116 TRANSACTIONS OF THE [mAR. 14,. 



will only make twenty-five miles of the distance ; it must then 

 become helpless and unable to go further unless more fuel is sup- 

 plied. 



This is an important law, which, if it be found applicable to 

 the expenditure of muscular energy, should be heeded by every 

 one : It is that the time of exhaustion is inversely as the cube 

 of the speed with which work is performed ; when resistances 

 overcome are proportional to the square of the velocity. In 

 ordinary daily work, however, the law takes a somewhat differ- 

 ent form. In walking, for instance, the resistance is not pro- 

 portional to the square of the speed, but to the speed or velocity 

 simply ; the exhaustion being that of raising the body about one 

 and two-tenths inches at each step against the resistance of 

 gravity and inertia, the latter being proportional to the velocity 

 with which the body is lifted. In walking, therefore, the time 

 of exhaustion.is inversely proportional to the square of the velo- 

 city, and the space passed over inversely to the velocity. 



The law that the time of exhaustion is inversely as the cube 

 of the velocity is, however, strictly applicable to the boat-race, 

 since the resistance of the boat is proportional to the square of 

 the velocity ; and as the test of victory is the speed, it follows 

 that the price of victory is a certain degree of exhaustion. How 

 great that exhaustion shall be, depends on the length of course. 

 Unfortunately, it is not the fatigue of the muscles of the legs, 

 arms, and back that are most concerned, but those of the respira- 

 tory and circulatory organs, the lungs and the heart, are in- 

 volved. It is well known that the action of a muscle in con- 

 tracting is accompanied by a destruction of tissue, a true com- 

 bustion in one sense, carbonic acid, water, and other products 

 being formed, and that the refreshment of the muscle consists in 

 the rejection of these products, and a building up of tissue 

 through the blood, which flows to the muscle from the heart. 

 This refreshment is essential to continued action. Muscular 

 work tiierefore involves both fatigue and refreshment as well as 

 strength or muscular force. It has been ascertained by careful 

 estimates that the average laborer in various callings performs 

 work equivalent to about 350 foot-tons in ten hours ; i. e., work 

 equivalent to raising 350 tons one foot high in ten hours. But 



