GYROSCOPE. 



OYROSCOPE. 



force, influencing the axis all around, cauam the rotating Iwdy to tend 

 to preserve iti plane uf roUtioo. and with the sue of the rotating body 

 it requires a cotuidenble increasing force to displace iU axis. This 

 fact being well understood. present* tha key to the explanation of all 

 the experiiiMiiU that the instrument is capable of exhibiting. 



When the disc B u rapidly routing, and the stand D it turned, the 

 axis 1 1 uf the din will constantly point in tha auiie direction. The 

 friction of tha vertical axis mint be considered u nothing ; therefore, 

 the tendency of the due to keep the plane of rotation U not impeded, 

 and no effect u produced upon the name ; and similar U tha case whan 

 tha gyroscope U taken by the stand and moved in any direction. Even 

 an inclination of the stand D in the plane of the axis will produce no 

 effect : that is, if the axis stand horizontally, it will continue to do so ; 

 but attempting to turn the semicircle c to the right or to the left hand, 

 the axis of the disc will take up such a position as to coincide with the 

 new axis which tha experimenter is endeavouring to confer. In such 

 instance two forces are simultaneously summoned into activity the 

 force of the hand, and the tendency of the disc to keep the plane of 

 rotation ; and the former being infinitely greater than uut latter, the 

 disc can only move in the prescribed direction. If the semicircle c and 

 the gymbal A be connected by means of a milled headed screw K, no 

 resistance will be felt either way. The same will be the case in one 

 direction if the quadrant a be attached to the semicircle c ; but then 

 some other phenomena occur, because the two axes are at right angles 

 with each other. The impossibility of the one force exerting its 

 influence, leaves the other force free to act, as though the other were 

 not in existence ; but the force is only apparently lost, for a slight 

 push against the semicircle will cause the instrument, as it were, to 

 revolve round the stand on the table : that is to say, the instrument 

 lifts a little from the table, and plays around the surface of the stand. 

 In this manner the force that is stopped by the quadrant shows again 

 at the bottom of the stand. If a weight v be suspended in the 

 continuation of the axis on the screws L L, it will be unable to draw 

 the same down, but will impart a slow horizontal motion to the 

 spindle M. This is a beautiful and important experiment : if the 

 rotation of the disc be stopped, the weight will draw it down ; if the 

 horizontal motion of the semicircle be stopped, the weight will draw 

 the disc down, however rapid may be the rotation ; that is, remove the 

 possibility that the compound effect can take place, and the one that 

 is left at liberty will act as though the other had no existence. This 

 remarkable fact bears analogy to some of the most important truths 

 of the ' Mecanique Celeste.' If the rotation of the earth were stopped 

 it would fall upon the sun, and if the possibility of the orbital 

 revolution of the earth round the sun were stopped, it would 

 fall upon the sun, notwithstanding its axial rotation. When the 

 ring A with the rotating disc B is detached from the semicircle c, 

 by lifting the screw K, and suspended by a string on the screw-head L, 

 the disc will stand horizontally, and whilst so suspended it will revolve 

 slowly round the suspending string as a centre of motion ; the tendency 

 of the rotating body to keep the position of its axis is so great as to 

 resist the action of gravity on the mass, even if an extra weight be 

 suspended on the opposite screw-head L. Another modification of the 

 experiment is to let the arrangement rest on a hook R in the con- 

 tinuation of the axis in a hollow attache*! to the stand. If the weight 

 be changed to the opposite side, the semicircle will turn in the opposite 

 direction. The rotating disc freely moved in all directions by the hand, 

 will furnish a very good proof of the resisting force which is opposed 

 to any endeavour to change the plane of rotation ; and if placed with 

 the screw-head L on the table, it will keep itself upright like a spinning- 

 top; and if the friction between the screw-head and the table be 

 greater than between it and the point on which the axis turns, the 

 ring will remain stationary. Close to the disc on the axis is a milled 

 wheel, which may serve as a means of calculating the number of revo- 

 lutions in a second. If a card be held against it, a musical tone is 

 produced, which will rise higher with the rapidity of the rotation ; if 

 tha note be taken, and the number of the teeth in the milled wheel be 

 known, the number of the rotations can be calculated by an acoustical 

 table." 



