466 PHILOSOPHICAL TRANSACTIONS. [aNNO 1/20. 



centripetal force, to that Force by which it would describe the curve in vacuo, 

 multiplied by the fluxion of the curve. It is also demonstrated, that if a body 

 describe any curve in a resisting medium, which in vacuo could have been de- 

 scribed by a centripetal force, proportional to any power of the distance, the 

 density of that medium will be reciprocally as the part of the tangent intercepted 

 between the point of contact, and a line perpendicular to the radius at the 

 centre of the forces. This theorem is applied to several curves ; and then the 

 J 0th Prop, of the 2d Book of the Principia, and all its examples, are demon- 

 strated from it. These propositions are treated of here, not only because they 

 show the use of curves in philosophy, but because more simple ideas of the de 

 scriptions of some curves may be drawn from them, than from any other 

 method ; and because this is the method by which nature herself describes 

 curve lines. 



The whole is concluded with an attempt to draw a line of any given order, 

 through any given number of points, that is sufficient to determine the curve. 

 Thus if a curve of the order 2 m is to be described through as many points, as 

 determine a line of the order m, and 3 more points, each of which are nodes, 

 formed by the concourse of as many arches of the curve, as there are units in 

 m ; then the curve is determined, and a method how to describe it is demon- 

 strated. This, and some other theorems relating to the number of points that 

 determine curves, and the manner of describing them through these points, 

 conclude this part. 



A Case in Surgery j which is commonly mistaken for a Fracture of the Patella. 

 By Mr. D ever el , Surgeon at Bristol, N° 365, p. 44. 



One Richard Burt was thrown from his horse, and in the fall received such a 

 hurt in one of his knees, as made him incapable of remounting: he felt some- 

 thing crack in that knee, as he expressed it, before it touched the ground. On 

 examining the part, I found, as I then thought, the ends of the fractured bone 

 drawn above 4 fingers distance from each other : but on a stricter examination 

 of the parts, I found the patella, which was drawn upwards by the extensors of 

 the leg, retained its natural figure, and that the hardness which was felt below, 

 was the end of the torn ligament that ties it to the tibia. The ends of the 

 ligament were brought as near as possible, and kept so about 3 weeks without 

 any very remarkable accident. He then began to walk, which was a little too 

 soon, causing some pain, and loosening the cicatrix, which made it the longer 

 before it was perfectly firm ; however he now walks without any perceptible 

 lameness. I have met with two others in the same case; the one does not 

 walk so well as she used, though not for want of all the care and circumspection 



