THEOREM IN MECHANICS. 27 



land, Stevin and Huyghens ; in Italy, Galileo and Tor- 

 ricelli ; in England, Newton and Maclaurin ; in Swit- 

 zerland, Bernouilli and Euler ; in France, Pascal, Va- 

 rignon, D'Alembert, Lagrange, and Laplace. 



Well, Gentlemen, those are the illustrious personages 

 amongst whom Carnot made a place for himself by his 

 beautiful theorem. 



Perhaps, indeed, I ought to be afraid that, by insisting 

 any longer on the inconvenience of abrupt changes, I 

 may inspire my audience with the desire that I should, 

 notwithstanding every inconvenience, pass "abruptly" to 

 another subject ; nevertheless, I will hazard a few more 

 words. 



We have just been talking frequently of lost force ; the 

 expression is correct when we compare the actual effect 

 of a machine with that which it might have produced if, 

 all other circumstances remaining the same, the construc- 

 tor had carefully avoided sudden changes of speed ; but 

 it must not be imagined that any force, or fraction of a 

 force, can be ever annihilated, in the grammatical accep- 

 tation 'of the word ; all that which is not found in the 

 useful effect produced by the motive power, nor in the 

 amount of force which it retains after having acted, must 

 have gone towards the shaking and destroying of the 

 machine. 



This last remark was necessary for the appreciation of 

 the eminent and incontestable services which Carnot's 

 theorem has already rendered and will render more and 

 more to art and industry. If I were not afraid of the 

 incredulity which would, at first sight, attach itself to my 

 words, I would add that this same theorem of analysis and 

 mechanics has also played a great part in the numerous 

 events of our Revolution, whose character Carnot's deter- 



