methods Of Detecting Errors In Plane Surf 484 6d

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.