expansion pipe and a valve 3 in. diameter, the next size 1¼ in. expansion pipe and a valve 4½ in. diameter, and the largest size has a pipe 1½ in. and a valve 6 in. diameter. Altogether, the contrivance has some important practical advantages to recommend it.--_Mech. World._ * * * * * CRITICAL METHODS OF DETECTING ERRORS IN PLANE SURFACES.[3] [Footnote 3: A paper read before the Engineers' Society of Western Pennsylvania, Dec. 10, 1884.] 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. [Illustration: 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?_ [Illustration: FIG. 2.]