The force B D can be decomposed into two others, B E 

 in the direction of the iHum, which will be absorbed by 

 the muscles of the hind quarter, and the other B F, per- 

 pendicular to the ilium. 



The force B F which acts obliquely upon the loin is 

 also decomposed into two others, one B H, horizontal, 

 is taken up by the mass of the body ; the other, vertical, 

 B G, represents exactly the weight which is felt upon the 

 lumbar region. 



Now we have B G = B F Cos F B G. 



And as the angle B F G = a 



We have B G = B F Cos a, 



But, B F = B D Cos B F G = B D Cos a. 



Hence, B G = B D Cos- a. 



From recent experiments of M. Barrier, B D is equal 



to a quarter of the rider's weight hence B G = — cos- a. 



The weight on the loin is then proportional to the square 

 of the cosine of the angle made by the croup with the 

 horizontal ; and since the cosine decreases, as the angle 

 increases, it will be seen that the weight supported by the 

 loin will be smaller as the slope of the croup increases. 



To fix the idea more clearly, let us consider two croups 

 inclined, one at 20° (horizontal croup) and the other at 

 40° (very sloping croup) and let us suppose the weight of 

 the rider to be 100 kilos. 



The Cos of 20° = 0.9425. 

 Cos^ 20° = 0.8883. 

 The Cos of 40° = 0.7675. 

 Cos- 40° = 0.589. 



In the case of the horizontal croup, we will have 

 BG = 25 Cos^ 20° ^ 22.2075 kilos. 



And in the case of the sloping croup, we have 

 BG = 25 Cos- 40° = 14.725 kilos. 



53 



