172 KINEMATICS OF MACHINERY.
railways has been directly dependent on it. Every one is familiar with the fact that at the first the notion of " adhesion " between the wheels and the rails was thought so illusory that it could scarcely obtain a trial, restraint being obtained by the use of suitably profiled pairs of elements. Blenkinsop's toothed-rail, and those of the Liverpool and Manchester Railway, Brunton's revolv- ing legs, and other even less practical constructions all illustrate this.
The constrained rolling of axoids under force-closure differs essentially from the mere closure of an incomplete pair of elements. The two things may, however, occur together as well as singly. In the driving-wheels of locomotives they are united ; in the wheels of the carriages there is nothing more than closure of elements by pressure.
In the latter case it would be possible to bring about the element- closure by the addition of a second pair of elements, an additional rail, for instance, which could be so embraced by a suitably formed piece connected with the carriage as to render any rising of the latter from the main rails impossible ; but this would not in any way make the wheels more like the driving-wheels. Such an ar- rangement has indeed been employed on the Eigi railway. With it the motion of the carriage on the line may be more accurately described as that of an ordinary closed pair than as occurring with, force-closure.
We see that force- closure finds important and numerous appli- cations. It always retains, however, a certain incompleteness. If the closing forces be not sufficiently large, or if unforeseen disturbances occur, the constraint may be destroyed or temporarily broken. Not- withstanding this, force-closure as the examples given show is of most essential service in machinery. It leads us besides to an entirely different kind of pairs of elements, which are in machinery of even greater importance than those just considered. We shall examine these more closely in the following paragraphs.
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