182 AN EMPIRICAL STUDY OF GYRATING BODIES. 



those of the moon, the nutational effect of the former are 

 less than those of the latter. 



Prof. Nichol, in his Physical Sciences, says : "If the 

 moon's orbit had been coincident with the ecliptic we 

 should simply have had a luni-solar precession.' 1 



It is trne that the inclination of the moon's orbit to 

 the ecliptic gives it, for half of the time, a greater tilting 

 power than if it were always inclined 23^° to the earth's 

 eqnator (in the ratio of the sine of 29° to the sine of 23£°), 

 and hence the nutational movement would be less than 

 at present if the moon's orbit were in the ecliptic. But 

 so long as the lunar pull varied, nutation would go on. 



It is easy to imagine a system in which the moon, al- 

 though in the ecliptic, would cause a more rapid and 

 deeper nutation than at present. If the eccentricity of 

 the moon's orbit were so increased that it was much 

 nearer at perigee than at present, or if, with present ec- 

 centricity, its mass were greatly increased, such an ef- 

 fect would follow. 



CONCLUSION. 



All the phenomena of precession and nutation are cor- 

 related by this new law, as the effect of that principle 

 with which we started in the beginning of the study of 

 the gyroscope ; to wit, a body in motion will continue 

 to move in the same direction and without decrease of 

 momentum till some force directly opjDoses it. If to 

 this we add : Action and reaction always coexist and are 

 equal, we have the key to all the phenomena presented 

 by gyroscopic bodies. 



XOTE ON NUTATION. 



It may be thought that the experiment in which the 

 gyrating body rises as the tilting force (the weight ap- 

 plied) grows less, contradicts that which I have else- 

 where spoken of as the foundation principle of gyra- 

 tional action, to wit: no descent, no gyration. 



lee 



