54 



axis KL, will now produce its maximum effect upon the 

 same line of particles when the sphere revolves about 

 the axis HF, and the sphere will revolve with an accele- 

 rating velocity. 



From this reasoning it seems to follow, that if any 

 sphere ADBC, Fig. 6, revolving about an axis AB, with a 

 velocity however great, is acted on by a constant force, how- 

 ever small, tending to make it revolve about the axis CD, 

 the sphere will revolve about a third axis perpendicular 

 to both AB and CD, until AB is brought to coincide with 

 CD. 



If the force at A (Fig. 4), instead of acting in a fixed 

 direction in space AR, acts always in a line at right 

 angles to the plane of the lamina AFBH, the sphere will 

 continue revolving about the axis AB in the direction of 

 the arrows MM'. The oscillatory motion of the axis AB, 

 compounded with this rotation, will cause the pole to de- 

 scribe an undulating line about the circumference of a 

 small circle, whose diameter will depend on the intensity 

 of the disturbing force applied at A. 



II. APPLICATION OF THE PRINCIPLE TO PLANETARY MOTIONS. 



Let S (Fig. 7) be the sun, and AMBM' the earth. Let 

 the whole sphere AMBM' be divided into laminas AB, &c., 

 whose planes are parallel to each other, and at right 

 angles to SC. If the whole of the matter of each lamina 

 be collected into its centre of gravity, the equilibrium of 

 the system will remain unchanged ; the sphere will thus 

 become a line of material particles M' M, whose centre is C. 



Now, because the particle at M' is nearer to S. it will 

 be more strongly attracted than an equal particle at M. 

 The same may be said of every pair of particles equi- 

 distant from C, hence the centre of gravity G, of the 

 Avhole line M'M, will always be nearer than its centre C 

 to the sun S. 



