176 KINEMATICS OF MACHINERY.
forward by a fluid pressure on one side, Fig. 128, corresponds to the drum in Fig. 126. The application of a column of water for transmitting pressure, which has lately been made in mining operations, furnishes again the opposite of a rope used in tension. Thus the tension- and pressure-organs are contra-positive. They must therefore be equally reckoned among kinematic elements. Willis' exclusion of all mechanisms of which fluid organs form a part, to which we alluded in the Introduction, was therefore incorrect. If belts, pulleys and so on, are to be considered as forming portions of "pure mechanism," it is logically impossible to omit water- and wind-mills, or steam-engines. We have only to think of the importance of the latter to be astonished that one of the most valuable and most extensively applied of machines, one possessing also the greatest delicacy and accuracy in its motion, should ever have been considered unkinematic, incapable of scientific kinematic treatment, "impure." We shall on the other hand be able to see further with what scientific force and with what important consequences kinematic science can be brought to bear upon these machines. Although Willis' view of the matter is not acknowledged as a principle, its incorrectness has not been specially pointed out; practically it has had the result that this class of machinery has scarcely ever been treated kinematically by English writers, and by others only seldom, and even then generally not with the requisite thoroughness.
§42,
Springs.
While in the tension- and pressure-organs we have had elements in which the application of force could occur only in a certain very simple manner, there is in machinery another class of elements which can be arranged so as to be used with any possible application of force. These elements are springs. They are familiar in many forms and for many purposes; always, however, under the con- dition which we found to be necessary in the case of the flectional elements, with the limitation, that is, that in each special case a single force-application only can be used. The various con- structions of springs may be classified according to the nature of
