153 



ON PENDULUMS. 



rabola which I knew was inferted in it, I perceived therein 

 alfo a geometrical method of finding a right line equal to any 

 given portion of the circumference of a circle; and having 

 by this method drawn a right line equal to the fourth of the 

 circumference of a circle, and with it and the diameter formed 

 a parallelogram equal to the circle, and then a fquare equal 

 to this parallelogram, in the ufual manner : I afterwards formed 

 another fquare equal to the fame circle, according to my me- 

 thod before defcribed, and found no perceivable difference be- 

 tween it and the former fquare. 



The difcovery of a facf in geometry often leads to another; 

 one of this kind I have to add here, which is, that a right line 

 (B E) drawn from the extremity B of the line I B, at right 

 angles through the oppofite diameter (I F) to the circum- 

 ference, will be equal to a fourth of the circumference. 



The problem of Kircher above mentioned, may be found in 

 the Ars magna Lucis et Umbra, prop. 3, lib. 3, pars 2, page 

 239, and the two following pages. 



As the circles which I ufed were under three inches diame- 

 ter, it is poffible on fo fmall a fcale a minute error might not 

 be vifible; but even in this cafe it muft be very inconfiderable. 



I take the opportunity of forwarding the above to fend an Properties of 

 explanation in reply to the annotations on my paper on pen- P endu ' ums » &c« 

 dulums, which I hope you will do me the favour to infert, as 

 you have in fome degree called on me for it. 



I beg leave to obferve, that in that paper I have endea- 

 voured to put a marked diftinclion (though perhaps not fuffi- 

 ciently forcible) between «he obfervations which admitted of 

 proof, and ("peculations on new fubjecls : The latter may be 

 confidered to commence with Huygens' pendulum ; and the 

 others on fimilar principles, along with this, were merely de- 

 figned as objects propofed for experiment, not as things proved, 

 and nothing is inferted about them but what was intended to 

 be noted as conjectural by the mode of expreflion. 



I confider it ufeful to propofe experiments (exclufive of my 

 partiality to this mode of afcertaining facls), becaufe among 

 your numerous readers there might be fome who, with little 

 trouble or expence, have opportunities to make trials of this 



kind. 



