VOL. XLI.J PHILOSOPHICAL TRANSACTIONS, SOQ 



zontal, and without a pericardium ; a new and remarkable phenomenon ; as if 

 the heart, not bearing so close a confinement, burst through the breast, and, 

 having broke the sternum, appeared on the outside. 



Dr. T. omits Benivenus, Muretus, Scultetus, and Giersdorf, who observed 

 the heart hairy, and found stones, polypuses and abscesses in its ventricles.* 



He then states that he had observed, in a new-born female infant, the heart 

 without a pericardium, and turned upside down, so that its basis, with all the 

 vessels, had fallen down as low as the navel; and its apex, still on the left side, 

 lay hid between the 2 lungs. It is amazing how the circulation could be car- 

 ried on, the heart being thus inverted; and yet the child lived several days after 

 birth. He observed the heart from its basis, whence the aorta and pulmonary 

 artery spring, and where the cava and pulmonary vein enter it, to its cone, 

 surround loosely with several windings of these vessels, through which the 

 blood's circulation must necessarily be performed. 



Of the Curve called, from its Form, a Cardioide. By M. John Castillion, of 

 Montagny, Prof. Philos. in the Acad, of Lausanne, and F. R. S. N" 461, 

 p. 778. From the Latin. 



The diameter ab of the semicircle amb, fig. J, pi. 11, touching the circum- 

 ference in the point b, so as always to pass through the point a, will generate 

 this curve. 



From this genesis of the curve, it appears, 1. That DAa, perpendicular to 

 ab, is equal to double the diameter. 



1. That the periphery of this curve ADNnaNA terminates in a. 



Now through a and a draw ge and Aa perpendicular to ca, and en any where 

 perpendicular to an. Then, from the genesis, it follows that an = ba + am; 

 and, by the similar triangles uan and mba, Aa ^ bm + mp, and nq =. 



ma + AP. 



This is the chief property of the curve. There is also another pretty pro- 

 perty, that the line nn is always equal to double the diameter, and is always 

 bisected by the circle in m. 



Now put BA = a, aE = X, en =: y; then will qn = "^ y + 2a, and an =: 

 'Z x^ -\- y^ — 4ay + Aa^, and ma = + a + Var'^ -\- y^ — Aay -\- 4a^; which 4 

 lines being compared by analogy give this equation of the curve, 

 4 « 3 + "i^y — 6ax-y + x* ? „ 



Hence the subtangent of the curve is easily found by the common fluxionary 

 method. But an easier way of drawing the tangent may be deduced from the 

 generation of the curve. Let man come into the nearest place to the first 



