U PRECESSION OF THE EQUINOXES AND NUTATIOX. 



almost all forms of projectiles) passes above, not through, the centre of gravity 

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

 revolving rapidly about its axis, and a dynamic "couple" (I. e., the inertia of the 



projectile's motion of translation acting through its centre of gravity, and the 

 resistance of the air acting through a point of the axis more or less distant from </) 

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

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

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

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

 revolve down the axis of the projectile, and we should ultimately find it assuming 

 horizontal and even sub-horizontal directions. But 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 R 

 (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 corresponding 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 the projectile remains constant, or nearly so, while its 

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

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

 cession of the equinoxes. 1 



In what precedes I do not profess to throw now 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. 



1 It is quite probable that there are other causes of deviation, the friction of the air being (in case 

 of long ranges) one. Experimental facts are needed for a full discussion of this subject. 



