Certain hippologists have said : " There are two ways 

 of producing speed : first, by short and rapidly repeated 

 strides ; second, by long and relatively slow strides. Con- 

 sequently, short distance races can serve for picking out 

 types corresponding to these two ways of galloping." 



This argument is but specious. 



However long a stride may be, the gallop resulting 

 from it will still be slower than that which is the result 

 of short rapid strides so long as the average speed of 

 the long stride is less than the average speed of the short 

 stride. 



Suppose two horses, of which the one makes a stride 

 of the length F, equal to n strides of the other. But the 

 velocity V of the stride F is less than the velocity V of 

 the stride f ; we have therefore by hypothesis : 



F = nf 



On the other hand, F = Vt and n f = V t' 



Therefore, Vt = V t' 



But since by hypothesis V is greater than V, the last 

 equation cannot be true unless t' is less than t. 



So the horse with short and rapid strides will consume 

 less time in covering the distance F than the horse which 

 covers this distance in a single stride. 



Therefore the long striding horse must find a means 

 of increasing the average speed of his stride if he is to 

 compete with the short striding horse. 



It is evident that he will not increase this average speed 

 by increasing the period of suspension or the period of 

 oscillation of the legs in their supporting positions, since 

 these phases of the stride correspond to minimum speed ; 

 he must therefore increase the extent of his diagonal base 

 (between the second or third steps of the gallop), his 

 compass opening, which corresponds with maximum 

 speed. 



Let us say right away that the dift'erences of compass 



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