282 KINEMATICS OF MACHINERY.
all this may be found in the general mode of development of machinal ideas which we have already studied, and under which we have seen the early machines to have grown up gradually from force-closed combinations of fixed and moving bodies. In the history of machine-development the simple machines formed the first experiment at a scientific arrangement of existing material ; the same train of ideas which governed its phenomena as a whole repeated itself upon a smaller scale in the early attempts at the scientific explanation of what had been empirically determined.
Beyond this, we may ask further whether, when the necessary strictness of conception and definition has been obtained, the " mechanical powers " do really constitute the elementary parts of all machines ? The answer must be most distinctly negative.
Three of the simple machines indeed, stripped of their con- ventional disguise, are no other than the three lower pairs (R), (P) and ($), and another the higher pair R,T\ but all the other higher pairs are wanting, while there is no representative of the pressure- organs, not to speak of the springs. With steam-engines and pumps the triumphs of pressure organs before us, how is it possible to assert that the traditional simple machines have formed the foundation for all others ? It seems scarcely conceivable that this should ever have been said. It has been so far modified as to be replaced by the statement that all the static problems of machinery were contained in the simple machines, and that it was this that gave them their importance and formed the real connec- tion between them. This also, however, is incorrect. The " principle of the lever " does not teach the relations among forces in the higher cylinder-pairs for that purpose we have to go back to the infinitely small instantaneous motions nor in the hyperboloidic pair. There are many dynamic problems in machinery of which the simple machines teach us nothing. In themselves they teach nothing of couples, and they leave entirely without notice the application of fluid-organs as elements in machinery, although they recognise their contra-positives the tension-organs. In short, the assertion that all machines can be traced back to those which have re- ceived the name of "simple" is justified from no point of view whatever.
We can now well understand the increasing fear of recognising the simple machines, in spite of their historical position, which
