220 THE GRAMMAR OF SCIENCE 



to determine velocity, we construct a new figure in the 

 following manner : From any point I we draw a series of 

 rays, IV^, IVg, IV^, IV^, . . . IV^^,, parallel to the tangents 

 at the successive points P^, P^, P3) • • • P^e. and we measure 

 off along these rays in the sense of the motion as many 

 units of length as there are units of speed in the motion 

 at these points. Each of these rays will, by what precedes, 

 be a step representing the velocity at the corresponding 

 point of the path. If this be done for a very great 



Fig. 13. 



number of positions the points V^, V^, V^, etc., will be a 

 series approaching more and more closely to a curve. 

 This curve is termed the hodograph, from two Greek words 

 signifying a " description of the path." The name has 

 been somewhat unfortunately chosen, as the curve is not 

 a " description of the path," but a " description of the 

 motion in the path," rather a kinesigraph than a hodograph. 

 Fig. 1 3 is supposed to represent the hodograph of the 

 motion dealt with in our Figs. 9 and 10.^ Thus while 



1 The true hodograph would require a great number of points, such as V, 

 to determine its shape at all accurately. The constant changes in the direction 

 of the railway (see Fig. 9, p. 210) cause the hodograph curve to bend back- 

 wards and forwards, while the slight variations of the speed produce the 

 tangles in the curve. 



