480 



ANIMAL MECHANICS. 



given signal, raised both amis to the horizontal position, and 

 kept them in that position until compelled by fatigue to lower 

 the weights. After a fixed interval of rest, the operation was 

 repeated, and so on ; the successive times of holding up the 

 arms were noted, and formed, as may be well supposed, a 

 series which diminished rapidly at the commencement, and 

 afterwards more slowly. On plotting the experiments, taking 

 the number of the observation as the x, and the time of hold- 

 ing up the arms as the y of the curve, it became apparent that 

 the form of the curve was hyperbolic, and convex towards 

 the axis of x. We can find the horizontal asymptote of this 

 curve, and so determine the time of holding out the arms, 

 during which the fatigue incurred is exactly counterbalanced 

 by the refreshment supplied in each cycle of rest and work. 

 When this condition is attained, the shoulder muscles can 

 continue to work for hours without sensible fatigue, as in the 

 case of the muscles employed in walking. 



Experiments No 

 i st Effort, 

 6th „ 



3 Ist » 

 56th ., 



/. — Interval of Rest ■■ 

 . 60 seconds . 

 .25 

 . 16 „ 



60 seconds. 

 (mean). 



14 



These results are the means of many observations made 

 on different days; and I selected the 6th, 31st, and 55th ob- 

 servations in order to simplify the calculations. It is evident 

 that the hyperbola which ultimately coincides with the curve 

 of observations must have for its equation, 



(x + a) 0/-j3) 



(143) 



and we are to determine a, j3, and & 2 , from assuming any 



