IKVENTION OF THE BALANCE STRING, /3 ,' J 



'' signed. Some of tliese ways were applicable to lesser vibra- 

 *' tions, others to greater, as of 2, 3, 4, 5, 6, or whatever 

 '* number of revolutions was desired : the models of which I 

 • * there produced; and I did at the same time shew wherein 

 " the aforesaid sea clocks (meaning Iluyghens') were dcfec- 

 *' tive. 



*' All these paiticulars also were at several other times, at — and before 

 ** the public meetings of the Royal Society, discoursed, experi- sy%g[2 

 " raented, and several models produced. 1 did also, at the 

 ** earnest desire of some friends, in the years l66"4 and \665, 

 ** cause some of the said watches to be made, though I was un- 

 *' willing to add any af the iatier applications of the spring to 

 ^' them, as waiting a fitter opporttinity for my own advantage." 



In 1678, Dr. Hooke published Fotentia Besiitutwa., or 

 Spring ; and says, " The theory of springs, though attempted 

 " by divers eminent mathematicians of this age, has hitherto 

 " not been published by any. It is now about eighteen years 

 " since I first found it out, but designing to apply it to some par- 

 " ticular use, I omitted the publishing thereof, 



" About three years since, his majesty was pleased to see the Other pointsof 

 " experiment, that made out this theory, tried at Whitehall, as ^^^ I'lstory, 

 " also my spring watch. About two years since, I printed this 

 *' theory in an anagram, at the end of my book of the Dcscrip- 

 *' tion of Helioscopes, viz. Uttensiosic ris. That is, The power 

 " of any spring is in the same proportion with the tension there- 

 *'of: that is, if one power stretch or bend it one space, two 

 *' will bend it two, and three will bend it three, and so for- 

 " ward. Now, as the theory is very short, so the way of trying 

 *' it is very easy," Then he proceeds with describing his man- 

 ner of proving both the cylindrical and the Jlat helix, diad he 

 £ven tried straight wires. The apparatus to which he applied Dr. Hooke 

 his flat spiral springs, in order to prove or show their isochron- ment^for "^ "^ 

 iara, differs little or nothing from the elastic balance, as ]M. springs, since . 

 Berthoud calls it, and which he boasts much of having invent- Beitlioud 

 ed, in order to prove bis theory of pendulum springs^ which he 

 forms in such a way, that when bending them up equal degrees x 



of tension, they shall have their forces in an arithmetical pio- 

 gression, which is just what Dr. Hooke, above an hundred 

 years before, shows he had invented and done. 



B b b 2 M. Le 



