352 GYROSCOPE be directly proved. He says : " While using Troughton s top an idea occurred to me that a similar principle might be applied to the exhibition of the rotation of the earth. Conceive a large flat wheel, poised on several axes all passing exactly through its centre of gravity, and whose axis of motion is coincident with its principal axis of permanent rotation, to be put in very rapid motion. The direction of its axis would then remain unchanged. But the directions of all surrounding objects varying, on account of the motion of the earth, it would result that the axis of the revolving wheel would appear to move slowly." This suggested experiment was actually carried out in 1852 by M. Leon Foucault, although, in all probability, without any knowledge on his part of Mr Sang s suggestion. Already, in 1851, Foucault, in his famous experiment with the pendulum at the Pantheon in Paris, had shown how the constancy of the plane of a pendulum s vibration could be used to show the rotation of the earth, and now, in 1852, he applied the property of the " constancy of the plane of rotation " of a gyroscope for the same purpose. The name gyroscope was given to the instrument by Foucault at this time, and in order to perform the experiment successfully the instrument had to be constructed with the utmost exactness. The experiment was repeated at the Liverpool meeting of the British Association, and by causing a con siderable sensation in the scientific world at the time was the means of bringing the gyroscope into public notoriety. In Poggendorff s Annalen for 1853 there is a description of a gyroscope made some time before by Fessel, and about the same time we hear of various modifications of the instrument introduced by Profs. Baden Powell, Wheatstone,and others. Quite recently, in 1878, there has appeared in the Scientific American an account of a new form of gyroscope made by Mr G. M. Hopkins. In this instrument the heavy ft y- wheel is driven by an electric current after the manner of an electromagnetic engine, and so its rotation can be kept up for any length of time. The construction of the gyroscope will be readily under stood from fig. 1, which is engraved from a photograph of a large instrument made by Mr Sang. It consists of a fly-wheel, with a heavy rim accurately turned and balanced, which can rotate round an axis GO forming a diameter of the ring K. This ring also can rotate about the axis AF which is at right angles to GC, and is a diameter of the ring L. Similarly this ring L can rotate about the vertical axis Bli, which is perpendicular both to GC and AF, and forms a diameter of the ring M, which is screwed to the heavy sole-plate N. In order to suit certain experiments the ring M, by means of a clamp arrangement seen at X, can be turned round to make the axis BH inclined at any angle with the vertical. With this instru ment the following among many interesting experiments may be made. 1. Either by a large fly-wheel and band, or by running out a long cord coiled several times round the V-grooved wheel on the end of the axis, let a very rapid rotation be given to the fly-wheel round the axis 00, and in the positive direction (that is, counter- clock-wise as seen from C). Such a rotation can readily be given so rapid as to last a long time. While so revolving let a weight be placed at G so as to cause a rotation round OA, also in the positive direction, and it will then be observed that a slow rotation of the whole mass takes place about the vertical axis OB, but in the nega tive direction. If the weight be put at C, the wheel rotating as before, the rotation round OB will be in the positive direction. Reversing the rotation of the wheel will in both cases produce a reversal of the rotation round OB. 2. The fly-wheel still rotating in the positive direction, Lst a positive rotation be given to the ring L round OB, and immediately the axis of the wheel OC will tilt up, rotating in the positive direc tion round OA till it reach the vertical position, where it will remain, and then it will be observed that the fly-wheel is rotating in the positive direction round OB. Should the axis OC, in con sequence of inertia, be carried a little past the vertical, and the direction of rotation round OB be then suddenly reversed, the axis OC will continue to revolve in the positive direction round OA, till it reaches the vertical pointing downwards, when it will again be stationary, and the wheel will now be rotating in the negative direction round OB. By gently oscillating the ring L at the instant the axis of the fly-wheel is passing the vertical, a continuous rapid rotation round OA can be given to the ring K carrying the rotating fly-wheel with it. 3. Let the fly-wheel be now made stationary, and, while in this position, let simultaneous rotations in the positive direction be given round both OA and OB ; the fly-wheel will then be observed to begin to move in the negative direction round OC. The explanation of all these experiments follows readily from the theory of the composition of rotations round different axes. Let the angular velocities about OA, OB, OC, be &, p, a respectively. If simultaneous angular velocities <r and be given about OC and OA in the positive direction, these can be compounded into an angular velocity about a new axis 01, which divides the angle AOC into two parts such that a sin COI sin COI ^ = sln^Ol = c^COl = tau COI = tan (suppose). 01 is, therefore, the position of the instantaneous axis, and as OC will always tend to coincide with it, OC will move round the axis OB in the negative direction. It will be noticed also that, -a remaining the same, tan will be less as a is greater. This shows that the rotation round OB, or the motion in azimuth, will be slower as the speed of the fly-wheel is greater. This accords with experi ment. In precisely the same way by considering simultaneous angular velocities about OC and OB and OA and OB, can experi ments 2 and 3 be explained. Perhaps the most common form of gyroscope is that which has been largely sold under the name of the gyroscope top. It is a modification of the gyroscope intro duced by Fessel. In it the ring containing the rotating wheel is either supported on a vertical pivot at the end of the axis, or simply held suspended by a string attached to the same point, as represented in fig. 2. In this case, when the wheel is rapidly rota- Fig. 2. ted, and its axis initially inclined at an angle with the vertical, a slow motion round the vertical axis is observed to take place. This rotation is accom panied by a feeble nutation of the axis, which is unobserv- able by the eye so long as the wheel rotates rapidly. The rotation in azimuth would continue uni form if the velocity of the wheel re mained constant, but it grad ually increases in speed, the nuta tion at the same time . . Fig. 3. becoming more ap parent as the velocity dies away, till the gyroscope finally
settles with the axis of the wheel in the direction of the