From a mean of numerous experiments with a hemisphere whose diameter was 6.375 inches, and which revolved with velocities varying from 3 feet to 20 feet per second, Dr. Hutton found that the resistance of the air against the flat side was to the resistance against the convex side as 2.48 to 1 : by theory it should be as 2 to I only. From experi ments made with hemispheres of different magnitudes, also with a whole sphere, a cone, and a very short cylinder, it was found that the resistance experienced by similar surfaces (the velocities varying from 10 feet to 20 feet per second) were nearly proportional to the surfaces, increasing a little above that proportion with the greater surfaces; and that the resistances on the same surface varied, at a mean, with the 2.04 power of the velocity, gradually increasing with the increasing velocities. When a hemispherical or conical surface was acted on by the air, the resistance was less than that which was experienced by a plane surface of equal diameter ; but the sharper surface had not always less resistance than one which was round : the convex surface of a hemisphere, for example, experienced less resistance than that of a cone, contrary to the result of theory. The resistance on the base of a cone was to the resistance on the convex surface as 2'3 to 1 : by theory it should be as 4 to 1. The resistance on the base of a short cylinder was less than that on the base of a cone, though the areas were equal ; also, on account of the different manner in which air acts on the posterior surfaces, the base of a hemisphere experienced less resistance than that of a cone, and the convex surface of a hemisphere less than that of a whole sphere of equal diameter.
The whirling-machine invented by Ferguson is a frame or box of wood, containing a wheel about 2 feet in diameter, on each side of which is a pulley about 6 inches in diameter ; the axes of all are in vertical positions, and, by strings passing over the wheel and pulleys, the latter are made to revolve on turning the wheel by means of a handle. The machine was intended to exhibit, in a popular manner, the principal effects of centripetal or centrifugal forces, when bodies revolve in the circumferences of circles.
On the axle of each pulley there is fixed, at its middle point, a bar of wood in a horizontal position, and on this a small plate or carriage of brass is made to elide easily along two horizontal wires extending from the centre to one extremity of the bar : a silk line attached to this plate passes under a small brass pulley near the centre of the bar, and over a similar pulley fixed in a brass frame, about 6 inches above the first pulley ; the line is aftentards attached to a brass plate or carriage, which is capable of sliding up or down in the brass frame, according as the first plate moves from or towards the centre, along the wires on the horizontal bar. A given weight is placed on this first
carriage at any distance from the centre, and the pulley, to whose axle the bar is fixed, is made to revolve by turning the handle on the axle of the wheel : then, on placing such a weight on the carriage in the brass frame as will just allow the former weight to recede in conse quence of the centrifugal force which that weight with its carriage acquires by the revolution, the Weight in the frame, including that of its carriage, is to be considered as the equivalent of the centrifugal force.
For example, let the two pulleys be of equal diameters, and let each be made to carry on its axle a horizontal bar with a sliding plate or carriage: then, if a weight of 6 ounces, including the carriage, be placed at 3 inches from the centre of Motion on one bar, and 2 ounces, including the carriage, on the other bar, at 9 inches from its centre of motion ; upon making the two bars revolve rapidly, the centrifugal forces will cause any equal weights on the carriages in the two brass frames to rise to the tops of those frames at the same instant. Here the velocities of rotation are represented by 3 and 9, and the weights by 6 and 2, so that the ratio compounded of the velocities and masses is one of equality ; and this is considered as verifying the proposition that if bodies revolve in circular orbits, the centrifugal forces are equal when the products of the masses and velocities are equal. Again, let the diameter of one of the pulleys be twice as great as that of the other, so that when the bars are placed on the axles and are made to revolve by turning the wheel, the angular velocity of one may be half the angular velocity of the other : then, if any equal weights, for example, be fixed ou the carriages which slide on the two bars, at equal distances from the centres of motiorwpand if there be placed on the carriages in the brass frames above those centres, weights, including those of the carriages, such that the weight above the larger pulley may be one-fourth of that which is above the smaller pulley ; the cen trifugal forces arising from the revolutions will allow these weights to be raised at the same instant, proving that both the revolving bodies are retained in circular orbits. Here the angular velocities of the revolving bodies are as I to 2, and the weights in the frames, which represent the centrifugal forces, are as 1 to 4 ; and the experiment shows that when equal bodies revolve in equal circular orbits, the centrifugal or centripetal forces are to one another as the squares of the angular velocities.
It is easy to understand that such experiments may be varied so as to exhibit all the phenomena of circular movements.