44 LEVERS. 



calcis gives increased leverage in the hind limb, so does length of trapezium 

 afford it in the fore leg. 



If we wish to express these relations mathematically, we have the 

 following proportions for the three orders of levers :- 



P -zy F 



P : W : : ^ F : ^ F, or— =---— 



Here, w'F is the distance of the point of application of the weight from 

 the fulcrum ; and f F, the distance of the power from the fulcrum. 



Comparisons between Power and Weight in Muscular 

 Levers. — We may observe that the power always acts at a mechanical 

 disadvantage in levers of the third order. As the majority of the levers 

 which are used in animal locomotion, act at a mechanical disadvantage ; I 

 shall now investigate the cause of this apparent anomaly. I may first remark 

 that the measure of work done by a force is found by multiplying the 

 weight by the distance through which it has been moved. Thus, suppose 

 two men are engaged in raising weights, one having a single block pulley 

 to lift a weight of 25 lbs., while the other, to raise 100 lbs,, uses a multiplying 

 block which increases the power fourfold; the former will raise his 25 lbs. 

 4 ft. off the ground in the same time and with the same expenditure of force 

 as the latter will lift his 100 lbs. to a height of i ft. In fact, what is gained 

 in power is lost in distance. This law holds equally good with levers, as 

 we may see from the fact, for instance, that a small amount of contraction of 

 the muscle which bends the hock, causes the hind foot to move through a 

 considerable space. Were the hock bent, for example, by a muscle that had 

 its two points of attachment at the stifle and fetlock (instead, as is actually 

 the case, at the stifle and a little below the hock), such muscle would act at 

 far greater mechanical advantage than the present flexor of the hock ; but 

 it could not bend that joint to anything like the same extent, because 

 muscles cannot contract to more than about two-thirds of their normal length. 

 Besides, such an arrangement would be extremely inconvenient for every- 

 day work, and would increase the liability of the limb to injury. Although 

 there is, therefore, a very large expenditure of muscular force in the action 

 of the levers of the limbs; there is an equally large gain in flexion and 

 extension, and consequently in speed. Their arrangement, also, enables the 

 body to be made of a compact form, and to be suited to its surroundings. 



Directions in which the Power and Weight respectively 

 Act. — In the theoretical levers which I have given (Figs. 15, 16, and 17), I 

 have assumed that the power and weight acted at right angles to the lever, 

 and that they weie consequently parallel to each other. In the actual levers 

 (those of the hock) which I have taken into consideration, we may see that 

 this is not the case. I may mention that the nearer a force is to being at 

 right angles with its lever, the greater is the mechanical advantage at which 



