Exp. 4. Equal weights whirled at distances which are as two to three, with angular velocities which are as one to two, will raise weights which are as two to twelve; that is, as the products of the distances two and three, and the squares one and four, of the angular velocities. Hence, the centrifugal forces are in this proportion. The centrifugal force must also increase as the mass of the body moved increases; for, like attraction, each particle of the moving body is separately and equally affected by it. Hence a double mass, moving at the same distance, and with the same velocity, will have a double force. The following experiment verifies this:-- Exp. 5. If weights, which are as one to two, be whirled at equal distances with the same velocity, they will raise weights which are as one to two. The law which governs centrifugal force may then be expressed in general symbols briefly thus:-- Let _c_ = the centrifugal force with which a weight of one lb. revolving in a circle in one second, the radius of which is one foot, would act on a string connecting it with the centre. The force with which it would act on a string, the length of which is R feet, would be _c_ × R; and if instead of revolving in one second it revolved in T seconds, the force would be (_c_ × R)/T^2; and if the revolving mass were W lbs. the force would be C = (_c_ × W × R)/T^2. This formula includes the entire theory of centrifugal force. But it can be shown that the number expressed by _c_ is 1·226, and consequently C = (1·226 × W × R)/T^2. It is often more convenient to use the number of revolutions made in a given time than the time of one revolution. Let N then express the number of revolutions, or fraction of a revolution, made in one second, and we shall have T = 1/N. Therefore C = 1·226 × W × R × N^2.