PLACE- AND FORM-CHANGING MACHINES. 493
bodies by removing a portion of them. The nail-making machine and rolling-mill rearrange the molecules or larger portions of bodies worked on, of which at the same time they alter the position. The same is true of the card-making machine. The millstones divide the body into minute pieces, altering its position at the same time. All, however, have one or more tools, and we see that in every case where there has been any indefiniteness about these, it has arisen from the fact that the machine served the double pur- pose of changing both the form and the position of the bodies worked upon. Apart from this, however, we may now divide ma- chines into two great classes according to the purposes for which they are used, namely :
I. Machines for altering position, or place-changing machines.
II. Machines for altering form, or form -changing machines.
There is no sharp division line between these two classes, for some form-changes are, as we have seen, necessarily accompanied by changes of position, while some machines, as the corn-mill, seem to belong equally to the two classes. In every case however, those machines which belong wholly or partly to the second class are characterised by the possession of the tool, while this organ is not found in any machine whose object is place- changing alone. The latter are therefore the simpler, and for that reason we have placed them first.
The theory, therefore, which makes the tool an essential part of the machine, is correct only so far as one of these two great sub- divisions of machinery is concerned. The tool is not an essential part of the machine ; it is accidental to it only, and for this reason cannot form part of the foun- dation upon which our comprehension of the complete machine is to rest.
131. Kinematic Nature of the Tool.
Now that we have found what the tool is not, we must turn to the question of what it is, and endeavour to find the kinematic meaning of this organ in the class of form-changing machines, in
