THE PRECESSION OF THE EQUINOXES AND NUTATION AS RESULTING 

 FROM THE THEORY OF THE GYROSCOPE. 



In a paper published in the American Journal of Science, in 1857, and in Bar- 

 nard's American Journal ot" Education' [No. 9] of the same year, I remarked: — 



" 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 idtimate analysis, the phenomena, doubtless, are identical," &c. 



It is the object of the present paper to deduce the analytical expressions of this 

 phenomenon directly from the theory of the gyroscope. 



A brief summary of the processes used and results arrived at in the paper referred 

 to is necessary as a preliminary. 



Let A, B, (\ D (Fig. 1) be a solid body of any shape, retained by the fixed point 

 (within or without its mass). Ox, Oy, and Oz are the three co-ordinate axes, 



Tiff. 1. 



fixed in space, to which the motion of the body is referred. Ox~^, Oy,, Oz^ are the 

 ihxee principal axes belonging to the point 0, and wliich, of course, partake of the 



' "TliP Plicnomcna of the Gyroscope Analytically Examined." 

 October 1871. 



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