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GYROSCOPE. 



GYROSCOPE. 



the latter axis, or polar axis of the place, cannot affect the apparent 

 motions of a pendulum suspended at the equator of that axis, which is 

 the great circle through the place of observation. The pendulum will 

 therefore be affected only by a motion round the axis through the 

 place, which is the case first investigated. And the amount of this 

 motion will evidently vary as the sine of the latitude. Hence the time 

 of apparent revolution of the plane of oscillation=a sidereal day x sine 

 of latitude. 



The gyroscope is an application of the well-known principle of the 

 dynamics of a rigid body, that if a mass be set in rotation freely hi 

 space, it will, unless it be disturbed, preserve in air cases its original 

 plane of rotation, and to effect this, will even overcome slight impedi- 

 ments. It will be easily seen from fig. 2, and from the description 

 given above of the instrument itself, how the rotation of the earth is 

 hence deduced. It was in September, 1852, that M. Foucault presented 

 to the Academy of Sciences an account of the gyroscope. In this 

 apparatus also there is a fixed plane below which the earth turns, and 

 as it carries with it the spectator, causes it to appear to him as if the 

 plane of the disc actually revolved. 



The disc has the mass composing it disposed as much as possible 

 around its edge, in order that, when put in rotation, it may revolve for 

 a longer time than it otherwise would. 



Since all the particles of this rotating disc have a tendency by virtue 

 of centrifugal force to fly off at a tangent to the circumference of the 

 disc, in the plane in which it is vibrating ; hence, any attempt to change 

 the direction of this plane in space will be opposed by part of the 

 force with which, were they not restrained by the law of cohesion, 

 each particle of the disc would fly off. 



Mr. Wheatstone has described in a paper, read before the Royal 

 Society in April, 1854, a form of the gyroscope, fig. 1, which we will 

 briefly describe, as the experiments performed with it will be very 

 easily transferred to the more perfect form, fiij. 3. It is thus con- 

 Fig. 3. 



structed : a beam is capable of moving freely round a horizontal axis, 

 which is itself moveable round a vertical axis, so that the beam may 

 move in any direction round a fixed point ; at one end of the beam is 

 fixed a horizontal ring which carries a heavy disc, the axis of rotation 

 of which is in a line with the beam ; at the other end is a shifting 

 weight by means of which the equilibrium of the beam may be esta- 

 blished or disturbed at pleasure. 



If the beam be brought into equilibrium, and the disc be rapidly 

 rotated, as by means of a string quickly unrolled from its axis, the 

 beam will have no tendency to displace itself hi any direction. But if 

 we now disturb hi any way the equilibrium, moving the weight towards 

 the centre of the beam, and thus causing the due to preponderate, 

 thn, if the disc rotates from right to left, the beam will move round 

 the vertical axis also from right to left, and vice rend. If we cause 

 the equipt/iit to preponderate, contrary effects will take place. 



The velocity of rotation of the beam round the vertical axis in- 

 creases in proportion to the disturbance of the equilibrium. Notwith- 

 standing too the increased or diminished action of gravity on the disc, 

 its axil of rotation always preserves the same inclination to the vertical 

 axis at which it was originally placed. When the equilibrium is dis- 

 turbed while the disc is at rest, the beam being placed in any other 

 position than the vertical, gravity acts so as to turn it round a horizontal 



ARTS AND SCI. DIV. VOL. IV. 



axis ; but when the disc is in motion, the usual effect of gravity dis- 

 appears, and there is substituted for it a continued rotation round a 

 vertical axis, that is, round an axis perpendicular to the plane contain- 

 ing the axes of the two impressed rotations. 



A similar composition of forces takes place when the disc is caused 

 to rotate while the equilibrium of the beam ia preserved, by impressing 

 on the beam a rotation round a vertical axis. When the disc rotates 

 from right to left, the slightest pressure tending to produce rotation 

 round the vertical axis in the same direction, causes the end of the 

 beam carrying the disc to ascend, and a pressure in the opposite direc- 

 tion causes it to descend, that is, the beam is constrained to move 

 round" a horizontal axis perpendicular to the vertical plane containing 

 the two axes of impressed rotation a case exactly analogous to the 

 preceding. The beam ascends and descends in like manner, after rota- 

 tion has spontaneously taken place round the vertical axis in conse- 

 quence of the equilibrium being disturbed, whenever this rotation is 

 in any way accelerated or retarded. As the centre of gravity of the 

 beam is below its point of suspension, even when equipoised, it is in 

 perfect equilibrium only when it is horizontal, consequently, if it be 

 elevated above or depressed below this position, it will endeavour to 

 resume it, tending to produce in the two cases rotation in opposite 

 directions round a horizontal axis ; the rotation of the disc combined 

 with this tendency, gives rise, as in the other cases, to continued rota- 

 tion round a vertical axis ; the direction being determined in a similar 

 manner. 



