To comprehend the method of working the other piston, conceive a rod G P′, equal in length to B D, to be attached to the end G of the beam by a pivot on which it moves freely; and let its extremity P′ be connected with D by another rod P′ D, equal in length to G B, and playing on points at P′ and D. The piston rod of the cylinder is attached to the point P′, and this point has a motion precisely similar to that of P, without any lateral derangement, but with a range in the perpendicular direction twice as great. This will be apparent by conceiving a straight line drawn from the centre A of the beam to P′, which will also pass through P. Since G P′ is always parallel to B P, it is evident that the triangle P′ G A is always similar to P B A, and has its sides and angles similarly placed, but those sides are each twice the magnitude of the corresponding sides of the other triangle. Hence the point P′ must be subject to the same changes of position as the point P, with this difference only, that in the same time it moves over a space of twice the magnitude. In fact, the line traced by P′ is the same as that traced by P, but on a scale twice as large. This contrivance is usually called the _parallel motion_, but the same name is generally applied to all contrivances by which a circular motion is made to produce a rectilinear one. CHAP. XIX. OF FRICTION AND THE RIGIDITY OF CORDAGE. (320.) With a view to the simplification of the elementary theory of machines, the consideration of several mechanical effects of great practical importance has been postponed, and the attention of the student has been directed exclusively to the way in which the moving power is modified in being transmitted to the resistance independently of such effects. A machine has been regarded as an instrument by which a moving principle, inapplicable in its existing state to the purpose for which it is required, may be changed either in its velocity or direction, or in some other character, so as to be adapted to that purpose. But in accomplishing this, the several parts of the machine have been considered as possessing in a perfect degree qualities which they enjoy only in an imperfect degree; and accordingly the conclusions to which by such reasoning we are conducted are infected with errors, the amount of which will depend on the degree in which the machinery falls short of perfection in those qualities which theoretically are imputed to it. [Illustration: _C. Varley, del._ _H. Adlard, sc._ _London, Pubd. by Longman & Co._]