THE MOVEMENTS AND POSITIONS OF THE BODY. 229 



the mesial plane of the body ; a rotation of the head is described as 

 taking place in a horizontal plane. By the use of co-ordinate planes and 

 axes — a method extensively employed in mechanics — it is possible to 

 express in exact terms and without ambiguity the position of any portion 

 of the body in space, and to define its position relative to any other 

 part. By this means we can exactly measure the extent and direction 

 of a movement, say that which occurs at a joint, and determine what 

 new position the limb has assumed as a result of that movement. 



This method has been of late years so extensively used by those who 

 are attempting to obtain more exact data in connection with animal 

 mechanics, that it is necessary to master its principle at the outset, in 

 order to understand the results at which they have arrived. 



Let us, in the first case, confine our attention to space of two 

 dimensions, and study the methods for determining the position of 

 points which lie, or which change their position, in one plane. There 

 are two methods, 



known as the +y 



method of rect- 

 angular, and the 

 method of polar 

 co-ordinates. 



In the first of 

 these we describe 

 the position of 

 any given point, 

 by reference to 

 two lines at right 

 angles to each 

 other. If, for 

 example, we want 

 to define the 

 positions of a 

 series of points 

 in the upper 

 limb, and to in- 

 vestigate their 

 changes in posi- 

 tion during the 

 movement of that 

 limb 



Fig. 119. — This figure represents the method of expressing the 

 position of a point p — the centre of rotation of the elbow- 

 joint — in reference to two co-ordinate axes (xx and yy). 



in a 



given 



plane, we choose two convenient reference lines. As the plumb-line 

 is a definite direction in space, and readily determined by a thread and 

 plummet, we take as one of our reference lines the plumb-line (+ y ■- y) 

 falling through the centre of rotation of the shoulder-joint. The other 

 reference line must intersect this at right angles, and in the plane 

 in which displacements are to be studied ; this second line (+ x - x) may 

 itself pass through the shoulder-joint (Fig. 119), or, in many cases, may 

 more conveniently form the ground-line. 



If we draw the lines pa, p>b at right angles to the reference lines, the 

 position of the point p is defined without ambiguity, by saying that its 

 ordinate is -pa, and its abscissa is-pb, which lengths we may express in centi- 

 metres. 



