INVENTION OF THE BALANCE SPRINff, 377 



** confess that I am more flattered that M. Bernouilli has Account of the 

 " understood me, and has approved of me, than if I had ^""^^Jj^^'^g^ 

 ** only been barely understood by M. L. R. and Berthcud 



" Although M^L. R. has not understood me, he under- [f^Pg^^^'j^fg^ 

 " stands how to reason upon my theory, and censures the 

 ** course that I have taken." " Mr. B." " says he (page IS 

 *' of the Precis),". " supposes, from the beginning, that the 

 *' force of long and weak springs increases in a less ratio than 

 " the spaces described in its different tensions, since he con- 

 *' eludes from it that the great vibrations are, in this case, 

 ** slower than the small ones, and vice versa for the short and 

 ** strong spring : but he should not suppose, he should show that 

 ** the things are so in nature, of which it is only experiment 

 ** can instruct us.'* 



" I confess, that my Course has always been the opposite 

 " of the precept of M. L. R. In all my researches, I have 

 *' begun by adopting or assuming principles : I have endea- 

 " voured to sift these well, and have called experiments to 

 " my assistance with a view to confirm these principles. It 

 "• is true, that by this method we lose the advantage of 

 ** meeting sometimes with lucky chances, which discover 

 *' what we were not seeking ; but, in return, when we have 

 " made a discovery, we know to what principle we must 

 " attribute it, and are not in the state of him who lends one 

 " to it purely imaginary. 



" M. L. R. is not satisfied with attacking me on my pro- 

 " perty in my theory ; he wants even to attack the solidity of 

 " it, I have defended this property by facts, which prove 

 " that I could not know the researches of M. L. R. I shall 

 " now defend the solidity of it by reasons, at the risk of not 

 " being understood by the author of the Precis. 



" The criticism that M. L. R. has made on my theory, 

 " obliges me to enter here into some discussion. It is ne- 

 " cessary, first, to bring under one point of view all that he 

 i*, has said on the isochronism by the spiral, in his Memoire 

 " sur la Mesure du Temps en Mer, piinted in 1770, at the 

 " end of the Voyage de M. Cassinijils, 



- *' I have always discovered,'' (says M. L. R.) *' as the 

 ^* most famous philosophers and artists have done, that the 



Vol. XIV.— September, 1S06. C c c *' great 



