1880.] Elementary Principles of Animal Mechanics. 



223 



It will be observed that, with light weights, the experiments vary 

 much more than with heavy weights. The discussion of these experi- 

 ments shows a less satisfactory agreement with equation (1) than the 

 other experiments with heavier weights. The most probable values 

 of the constants are as follows :— 



26 



1 26 



2 25 



3 25 



4 25 



5 24 



6 24 



7 24 



8 25 



9 25 



25 



2(A)* 

 5 per cent. 

 1 

 7 



4 

 



Hence we find 



A=1128, 



1-55, 



7=0-645. 



Bringing all the results into one table, we have 



No. 



w. 



A. 



/3. 



T. 



1 .. 



. 975 lbs. . . 



50-7 . . 



. . 1-000 . . 



. . 1-000 



2 .. 



. 7-75 „ 



. . 1137 . . 



. . 1-300 . . 



. . 0-770 



3 .. 



. 5-87 „ .. 



. . 182-2 . . 



. . 1-395 . . 



. . 0-716 



4 



. 2-62 „ ... 



1128-0 .. 



. . 1-550 . . 



. . 0-645 



From all these experiments, it appears that the central cubic (1) 

 derived from the law of fatigue, represents fairly the relation between 

 n and t ; and that n reaches a maximum for a time of lift t, which 

 varies with the weight, increasing with it, but not proportionally. 



The time of lift corresponding to the maximum work done with 

 each weight, ranges from 0*645 sec. to 1 sec. Within these limits (in 

 order to interpolate) let us assume : — 



w=a + bT + CT* + dTZ . (3).. 



Introducing the four results from the table just given, we find: — 



a—- 69-52, 

 b= +169 -85, 

 c=- 89-65, 

 d=- 0-93, 



from which the curve (3) can be plotted. 



