CLASSIFICATION OF CONSTRUCTIVE ELEMENTS. 481
couplings, brake-gear, click-gear, &c., are more complex, and seem more distinctly to be complete kinematic chains. These, however, occur so frequently as subordinate parts of larger chains that relatively to the latter they appear elementary, and their appear- ance among the constructive elements may be justified upon this ground.
The question now presents itself whether we cannot, from the point of view now reached, find some rational classification for the constructive elements, based upon their real kinematic nature. This can certainly be done, and the matter is of sufficient im- portance to merit a short examination here.
It must be quite understood, in the first place, that no absolutely rigid systematic treatment is here possible. The classification must be based throughout on judicious compromise ; we must be content to give and take, that we may accommodate ourselves to the exigencies of the numerous practical questions which refuse to remain within the bounds of a rigid system. This, however, does not of itself involve any error, for it is a consequence of the real nature of the problem before us (p. 437), and in no way interferes with our firm grasp of the scientific kinematic basis upon which the whole matter rests.
We shall in the first place make a more distinct separation than has hitherto been usual between the rigid and the fiectional elements. We may begin with the former, placing first the most simple cases which occur. For this purpose, however, we must remember that the simplest things are not always those having fewest parts, and that a combination, therefore, is not to be rejected simply because it contains more than a single element, or a pair of elements. For our purposes those combinations in which no motion occurs the immoveable fastenings used for forming links may be considered simpler than the moveable pairs of elements ; we may therefore place them first in our list. Next to them come the kinematic elements, pairs and links which give us simple moveable connections. Within these pieces themselves also the immoveable fastenings very frequently occur.
Arranged in this way the following will then be the first series of constructive elements ;
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