302 PHILOSOPHICAL TRANSACTIONS. [anNO 1706. 



by retarding the ill effects just now mentioned: the first is the heart, which in 

 both was strong and fibrous; for that being left alone to labour the circulation 

 of a large quantity of languid blood, a great force is absolutely requisite to 

 propel it through unactive vessels, to the extremities of the body, and back 

 again : no doubt this is more easily done in men of a low stature (as old Bayles 

 was) which I am apt to think is a qualification to old age. The second was the 

 largeness of their chests, and goodness of their lungs, by which the air had its 

 full effort on every particle of the blood, in rendering it florid, and attenuating 

 it so that it might easily move through the contracted channels of an old body. 

 Few have the happiness of such a heart and lungs, yet most men wish to live 

 long; nor was it easy for physicians to give rules for preventing the ill conse- 

 quences of extreme old age, while the effects of a long circulation of the blood 

 were unknown ; of which we can be certain only by dissections of old persons, 

 and these are not numerous enough to ground any thing certain upon : but if 

 future observations shall confirm the remarks that have been now made, no 

 doubt the indication will be to preserve such a softness in all the fibres, that they 

 fnay easily yield to the pressure of the blood, and by their elasticity restore 

 themselves to their former state, thereby giving a new impetus to the blood. 



The Construction and Properties of a new Quadra trix to the Hyperbola. By 

 Mr. . , Perks. Communicated by Mr. Abr. Demoivre, F. R.S. N° 306, p. 2253. 



The circle, ellipsis, and hyperbola, being not geometrically quadrable, two 

 ways have been used to find their areas. 1 . By converging series ; by which 

 approaches are made nearer and nearer, according to any desired exactness. 2. 

 By quadratices, that is, mechanical curves, which determine the length of cer- 

 tain lines, whose squares or rectangles give the area of the figure desired. Of 

 this sort is the old quadratrix of Dinostratus, by which the circle and ellipse are 

 squared ; and another sort, for the same purpose, I inserted in the Transactions 

 about 5 years ago. Since that, having found the construction of a curve, from 

 whence, besides its own quadrature and rectification, the quadrature of the hy- 

 perbola is derived, I thought the following account might not be unacceptable. 



Let ab, CD, fig. 8, pi. 9, be two straight rulers, of a convenient length. 

 Joined at a, and there making a right angle: ee is another ruler somewhat longer 

 than AB ; near the one end e, let a small truckle-wheel, represented edgewise 

 by gh, and made of a thin plate of brass or iron, be fastened to the ruler by a 

 pin, f, through its centre, so that the wheel may turn on the pin, f, tight to the 

 ruler, without joggling. On the under side of this ruler let there be pinned or 

 glued a small piece of wood, in the form of a quadrant, the part which is seen 

 being marked hi, whose edge or limb kl, is an arch of a circle to the centre /, 



