202 Mb. Edmund Hunt on Eotatory Motion. 



to be rotating, so as to move (in the absence of precessional action) 

 as just described, but with its peg point fixed, the precessional action 

 would cause its centre of gravity to move round in the direction north, 

 east, south, &c. This direction is the same as that of the change of 

 inclination which the rolling tendency of the point would cause (the 

 mere translation of the entire top not affectuig the precessional action), 

 therefore the rolling tendencj'^ must tend to accelerate the precessional 

 motion, and consequently cause the top to rise. If the point of the 

 io^ Jits a hollow in the supporting surface, its friction m the hollow 

 cannot make the top rise ; but if the hollow is somewhat larger than 

 the point, the latter will rise up the side of the hollow and move round 

 at a determinate level ; and the friction will act as on a level surface. 



1 exhibit a cm-ious experiment to show that much caution is neces- 

 sary in experimenting on the effects of friction. The gyroscope in its 

 single ring has a bent peg fixed to the ling close to one end of the 

 spindle. "When set spinning, the instrument supports itself on the peg, 

 the ring not turning with the fly-wheel, but merely partaking of the 

 conical precessional motion. The friction of the pivots acting on the 

 ring tends to accelerate the precessional motion, and thereby cause the 

 instrument to rise ; the friction of the peg point on the horizontal sup- 

 porting surface tends to retard the precessional motion, and thereby 

 cause the instrument to fall. If the peg rests on a soft substance, such 

 as soft deal or caoutchouc, the instrument falls ; if it rests on a hard 

 surface, such as glass, the instrument rises. 



Referring to fig. 14 in the plate illustrating my former paper : — If a 

 weight be fixed to the underside of the lever B, below the axis crossing 

 the ring d, so as to lower the centre of gravity of the whole, a great 

 variety of experiments can be shown by starting the instrument in 

 different ways. If the weight c is adjusted, so that thj whole is in 

 efjuilibrium with the lever horizontal ; then if the gyroscope A is raised 

 or lowered and started with a suitable determinate impulse, its 

 path win be a species of oval with its longest diameter vertical. The 

 other experiments are too numerous to detail. 



In my former paper, I mentioned that a demonstration of the funda- 

 mental theorem of the composition of rotatory motions was given in 

 Airy's Mathematical Tracts. There are other demonstrations extant, 

 but most of them are complicated, and need the aid of spherical 

 trigonometry. Poinsot's method of couples perhaps affords the simplest 

 and most elegant demonstration, but it necessitates a tedious wading 

 through numerous preparatory propositions. I beg to offer the fol- 

 lowing theorem as enabling us to directly apply to the case, the well 

 known " rarallologram of Rectilinear Velocities." It is capable of 



