mental. On the other hand, the operation of scraping, hitherto so much neglected, constitutes the only certain means we possess for the attainment of accuracy. A few remarks will clearly illustrate the truth of this statement.
It is required, in a plane surface for mechanical purposes, that all the bearing points should be in the same plane,—that they should be at equal distances from one another,—and that they should be sufficiently numerous for the particular application intended. Where surfaces remain fixed together, the bearing points may, without disadvantages be fewer in number, and, consequently, wider apart; but, in the case of sliding surfaces, the points should be numerous and close together.
A little consideration will make it evident that these conditions cannot be obtained by the process of grinding. And, first, with regard to general outline, how is the original error to be got rid of? Let it be supposed that one of the surfaces is concave, and the other a true plane. The tendency of grinding, no doubt, will be to reduce the error of the former, but the opposite error will, at the same time, be created in the true surface. The only case in which an original error could be extirpated, would be, when it was met by a corresponding error, of exactly the same amount, in the opposed sur-
