70 J. G. Barnard on the Qyroscoiye.- 



tlie opposite or furtlier side, to the right^ (as tlie arroAVs h and a.) 

 Hence the joint effect is to press the axis G (7 from its vertical 

 plane CGrC*^ horizontally and towards the eye* Eeverse the di- 

 rection of axial rotation and the curves A A' and BB' will be 

 the same, except that AA^ would be on the near, and BB on 

 the remote side of the axis G (7, and the direction of the result- 

 ing pressure will be reversed. 



■ A projection on the horizontal plane would likewise illustrate 

 this deflecting force and show at the same time that there is no 

 resistance in the plane of motion of ilie axis^ and that the whole 

 effect of these deflexions of the paths of the different material 

 points, is a mere iyiterchange of living forces between the different 

 material points of the dish ; but it is believed that the foregoing 

 illustration is sufficient to explain the origin of this force, whose 

 measure and direction I have analytically demonstrated. 



It may be remarked, however, that the intensity of the force 

 will evidently be directly as the velocities gained and lost in the 

 motion of the particles from one side of the axis to the other; 

 or as the angular velocity of the axis^ and as the distance, k^ of the 

 particles from that axis. It will also be as the number of particles 

 which undergo this gain and loss of living force in a given time; 

 or as the velocity of axial rotation. Considered as applied nor- 

 mally at G to produce rotation about any fixed point in the 

 axis, its intensity will evidently be directly as the arm of lever 7c, 

 and inversely as the distance of G from (y). Hence the meas- 



ure of this force already found, from analysis, g'= — nvs. 



In the foregoing analysis, the entire ponderable mass is sup- 

 posed to partake of the impressed rotation about the axis of fig- 

 ure Oz^ ; and such must be the case, in order that the results we 

 have arrived at may rigidly apply. Such, however, cannot be 

 the case in practice. A portion of the instrument must consist 

 of mountings which do not share in the rotation of the disk. 

 It is believed the analysis will apply to this case by simply in- 

 cluding the whole mass^ in computing the moment of inertia A 

 and the mass M] while the moment ^represents, as before, that 



of the disk alone. 



In this manner it would be easy to calculate w^hat amount of 

 extraneous weight (^vith an assumed maximum depression u)y the 

 instrument would sustain, with a given velocity of rotation. 



The analogy between the minute motions of the gyroscope 

 and that grand phenomenon exhibited in the heavens,— the 

 " precession of the equinoxes"— is often remarked. In an ulti- 

 mate analysis, the phenomena, doubtless, are identical; yet the 

 immediate causes of the latter are so much more complex, that 

 it is difficult to institute any profitable comparison. 



I 



