54 LEVERS. 



Relations between the Power and Weight in Levers.— 



The farther the power is from the fulcrum, the greater will be the mechanical 

 advantage at which it will act ; and vice versa. Thus, if one arm of a 

 see-saw is longer than the other, a comparatively light weight at the 

 end of the former will counterbalance a heavy one at the extremity of the 

 latter. Also, the longer an oar is " in-board," as in an outrigger, the greater 

 will be the power which a rower will have. If we apply this principle to the 

 horse, we shall see that the longer is the os calcis {see Figs. 30 and 31), 

 the greater will be the mechanical advantage at which the muscles of the 

 gaskin will act in kicking or propelling the body forward. As length of os 

 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 wF 

 P:W::.e/F:/F,or-=:— -. 



Here, iv F is the distance of the point of application of the weight from 

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



Comparisons between Power and Weight in Muscular 

 Lievers. — 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 



