14 



PRECESSION OF THE EQUINOXES AND NUTATION. 



almost all lonus of projectiles) passes ahovc, not tlirougli, the centre^ of gravity 

 (J. We have then the essential conditions of gyration, viz., a solid of revolution 

 revolving rapidly about its axis, and a dynanuc "couple" (/. e., tlie inertia of the 



-""S^ 

 --t^ 



projoctil(>'s motion of translation acting through its centre of gravity, and the 

 resistance of the air acting tlirongh a point of the axis more or less distant from (j) 

 tending to turn the projectile upwards about a horizontal (or " equatorial") axis 

 through 7, and there is in fact, at each instant, an elementary gyration about a. line 

 through r/, parallel to R (the atmospheric resistance). If this line retained an 

 invariable direction, the integral effect of these elementary gyrations would be to 

 revolve do%vn the axis of the projectile, and we should ultimately find it assuming 

 horizontal and even sub-horizontal directions, lint such cannot be the case ; the 

 direction of the axis is no sooner deviated, laterally, from its original direction, than 

 a (nearly) corresponding change takes place in the direction of the resistance It 

 (since from the elongated form of the projectile, the direction of its motion follows 

 pretty nearly that of its axis) and in that of the line (parallel to R) about which 

 gyration takes place. The integral of such a series of elementary gyrations, accom- 

 panied by a corrrxpond'iDri horizontal angular motion of the line about which they 

 take place, is angular motion about a line perpendicular to the plane in which that 

 line shifts direction, that is, about a vertical. Hence the vertical direction (or 

 "elevation") of the axis of tlie projectile remains constant, or nearly so, while its 

 liorizontal direction undergoes a progressive angular precession (if I may so term 

 it), and the deviation of riiied projectiles is thus seen to have analogy with the pre- 

 cessi6n of the equinoxes.' 



In what precedes I do not profess to throw new light on a. subject so thoroughly 

 studied as the Precession of the Equinoxes; my object has been rather to make 

 evident the analogy that exists between " the minute motions of the gyroscope and 

 that grand phenomenon exhibited in the heavens," and to show how a common 

 analysis applies to both. 



' II is quite probal.le that there are other cause, of .Irviation, Ihe friction of the air bein- (iu case 

 of long ranges) one. E.vperimental facts are iicuacd for a full discussion of this .subject. 



