1887.] NEW YORK ACADEMY OF SCIENCES. 115 



A lesson might be taken from the rules of horse-racing, where 

 such complete over-fatigue on the part of the horse is not toler- 

 ated, and would indeed be looked upon by spectators as a sort of 

 cruelty to animals not unlikely to bring about perhaps the offi- 

 cial interference of Mr. Bergh. The laws of fatigue and refresh- 

 ment, and of total exhaustion, applicable to muscular exertion, 

 are special exami:)les of a universal law as immutable and infal- 

 lible as any other law of nature. One of the most interesting of 

 all the developments of animal mechanics, is found in the dis- 

 covery that the law which governs the expenditure of energy in 

 artificial motors is not only analogous but identical with that 

 which applies to animal or muscular energy. This identity is 

 most clearly shown in comparing the consumption of a given 

 amount of coal in driving a vessel through the water through 

 the medium of a steam engine, with tlie consumption or exhaus- 

 tion of a given amount of muscular energy in propelling a boat. 

 It is well known that the resistance to the motion of a boat in 

 the water is proportional to the square of the velocity; and as 

 the work performed (or coal consumed) in a unit of time — one 

 hour, for example — is proportional to the resistance multiplied 

 by the velocity or speed per hour, it follows that the consump- 

 tion of fuel is proportional to the cube of the velocity. It is also 

 known that a given quantity of fuel is capable of doing only a 

 a fixed amount of work, whatever be the rate of combustion or 

 speed with which the vessel is driven. The number of hours re- 

 quired, therefore, for the consumption of equal quantities of 

 fuel in propelling the same vessel through the water at different 

 velocities, will be proportional inversely to the cubes of the veloci- 

 ties, while the space passed over will be inversely proportional to 

 the squares of the velocities. Suppose a steam- vessel with a 

 given amount of coal on board, to start on a passage of one hun- 

 dred miles, the speed to be five miles per hour. The time re- 

 quired to make the trip will be twenty hours, and the coal is 

 supposed to be just sufficient for this voyage with this velocity. 

 Suppose again the same vessel to undertake the same trip with 

 the same amount of coal, but with a velocity of ten miles per 

 hour. The result will be that the coal will all be consumed in 

 two and one-half hours, one-eighth of the time, and the boat 



