BALL-AND-SO CKE T JOINTS. 



237 



point of intersection x will be unaffected by the double rotation, the centre of 

 rotation will be at the same spot, and the line joining the centre of rotation 

 with x, will lie what is termed the resultant axis of rotation. For the 

 rotation (0) around the point O would carry the point x to the point x, and 

 the subsequent rotation around O' would bring it to the position x from which 

 it started. 



If the order of rotation be reversed, occurring first around O' and then 



JC 



Fig. 125. — To illustrate the method of compounding axes of rotation. 



around O, the resultant axis of rotation would pass through the point x. 

 Upon the other side of 00' draw the angles O'O.'"' equal to O'O'", and 00V 

 equal to 00'''. The two triangles will be equal in every respect. 



By constructions similar to those detailed above, the movements 

 of any given solid in space can be exactly determined, provided the 

 movements of three points (not in a 

 straight line) of the solid be known. This 

 axiom was applied by Braune and Fischer in 

 their study of the movements at the knee. 

 Since accuracy of observation depends 

 on the distance traversed by the three 

 points, rods of some length were fixed to 

 the foot of the subject. The excursions 

 of the tips of these rods, recorded by the 

 photographic method described on p. 2G6, 

 supplied the data for determining the 

 movements of the knee-joint with accuracy. 

 For most purposes simpler methods are 

 sufficient. 



In the case of the shoulder, as an 

 example, we proceed as follows : — Attach 

 to the outer surface of the arm, so as to run 

 vertically and parallel with the axis of the limb, a light wooden rod 

 bearing a small board 2 in. square, and marked out in equal squares. 

 The board should centre somewhere over the spot at which the centre 

 is supposed to lie. The arm is now allowed to swing pendulum-wise 

 from side to side. 



The observer now places himself with his eyes on a level with the 

 joint, and holds a straight rod — a pencil — so that it is parallel with one 

 of the horizontal lines on the board of equal squares (Fig. 126). 



Fig. 126. — Shows the author's 

 method of determining the 

 eentre of rotation of a joint. 

 During the experiment the 

 arm of the subject is allowed 

 to swing backwards and for- 

 wards like a pendulum. 



