378 INVENTION OF THE BALANCE SPRING. 



Account of ihe " great vibrations were slower tlum the small ones." " (pagi? 



and Berthoud *' I have, in general, proved the contrary, and shall adduce 



J? wl"° " proofs of it hereafter." 



timepieces. ^ 



" I have likewise remarked" (adds he), *' that on a double 

 *' arc the difference was for the most part tt-o^^. This effect 

 ** comes, I believe, from the mass of the spring when bending 

 *' and unbending, or perhaps frojn the obstacles that it fnds 

 " internally when bending and unbending itself." (Ibidem). 



*' What are these internal obstacles? This explanation does 

 *' not seem very intelligible. M. L. R. must undoubtedly be 

 *' understood ; the internal properties" of the spring must be 

 *' known to him ; since, from 1750, he had announced to 

 *' us that he would forthwith give" ^^ A complete Treatise on 

 ** the Nature of ihe Spring, and on its Effects, &c." 



" M. I/. R. continues :" " It is only very lately that I 

 " have discovered, as I shall explain it more particularly,'* 

 " (We find this explanation no where in his Memoire)." 

 '* this fact, so important, which henceforth must serve as the 

 ** basis of the theory of watches, and as a guide to work- 

 " men; to wit, that there is in every spring of a sufficient ex- 

 " tent, a certain length, where all the vibrations, great and 

 ** small, are isochrone" 



*' First — What is this extent? Secondly — This proposi- 

 " tion is not generally exact ; for we find a great number 

 *' of springs, which are such by their nature, that whatever 

 " be their sufficient extent, they never will be isochrone. 



" I have discovered,'* (adds M. L. R,) " that this length 

 *' being found, if you shorten' the spring, the great vibra- 

 " tions will be quicker than the small ones. Jf, on the con- 

 *' trary, you lengthen it, the small ones will be finished in 

 ** less time than the great ones," 



* " This second part of the proposition of M. L. R. is ge- 

 *' nerally exact ; and on this point we are agreed." 



" It is" (adds he) "from this importaiit property, hither^ 

 " to unknown, that the regularity of my marine waich par- 

 " ticidarly depends." 



" M. L. R. thinks that this property was universally w?j- 

 '* knoxm ; and it would have been indeed so, if it had been 



" only 



