POWER OF MACHINES. 23 



chine ; well, endow this machine, if you please, with the 

 power of thought and all the perfections imaginable, and 

 the product of the weight multiplied by the height it will 

 have passed through in a given time, will be exactly 

 equal to that obtained by the employment of the same 

 force without any intermediate operation. The real 

 effect, then or, to speak more strongly, the effect of 

 any machine when properly estimated will never sur 

 pass that which the motive force was capable of pro 

 ducing naturally. Doubtless you can, if you like, with 

 a machine, raise enormous masses, of millions or thou 

 sands of millions of pounds ; but since the product of the 

 weight, multiplied by the height, must remain constant, 

 the height to which these masses can be raised in a 

 minute will be millions or thousands of millions of times 

 smaller than that to which your hand might have raised 

 one pound in the same time. 



Every one will now understand the true meaning of 

 that aphorism in mechanics, Machines lose in time or 

 velocity what they gain in power ! Give me a point of 

 support situated outside the earth, cried Archimedes, 

 and I will, with the aid of a lever, raise this earth, so 

 large and massive, by the mere effort of my hand. The 

 exclamation of the immortal geometer was marvellously 

 characteristic of machines, in so far as they give to man 

 the means of realizing effects otherwise millions of mil 

 lions of times beyond his natural strength ; but antiquity 

 would no doubt have admired it much less if any one, 

 analyzing phenomena more closely, as we have just 

 done, had added : Yes, doubtless, mathematically speak 

 ing, with his fulcrum and lever Archimides might raise 

 the globe ; but, after forty million centuries of continu 

 ous effort (for such a calculation is not, at the present 



