their axes are parallel, and let the two slotted bars be also placed parallel to each other and joined. Then evidently, if be fixed, every point in must move parallel to the centre line of the slots, as shown by the arrow. All such points therefore describe equal straight lines. Thus the motion takes place exactly as it would if were a solid prism enclosed by a hollow one, like the pair in Fig. 8. Thus by combining two pairs we have obtained nothing but what we could have got by means of a single one. So far the experiment has led to no result.
Fig. 9.
But if we do not place and parallel to each other, but set them obliquely as shown in Fig. 9, the case is entirely altered. The centres of and no longer move in similar directions in the slots, and consequently the various points in no longer have similar paths,—the point , for example, describes a curve. The motion is thus quite different from what it was before.
Nevertheless in these two different cases, Figs. 7 and 9, the same relation obtains; in both, and form rigid bodies, or what may be considered as such,—that is to say, we have in the end one pair of elements only, by combining two pairs of bodies. With different methods of combination different results are obtained, but in every case there results only one pair.
Accordingly the reciprocal combination of the elements of two pairs gives us again a pair of elements, which may differ from either of the single pairs of which it is composed. Thus we obtain already an important result, and one having many consequences.
