Radius

in geometry, the semidiameter ef a circle; or a right line drawn from. the centre to the circumference.—It is implied in the definition of a circle, and it is apparent from its construction, that all the radii of the same circle are equal.—The radius is sometimes ealled, in trigonometry, the sinus tot us, or ' whole sine. The length of the radius of any circle, is equal to that of an are of 57°2957795 degrees of the same circle. Rapius, in the higher geometry. Radius of the evoluta, radius oscult, called also the radius of concavity, and the radius of curvuture, is the radius of a circle having the same curvature, in a given point of the curve, with that of the curve in that point. See Curva- TURE, Curve, and EvouuTe. RaADIUvs, in optics. See Ray. Rapivus vector, is used for a right line drawn from the centre of force im any curve im which a body is supposed to move by a centripetal force, to that point of the curve where ‘the body is supposed to be. In the elliptical orbit of a planet, let @ = semiaxis major, ae = distance from the centre to the focus, or e = eccentricity to semiaxis major =1, v =true anomaly, and u = eccentric anomaly, then the radins vector r is expre ed by either of the fol- Towing, for mule r==a (i-be cos. u), or r== a (l—e?) 1—ecos.v Raptiws. (radius, a staff or beam; so ealled from its resemblance.) This bone has gotten its name from its supposed resemblance to the spoke of a wheel, or to a weaver’s beam; and sometimes, from its supporting the hand, it has been called manubrium manus. Like the ulna, it is of a triangular figure, but it differs from that bene, in growing larger as it descends, so that its smaller part answers to the Jarger part of the ulna, and vice vers a. Of its two extremities, the uppermost and smallest is formed into a small rounded head, furnished with cartilage, and hollowed at its summit, for an articulation with the little head at the side of the pulley of the os humeri, The round horder of this head, next the ulna, is formed for an articulation with the le er syemoid cavity of that bone. ‘This little head of the radius is supported by a neck, at the bottom of which, laterally, is a considerable tuberosity, into the posterior half of which is inserted the posterior tendon of the biceps, while the anterior half is covered with cartilage, and surrounded with a capsular ligament, so as to allow this tendon to slide upon it as upon a pulley, Immediately below this tuberosity, the body of the bone may be said: to begin, We find it slightly curved throughout its whole length, by which means a greater space 1s formed for the lodgment of museles, and it is enabled to cro the ulna without compre ing them. Of the three surfaces, to be distinguished on the body of the bone, the external and internal ones are the broadest and flattest. The ‘anterior surface is narrower and more convex, Of its angles, the external and internal ones are rounded; but the posterior angle, which is turned towards the ulna, is fachien ate a sharp spine, which serves for the attachment of the intero eous ligament, of which mention made in the description of the ulna, This strong ligament, which is a little interrupted above and below, serves not only to connect the bones of the fore-arm to each other, but likewise to afford a greater surface for the lodg-: ment of muscles, On the fore part of the bone, and at about one third of its length, from its upper end, we observe a channel for ve els, slanting obliquely upwards. ‘Towards its lower extremity, the radius becomes broader, of an irregular shape, and somewhat flattened, affording three surfaces, of which the pester i or~ one is the smallest; the second, which is a continuation of the internal surface of the body of the bone, is broader and flatter than the first; and the third, which is the broadest of the three, answers to the anterior and external surface of the body of the bone. On this last we observe several sinuosities, covered with a thin layer of cartilage, upon which slide the tendons of several muscles of the wrist and fingers. The lowest part of the bone is formed into an oblong articulating cavity, divided into two by as light transverse rising. ‘This cavity is formed for an articulation with the bones of ~ the wrist. Towards the anterier and convex surface of the bone, this cavity is defended by a remarkable eminence, called the styloid proce of the radius, which is covered with a cartilage that is extended to the lower extremity of the ulna; a ligament is likewise stretched from it to the wrist. Besides this large cavity, the ra~ dius has another much smaller one, opposite its styloid proce , which is lined with cartilage, and receives the rounded surface of the ulna. The articulation of the radius with the le er sygmoid cavity of the ulna is strengthened by a circular ligament, which is attached to the two extremities of that cavity, and from thence surrounds the head of the radius. This ligament is narrowest, but thickest at its middle part. But, besides this ligament, which connects the two bones of the fore arm with each other, the ligaments which secure the articulation of the radius with the os humeri are mon both to it and to the ulna, and the cannot well be understood till both these bones, are described. ‘These ligaments are a capsular and two lateral ligaments, ‘The capsular ligament is attached to the anterior and posterior surfaces of the lower extremity of the os humeri, to the upper edges and sides of the cavities we remarked at the bottom of the pulley and little head, and likewise to some part of the condyles: from thence it is spread over the ulna, to the edges of the greater sygmoid cavity, so as to include in it the end of olecranon and of the coronoid proce ; and is likewise fixed round the neck of the radius, so as to include the head’ of that bone within it. The lateral ligaments may be distinguished into external and internal, or according to Winslow, into brachio radial is, and braechio cubital is. They both descend laterally from the lowest part of each condyle of the os humeri, and, from their fibres spreading wide as they descend, havé been compared to a goose’s foot. The internal ligament, or brach no cubital is, which is the longest and thickest of the two, ‘ is attached to the coronoid proce of the ulna. The external ligament, or brachio radial is, terminates in the circular ligament of the radius. Both these ligaments adhere firmly to the capsular ligament, and to the tendons of some of the adjacent muscles. In considering the articulation of the fore-arm with the os humeri, we find that when both the bones are moved together upon the os humeri, the motion of the ulna upon the pulley allows only of flexion and extension; whereas, when the palm of the hand is turned downwards or upwards, or in other words, in pronation and supination, we see the radius moving upon its axis, and in these motions its head turns upon the little head of the os humeri at the side of the pulley, while its circular edge -rolls in the le er sygmoid cavity of the ulnae At the lower end of the fore-arm the edge of the ulna is received intoa superficial cavity at the side of the radius. ‘This articulation, which surrounded by a loose capsular ligament, concurs with the articulation above, in enabling the radius to turn with great facility upon its axis; and it is chiefly with the a istance of this bone that we are enabled to turn the palm of the hand upwards or downwards, the ulna having but a very inconsiderable share in these motions. 73