58 LEVERS. 



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

 following i)roi)ortions tor tlic three orders of levers:— 



P wY 



r : \V : : lu F : /> F, or — ^--: 



W ^F 



Here, 5x; F is 11k' distance of tlic point of ai)p]ication of the weight 

 from the fiilcrinu ; and /) F, the distance of llic power from the fulcrum. 



Comparisons between Power and Weight in Muscular 

 Levers. W'c may ofjserve tliat tlie i)ower 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 thai tlu- measure of work done by a force is found by 

 multiplying the weight by the distance through which il has been 

 moved. Thus, suppose two men are engaged in raising weights, one 

 having a single ])l()ck pulley to lift a weight of 25 lbs., while the other, 

 to raise too Ihs., uses a multiplying block which increases the jiower 

 liHulold ; tile lornier will raise liis 25 lbs. 4 ft. off the ground in the 

 same time and with the same expenditure of force as the latter will 

 lilt his 100 tbs. to a height of I ft. In fact, what is gained in power 

 is lost ill distance. This law holds equally good with levers, as we may 

 see Iroin the fact, for instance, that a small amount of contraction of 

 tlie miis( le w liicji heuds 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 bek)w the hock), such 

 muscle would act at far greater mechanical advantage than the jiresent 

 Ik'xor ol the hock ; but it could not bend that joint to anything like 

 the same extent, because muscles cannot eontiacl to more than about 

 two-thirds of their noinial length. Besides, such an arrangement would 

 be extreinel\- ineoiu cnieiit lor every-day work, and would increase 

 the liability ol the liml) to injury. Although there is, therefore, a very 

 large expenditmi' ol muscular force in the action of tlu^ levers of the 

 limbs ; there is an e([ually large gain in llexion ami extension, and 

 consequently in speed. Their arrangement, also, enal)les 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), 1 have assumed that the power and weight act at right angles 

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



