140 STUDIES IN ADVANCED PHYSIOLOGY. 



near the elbow. Just as it is more difficult to lift a heavy 

 weight on the end of a long fork than it would be to pick it 

 up directly. But while such power is lost, rapidity of mo- 

 tion is gained, but a slight contraction of the biceps muscle 

 causing the hand to move through quite a distance. Such 

 arrangements in our bodies indicate that the levers were 

 intended rather for dexterity and rapidity of motion than 

 for the ability to lift mere weights. However, in the case 

 of the ankle, at which point we have to lift at each step 

 the weight of the entire body, a lever of the second class is 

 put, an arrangement by which a person is never obliged to 

 pull as much on his muscles as the weight of his body 

 actually is. 



THE MATHEMATICS OF LEVEES. 



In every lever, no matter whether of the first, second or 

 third class, the distance from the power to the fulcrum is 

 called the "power-arm" (pa) , while the distance from the 

 "weight" to the fulcrum is called the "weight-arm" (wa) . 

 In all three classes of levers the following simple arithmeti- 

 cal proportion holds true: That the P: W: \wa:pa. Hence, 

 if three of these factors are given, by the simplest mathemat- 

 ical process the fourth may be determined. To illustrate in a 

 specific case : If we assume in the case of the foot the dis- 

 tance from the toes to the astragalus to be seven inches, 

 and the distance from this point in the astragalus to the 

 point where the tendon is attached to the heel bone two 

 inches, we have the power-arm of seven inches plus two 

 inches, or nine inches, and the weight-arm seven inches. 

 If, now, a man's body weighs, say, 160 pounds, which is 

 therefore the weight, how many pounds must his tendon 

 Achilles pull in order to raise him on his toes? By the 

 equation P X pa = W X iva. Calling the power x gives 9;r 

 = 7X160. x = 124% pounds. Thus, by means of this 

 arrangement, to lift a body of 160 pounds requires a pull of 

 only 124 pounds at the heel. 



Or, to take a second example in the case of the fore- 

 arm. Suppose the distance from the elbow to the point in 



