ON PENDULUMS. 77 



fphe,re might move in it without friction ; for, being thus 

 P formed, it follows, from the 13th of the third book of Euclid, 

 that the (phere could never touch the trough but in one point 

 alone at the fame time. A third method of confirudtion is, 

 to place a cylindrical metallic rod, or thick wire, bent into 

 the parabolical curve before directed, in the fame pofition as 

 the above tube and trough ; with a fpherical weight put en it 

 fo as to move freely along it, which laft might be effected by 

 a friction-roller, either let into the upper part of the weight, 

 or placed above it, whofe furface (hould be formed into a cir- 

 cular groove of larger diameter than the rod. 



Thole laft conftructions feem to me to have befides the far- 

 ther advantage, that any dilation of their parts from change of 

 temperature, could only lengthen the tubes or rods, but would 

 not alter their fhape, on which alone their properties depend ; 

 which circumftance might perhaps make them even more ex- 

 act than that propofed by Huygens, the firings, or appending 

 part of which, would certainly vary in length ; which, though, 

 from the before-recited theorem, it appears to be a matter of 

 little confequence, yet Huvgens feems to hint that it would 

 be of lome, by recommending the ufe of fine chains infiead of 

 firings (that their length might vary the lefs), in thefe words: 

 " In locum fill catenulam tenuem exauro, aliove mtlallo, adhi- 

 berc licebit, quo melius invariata fcrvttur long kudo." 



There has alfo occurred to me a fpecies of ofcillatory pen- An ofcillatory or 

 dulum; which, as it appears to have the fame property as thofe, ng P enclu " 

 laft mentioned, (of nqt being affected by the expanfion of its 

 materials,) I fhali here defcribe: It conhfts of a cylinder of 

 hard metal, A f/%. \) turned very true and fmooth, placed 

 fo as to roll back and forwards alternately, in the cycloidal ca- 

 vity B, cut in a block of hard metal alfo, and well polifhed : 

 the communication of motion between the rolling cylinder and 

 the clock work to be effected by the rod C, fufpended by its 

 upper extremity, and connected with each extremity of the 

 axis of the cylinder by the joints D D : The diameter of the 

 generating circle of the cycloid being half the length of a 

 pendulum rod, which vibrates in the required time, and the 

 cycloidal part well levelled and firmly fuftained. It feems (o 

 me that the cylinder A, when put in motion, will ofcillate equal 

 times on its cycloidal fupport ; and, (as the expanfion of the 

 latter will not alter its fhape, on which alone its properties de- 

 pend,) 