The gyroscope than, illustrates the following principles : 



1. That inertia is a property of matter in motion, as well as of 

 matter at rest. 



2. That tha power poaaeiaed by tha shots projected from rified guns 

 of resisting the influence of gravity, is due to the ?yro<o motion given 

 to the ball. 



3. That orbital and axial motions arc intimately connected, and 

 that the speed of one may regulate that of the other. 



4. That the condition of mutaMt equilibrium in which bodies 



remain at if rfooie (for example, a common top) u due to their 

 rotation. 



Hence the gyroscope exhibits in a marked degree the three laws of 



1. That a body at rest cannot move itaelf. 



2. That a body in motion cannot stop itself. 



3. That a body in motion cannot change the plane in which it is 

 rotating, any more than it can diverge from a straight line if it has 

 only a motion of trarulatio*. 



The mathematical explanation of the movements of the gyroscope is 

 founded on the two following principles, given by the Rev. W. Cooke, 

 in the ' Proceedings of the Royal Society,' for March, 1857 : 



I. When a particle U made to more ^^f* plne by any 



applied force, but in consequence of its connection with some rigid body 

 on the same side of the plane, loses some of iU momentum in a 

 direction perpendicular to the plane ; all the momentum so lost is 



imparted to the rigid body, which is consequently impelled 4 

 the plane. 



II. When a particle is made to move 1 > a plane by any 



applied force, but in consequence of ita connexion with some rigid body 

 ou the same side of the plane, receives an extra momentum in a 

 direction perpendicular to the plane ; all the momentum so gained is 



taken from the rigid body, which is consequently impelled -j Awards r 



the plane. 



Let the mass of the disc of the instrument be supposed compressed 

 into its circumference ; let its radius = r, and let it revolve round its 

 axis with a given uniform angular velocity = w. 



Masses wUl be represented by weights ; hence any accelerating force 



fg 

 f, is due to a pressure p, acting on a mass w, so that / = ^-, g being 



the accelerating force of gravity. 



The centre of gravity of 'the disc, axle, and ring which carries the 

 pivots of the axle, is -fixed, and the whole is inoveable about that centre 

 in any manner, subject to the condition that the line of the pivots of 

 the ring is always horizontal. Let the line of the axis be denoted by 

 II (see fig. 3), and be = . 



Let a given force r be applied at I , in the form of a weight sus- 

 pended there perpendicular to the plane A A, so that the disc may 

 describe an angle <f> round the lines of the pivots F in the time t, 

 whereby any two particles m and m' in the disc describe the two arcs 

 y and if simultaneously. Suppose the circumference of the circle A A 

 divided into four quadrants, and let m and m' be in the first quadrant, 

 so that >/' > // ; then, if the disc is supposed to revolve, a particle m is 

 carried from y to j*, so as to acquire an increase of velocity from the 

 plane A A, independently of the force F, and consequently (by the first 

 of the above principles), all the momentum so required by the par- 

 ticle is lost to the disc, ring, &c. ; which are '.thus impelled as by a 

 force in the direction opposite to that along y or y", so as to oppose the 

 rotation imparted by F, but to impart another round the centre of the 

 disc, in the direction A L K in the plane of the ring, that is, in a plane 

 perpendicular to that in which r acts. A force having the same 

 tendency is found, by means of one or other of the above principles, in 

 the other quadrants. Hence it may, without much difficulty, be 

 deduced by D'Alembert's prin<:i]>l that 



, = il|.in = (-} 



v\ r-w \ 2 / 



Thin value being periodical, and ranging between the limits o and 

 trap 



shows that the disc makes an oscillation of leas extent and 



duration, as the spinning of the disc is more rapid, that in, as M* is 

 made greater compared with -. ; and if F be a small weight, as is gene- 



rally used, the extent of the oscillation becomes insensible. The 

 theoretical ma.rimm of for a common instrument has been found 

 = 18'. 



That these oscillations do exist will be evident, if we consider 

 that the gyroscope, with the weight attached, becomes an ordinary 

 pendulum ; and the effect of the spinning is to disturb it* oscillation*. 

 and lessen their extent indefinitely, when the angular velocity f tin 

 disc is sufficiently great. 



