(138.) The centrifugal pressure increases as the radius of curvature increases; but it also has a dependence on the velocity with which the moving body swings round the centre of the circle of curvature. This velocity is estimated either by the actual space through which the body moves, or by the _angular velocity_ of a line drawn from the centre of the circle to the moving body. That body carries one end of this line with it, while the other remains fixed at the centre. As this angular swing round the centre increases, the centrifugal pressure increases. To estimate the rate at which this pressure in general varies, it is necessary to multiply the square of the number expressing the angular velocity by that which expresses the radius of curvature, and the force increases in the same proportion as the product thus obtained. (139.) We have observed that the same causes which produce pressure on a body restrained, will produce motion if the body be free. Accordingly, if a body be moved by any efficient cause in a curve, it will, by reason of the centrifugal force, _fly off_, and the moving force with which it will thus retreat from the centre round which it is whirled will be a measure of the centrifugal force. Upon this principle an apparatus called a _whirling table_ has been constructed, for the purpose of exhibiting experimental illustrations of the laws of centrifugal force. By this machine we are enabled to place any proposed weights at any given distances from centres round which they are whirled, either with the same angular velocity, or with velocities having a certain proportion. Threads attached to the whirling weights are carried to the centres round which they respectively revolve, and there, passing over pulleys, are connected with weights which may be varied at pleasure. When the whirling weights fly from their respective centres, by reason of the centrifugal force, they draw up the weights attached to the other ends of the threads, and the amount of the centrifugal force is estimated by the weight which it is capable of raising. With this instrument the following experiments may be exhibited:-- Exp. 1. Equal weights whirled with the same velocity at equal distances from the centre raise the same weight, and therefore have the same centrifugal force. Exp. 2. Equal weights whirled with the same angular velocity at distances from the centre in the proportion of one to two, will raise weights in the same proportion. Therefore the centrifugal forces are in that proportion. Exp. 3. Equal weights whirled at equal distances with angular velocities which are as one to two, will raise weights as one to four, that is, as the squares of the angular velocities. Therefore the centrifugal forces are in that proportion.