ANIMAL MECHANICS. 39 

 but nSs varies as t ; therefore 



Total Work varies as (w + a) j t ; 

 and the rate of work varies as 



(w + «) 7 



Now, by the Ztfw o/" Fatigue, the total work varies in- 

 versely as the rate of work, and hence we have 



(w + a) 2 — t = Constant ; 



but, supposing the arm to be a simple uniform cylinder, we 

 have 



x 3 (2iv + a) 2 



I 4 (w + a) (2 W + a )' 



Squaring, and substituting in the preceding equation, we 

 obtain 



( 2w -f ay t _ A 



(3 W + a Y 



or, 



A (^w + a) 2 

 t = 2 — . (l2«) 



Jn order to compare this formula with observation, I 

 made use of Mr. Stanley Jevons' experiments published in 

 Nature (30th June, 1870), using the following constants, 

 which I found to answer best : — 



A = 22050, 

 a = 7.4 lbs. 



The comparison of observation and theory is shown in the 

 following Table : — 



