THEOREM IN MECHANICS. 27 
land, Stévin 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- 
