15i' ON PENDULUMS. 



Properties of kind, from the nature of their employments furnifhing them 

 s * ' with all the materials neceffary ready at hand, and who have 

 fufficient intereft in the fubject to induce them to undertake 

 them. 



I acknowledge that (as you obferve) I did not fiate all my 

 reafons far thinking that Huygens' circular pendulum, and 

 the others propofed on the fame principles, would not be Co 

 liable to alter their notation of time, as thofe in common ufe, 

 from a change of temperature; but this was caufed by the 

 oilier fubjects contained in that paper having extended it to 

 fuch a length as to oblige me to curtail this and other matters, 

 and leave out part of what I had written relative to pyrometers 

 alfo. My reafon for thinking well of Huygens' pendulum pro- 

 ceeded partly from my refpeci for his opinion, founded on 

 the high idea I have of his mathematical erudition; and be- 

 caufe it appeared to me, that the fize of the circle produced 

 by the gyration of the ball, depending on the impulfe of (he 

 moving power more than on the length of the fufpending 

 .firing; that if the firing lengthened a little, the circle would 

 not be thereby increafed ; and even if it was increased, that 

 the effect of (he paraboloidal lamina would prevent its altering 

 the time of each revolution of (he ball (granting the theorem 

 of Huygens, which I inferted, to be true) ; for though I was 

 „ aware that the parabola generated would, by the lengthening 

 of the firing, become of fomewhat lefs curvature, yet I thought 

 this change would be fo minute as not fenfibly to affect the 

 time, efpecially as a change apparently greater had not af- 

 fected it in a fimilar cafe, which will be mentioned a little 

 tart her on, but of this I had doubts then, as appears from what 

 is remarked in page 77, where I mention that I thought the 

 other eonftruftions which I propofed might be better on ac- 

 count of the firing of that of Huygens being- liable to lengthen. 

 I recommended the other pendulums, on fimilar principles, 

 for trial, becaufe though the exponfion will increafe the di- 

 menfions of the parabolical and cycioidal curves, yet fiill they 

 will not ceafe to be thole curves, which Huygens has proved 

 to have fuch remarkable properties for the regulation of pen- 

 dulums ; and as it has been found by experience, 'hat a pen- 

 dulum vibrating in a fmall arc of a large circle, lias (he fame 

 accuracy as when moving in a cycloid, I imagined that there 

 could not at lead be more difference between the effects of 



two 



