ALL MACHINES FORM-CHANGING. 503
We found that the pairing or chaining of the tool (in the form- changing machines) and the work-piece was such that the former constrained the latter to assume the form of the envelope for its relative motion, the giving of this form being the result aimed at in working the machine. The driver in the form-changing prime- movers passes through an exactly similar process. If we look, however, in this connection at any pair of elements whatever, lower or higher, a pin in its eye, a screw in a nut, a piston in its cylinder, a pair of spur-wheels, we see that in every case form- changes occur in one or the other element, or in both. These changes are of two kinds, viz. (1) temporary changes on account of the unavoidable alterations due to the action of sensible forces even upon the most rigid body, and (2) permanent changes, due to the separation of small portions from the body, In the latter class of changes wear gradually alters the form of the paired elements, and this alteration occurs so that the elements carry the reciprocal envelopes for the motion occurring between, them. This law is, however, exactly the same as for the motion between, tool and work-piece. In this case we endeavour to carry out the form- change quickly, it is the object of the constrained motion of the machine. In the former case the continuous change interferes with the object of the machine, and we therefore try to limit it in every possible way. In both cases, however, it exists.
The form-changing action which occurs between the tool and the work-piece differs in degree only, and not in kind, from the action taking place between the elements of every other pair in the machine.
We see, therefore, that all complete machines without exception follow the same general laws, and we are now able completely to realise the meaning of the definition of the machine with which we commenced our investigation (1) and which therefore we may conveniently repeat here :
A machine is a combination of resistant bodies so ar- ranged that by their means the mechanical forces of nature can be compelled to do' work accompanied by certain determinate motions.
The " arrangement " of the bodies here mentioned is the kine- matic chaining, Motion occurs in the machine when some part of the chain is in a position which cannot be retained under the