In all these experiments the axis of the rotating disc has been sup- 

 posed to be fixed in the prolongation of the beam ; but now let us suppose 

 this axis placed at any inclination and any azimuth with respect to it, 

 it is evident that the inclination of this axis should produce no differ- 

 ence in the character, but merely in the intensity, of the effects, since 

 hi any inclined position of the disc its rotation is resolvable into others, 

 one perpendicular to the beam, and the other, which produces no effect, 

 in a plane containing it. When the axis of the rotating disc is vertical 

 and at right angles to the beam, no rotation on the vertical axis ought 

 to take place in any case ; but it is found that, although the beam be 

 horizontal and in equilibrium, there is a motion round the vertical 

 axis in opposite directions, according as one or other end of the axis of 

 the disc is uppermost. This motion, however, is evidently due merely 

 to the friction of the pivots dragging the beam to a corresponding 

 motion ; because whether it be accelerated or retarded no change is 

 produced in the horizontality of the beam. 



To take a few more experimental illustrations : let the system of 

 rings carrying the disc be removed from the rest of the apparatus, and 

 let the inner ring be allowed to move freely within the outer. Having 

 set the disc in rotation, hold the outer ring at the end of the diameter 

 which is in the plane in which the axis of motion of the disc is free to 

 move ; then giving to the outer ring a tendency to rotation round that 

 diameter, in whatever position the axis is, it will fly to place itself in 

 the fixed axis thus determined, and rotation will take place round it in 

 the same direction ; while considerable resistance is felt so long as the 

 moveable axis is changing its position ; but when once it coincides 

 with the fixed axis, the rotation of the external ring is easily effected. 

 So, also, a slight alternate motion of the outer ring, tending to give it 

 rotation in opposite directions, will cause a continued rotation of the 

 moveable axis ; and similarly, when we try to rotate the outer ring 

 round an axis perpendicular to its plane. In all cases, when the axis 

 of the rotating disc is free to move in a plane, and the outer ring is 

 constrained to rotate round a line in this plane, the moveable axis will 

 place itself so as to coincide with that line, and so that the disc shall 

 rotate in the same direction as the ring ; if the fixed axis be in a differ- 

 ent plane, the moveable axis will assume permanently that position hi 

 its plane which approaches nearest to the former. The moveable axis 

 is thus apparently attracted towards the fixed axis, if the rotations are 

 in the same direction, and repelled from it if they are in opposite 

 directions. 



In all these experiments the free and constrained axes of rotation 

 are supposed to intersect, but in Fessel's apparatus they are distant 

 from each other. In this case, the rule must be thus modified, that 

 the free axis of rotation tends to place itself parallel to the constrained 

 axis, or as nearly so as possible. By this principle all the results are 

 easily explained. Thus, when the equilibrium of the beam is destroyed 

 gravity tends to make it rotate round a horizontal axis ; the axis of the 

 disc tries to place itself parallel with that axis, but being unchangeably 

 at right angles to it, the tendency to place itself there causes rotation 

 round the vertical axis. 



Again, fix the outer ring horizontally, and loosen the inner ring, 

 keeping them, however, both in the same plane ; then, on moving the 

 beam round the vertical axis, the axis of the disc will fly to place itself 

 parallel thereto. The rings being placed in the vertical plane, the same 

 result will follow, if the beam be moved in a vertical plane, that is, 

 round a horizontal axis of rotation. 



Before describing a few more experiments with the gyroscope, we 

 will again revert to its theoretic action, in order to explain more 

 clearly the phenomena. We quote from a pamphlet, by Mr. Ladd, of 

 Chancery-lane, accompanying his instrument : 



" Every particle of a disc revolving on an axis has a tendency to fly 

 therefrom, on account of centrifugal force ; but diametrically opposite 

 are the similar particles exerting the same influence on the axis. This 



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