58 LEVERS. 



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

 following proportions for the three orders of levers : — 



P w^ 



P : W : : jc F : /) F, or — = • 



\V pV 



Here, a^ F is the distance of the point of application of the weight 

 from the fulcrum ; and p 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, and 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 Ifes., while the other, 

 to raise 100 fts., 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 e.xpenditure of force as the latter will 

 lift his 100 Ifcs. 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 have been given (Figs. 21, 22, and 

 23), I have assumed that the power and weight act at right angles 

 to the lever, and that they are consequently parallel to each other. 



