fQ ON PENDULUMS. 



" THEOREMA. 



" In cava fuperficie conoidii parabolici, quod axem ad per- 

 pcndiculum crectum habeat, circuitus omnes inobilis, circumfe- 

 rential horizonti parallelas percurrcntis, five parviz five magna 

 fuerint, ccqualibus temporibus peraguntur : qua: tempora fmgula 

 (tquantur binis qfcillationibus penduli, cujus longitudo fit dimi- 

 dium lateris recti parabola genitricis." 



From the above theorem, and what has been already laid 

 down on the fubject, it is evident that the circular pendulum 

 is well worthy of a fair trial, and fhould be recommended to 

 the attention of all fcientific conftructors of horological move- 

 ments. 



As this circular pendulum will take up more room than a 

 common one, when this is any confiderable inconvenience, 

 one of the following conftructions on the fame principles (which 

 have occurred to me while writing this communication), may 

 be ufed in its place. 

 Various cr-- The firft is as follows: To a fhort fpindle afcending from 



ftrudions or the [he clock as before rfefcribed, let there be attached a glafs or 

 circular pendu- . ° 



! um . iron tube, bent in the form of the conoidal parabola before- 



mentioned, and placed as E F in Fig. 1 : into this tube let 

 there be poured a fufficient quantity of mercury to ferve as a 

 centrifugal weight. 



It appears to me that the mercury rifing in the tube, as it 

 circulates, by, the centrifugal force, along its parabolical 

 curve, will have the fame effect as (he weight in Huygens's 

 conftruction, caufed by other means to move in a fimilar line. 

 The tube mould be fuffieienily large to admit the air to pafs 

 freely above the mercury as it moves along its cavity, or elfe 

 a fmall aperture mould be made in the upper furface of the 

 tube near the fpindle, for the fame purpofe: to prevent alfo 

 the error which might otherwife be caufed by a varied rc- 

 fi fiance to the motion of the circulating tube from the muta- 

 bility of atmofpherical preffure, the tube may be inclofed in 

 a circular veffel covered at top, made of as light materials as 

 poffible, and very fmooth externally, through whofe axis the 

 fpindle mould pafs, and to which it fhould be united fo as to 

 revolve with the tube. A fecond method of effecting the fame 

 purpofe is, to have a femi-cylindrical trough fhaped and placed 

 in fame manner as the above tube, in which fhould be put a 

 metallic fphere of fmaller diameter than the trough, that the 



fphere 



