90 MECHANICAL RECREATIONS [CH. V 



fact that although, by means of a rigid lever and a fixed 

 fulcrum, any force however small may be caused to move any 

 mass however large, yet what is gained in power is lost in 

 speed — as the popular phrase runs. 



Montucla* inserted a striking illustration of this principle 

 founded on the well-known story of Archimedes who is said to 

 have declared to Hiero that, were he but given a fixed fulcrum, 

 he could move the world. Montucla assumed that a man could 

 work incessantly at the rate of 116 foot-lbs. per second, which 

 is a very high estimate. On this assumption it would take 

 over three billion centuries, i.e. 3 x 10" years, before a particle 

 whose mass was equal to that of the earth was moved as much 

 as one inch against gravity at the surface of the earth: to move 

 it one inch along a horizontal plane on the earth's surface 

 would take about 6,000 centuries. 



Stability of Equilibrium. It is known to all those who 

 have read the elements of mechanics that the centre of gravity 

 of a body, which is resting in equilibrium under its own weight, 

 must be vertically above its base : also, speaking generally, we 

 may say that, if every small displacement has the effect of 

 raising the centre of gravity, then the equilibrium is stable, 

 that is, the body when left to itself will return to its original 

 position ; but, if a displacement has the effect of lowering the 

 centre of gravity, then for that displacement the equilibrium 

 is unstable; while, if every displacement does not alter the 

 height above some fixed plane of the centre of gravity, then 

 the equilibrium is neutral. In other words, if in order to cause 

 a displacement work has to be done against the forces acting 

 on the body, then for that displacement the equilibrium is stable, 

 while if the forces do work the equilibrium is unstable. 



A good many of the simpler mechanical toys and tricks 

 afford illustrations of this principle. 



Magic Bottles\. Among the most common of such toys are 

 the small bottles — trays of which may be seen any day in the 

 streets of London — which keep always upright, and cannot 



* Ozanam, 1803 edition, vol. n, p. 18 ; 1840 edition, p. 202. 

 t Ozanam, 1803 edition, vol. n, p. IS ; 1840 edition, p. 201. 



