WHIRLING-MACHINE is an apparatus invented by 3I r. Robins for the purpose of determining the resistance of the air against bodies moving with velocities less than those for which the resistance can be determined by the Ballistic pendulum.
It consists of a brass cylinder, 2 inches in diameter and about 6 inches long, which is fitted in a frame so as to be capable of turning freely with its axis in a vertical position between the base of the frame and a horizontal plate of wood or metal which is supported above the base by four small pillars. The axle of the cylinder, which is of steel, passes through that plate, and terminates about 4 inches above it. To this is attached horizontally, and immediately upon the plate, a thin arm of wood or metal about 4 feet long, and formed with what is called a feather edge on each side: to the extremity of this arm is affixed the object which is to be used in the experiment, and a wire proceeding front the top of the steel axle to the extremity of the arm serves to prevent the latter from bending by its weight.
A silk line made fast at one end to the surface of the cylinder is in part wound round the Latter ; the line then passes over a pulley fixed in a vertical position at the opposite extremity of the machine, and to its lower end is attached sonic given weight : the descent of the weight causes the cylinder, and consequently the object at the extremity of the arm above mentioned, to revolve about the vertical axis during the experiment. The weight at the end of the line being acted on by gravity descends at first with an accelerated motion, and consequently the circular movement of the object at the extremity of the bar is also accelerated; but after a few revolutions the resistance of the air against the object becomes very nearly equal to the weight of the descending body, and from that time the descent of the weight and the revolving motion of the object become, as to sense, uniform. When this uniform or terminal velocity is obtained in any experiment, the descending weight evidently expresses the amount of the air's resistance together with the inertia of the machine.
An instrument of this kind was much used by Dr. Hutton, of Woolwich, during the years 1786 and 1787, in his researches concern ing the resistance experienced by military projectiles in passing through the air ; and the objects which this mathematician applied at the extremity of the revolving arm were hemispheres of pasteboard.
Any one of these he could at pleasure dispose so that either its con vex or plane surface might be resisted by the air : there was also provided a flat plate of lead equal in weight to the hemisphere employed, which could be fixed to the arm when the hemisphere was removed, for the purpose of ascertaining the resistance opposed by the air to the motion of the arm itself.
The radius of the circle described by each hemisphere in its revolu tion is measured from the axis of the cylinder to the centre of the sphere, of which the revolving object is the half, and the radius of the cylinder is measured from the same axis to the middle of the silk line passing round the surface : let the latter radius be represented by r, and the former, when any one of the hemispheres is applied, by a. The time is marked by a stop-watch at the end of each revolution, and the differences between them are taken for the times of the revolu tions. After a few revolutions the differences are very nearly constant; and a mean of ten or these nearly constant differences may be considered as the time of revolution, when the motion is uniform in consequence of the equality of the resistance and inertia to the weight of the descending body ; let this weight be represented by w.
In order to discover the resistance due to the inertia of the machine and the action of the air upon the arm (the plate of lead, with its plane in a horizontal position, being fixed at the end of the arm), different weights are attached to the silk line, till some one is found which causes the srm to revolve uniformly in the same time as the hemisphere may have been observed to revolve when its motion was uniform. This weight, which may be represented by w, is evidently the equivalent of that resistance and inertia ; and the difference w—w is the value of the air's resistance against the anterior surface of the revolving hemisphere only. The velocity of the latter is measured by the length, in feet, of the are described by its centre in one second, and the weight or resistance w—w is supposed to be applied at the cir cumference of the cylinder, to which the silk line is a tangent. This term must consequently be multiplied by in order to reduce it to the value of that which would be equivalent to it if applied at the centre of the revolving object.