where A denotes some quantity or set of quantities depending on the form, arrangement, weight and other properties of the mechanism. Moseley, however, has pointed out that in most cases this equation takes the much more simple form of
E = (1 + A) U + B,
(55)
where A and B are constants, depending on the form, arrangement and weight of the mechanism. The efficiency corresponding to the last equation is
| U | = | 1 | . |
| E | 1 + A + B/U |
(56)
§ 94. Trains of Mechanism.—In applying the preceding principles to a train of mechanism, it may either be treated as a whole, or it may be considered in sections consisting of single pieces, or of any convenient portion of the train—each section being treated as a machine, driven by the effort applied to it and energy exerted upon it through its line of connexion with the preceding section, performing useful work by driving the following section, and losing work by overcoming its own prejudicial resistances. It is evident that the efficiency of the whole train is the product of the efficiencies of its sections.
§ 95. Rotating Pieces: Couples of Forces.—It is often convenient to express the energy exerted upon and the work performed by a turning piece in a machine in terms of the moment of the couples of forces acting on it, and of the angular velocity. The ordinary British unit of moment is a foot-pound; but it is to be remembered that this is a foot-pound of a different sort from the unit of energy and work.
If a force be applied to a turning piece in a line not passing through its axis, the axis will press against its bearings with an equal and parallel force, and the equal and opposite reaction of the bearings will constitute, together with the first-mentioned force, a couple whose arm is the perpendicular distance from the axis to the line of action of the first force.
A couple is said to be right or left handed with reference to the observer, according to the direction in which it tends to turn the body, and is a driving couple or a resisting couple according as its tendency is with or against that of the actual rotation.