ANIMAL MECHANICS. 



29 



From these results I obtained my first conception of the 

 Law of Fatigue, which I shall fully develope further on, with 

 the proofs of it, derived from more extensive and varied ex- 

 periments ; and I shall also prove that the coefficient o> is 

 equal to unity. 



The Law of Fatigue may be thus stated : — 



When the same muscle {or group of muscles) is kept in con- 

 stant action until fatigue sets in, the total work done, multiplied 

 by the rate of work, is constant. 



Thus, if W denote the total work done, and T denote the 

 time of doing it, the rate of work will be expressed by W 

 divided by T, and 



W 



Total Work x Rate of Work = W x — . 



If this product be constant, we see that the work ana 

 rate of work may be represented by the coordinates of an 

 hyperbola referred to its asymptotes as axes of coordinates ; 

 while the relation of the total work to the time of doing it, 

 may be represented, as in equation (8), by the coordinates of 

 a parabola referred to a tangent and diameter as axes of 

 coordinates. 



As an illustration, let us suppose that a man walking at 

 the usual rate does not become tired until he has walked 

 30 miles. On another occasion, let him walk twice as fast, 

 then (neglecting the difference of action necessitated by the 

 different rates of walking) we should expect, by the Law of 

 Fatigue, that the man will be completely fatigued at the end 

 of 1 5 miles, having done only half the total work, in a quarter 

 of the original time. If the man walk three times as fast, he 

 will become tired out at the end of 1 o miles, in one-ninth part 

 of the original time ; and so on, the total work done always 

 varying as the square root of the time necessary to produce 

 fatigue. 



