134. EF. E. Nipher— Work done by a Muscle before exhaustion. 
able error (e) of this mean is given in the twelfth line, and is 
calculated from the formula e=ta/ ia: a, where v = the 
ry ee 
number of observations and d= difference from the m 
Assuming the arm to be a uniform cylinder, and donot 
by @ one-half the weight of the arm, and we have for any 
weight w the total dynamical work done before Pambes 
Total work =(w+a)h.n.. i (1) 
The value of a can be determined by direct weighing, as fol- 
lows: Exhaust the arm thoroughly, then holding it in the same 
position as when lifting, extend the arm horizontally, resting 
the hand in the scale-pan of a spring-balance, the dial of f which 
is turned from the experimenter. The reading off of the weight 
is done by an assistant. After a few minutes the muscles tire 
so that a practical experimenter can then gradually relax them 
fully. Untrained muscles, when thus tried, act involuntarily, 
and precise results can not be obtained. The value of a was 
thus determined twenty times, the values being here given. 
a (obs.) 
1-46 1°42 1°63 1°42 1-46 
1°42 1°58 1°42 1°48 1°40 
1°42 1°52 1°48 158 1°50 
1°50 1°49 1°62 1°58 1°57 
a=1'50 
The mean is 1°50 kgr. with a pe ee error of 0°01 kgr. 
Hence (calling the total work=W), (1) becomes 
W=(w+1°'50) 0°70. 
Coérdinating the values of W and w and the relation appears 
plainly hyperbolic. Hence the two most probable cases are 
ha= Sie eg AR: lest es 2) and 
(w+a) hd (wa)? ( ) 
(w+ a)hn= < - es wae |e tep 
where c and v are constants. 
From these we readily have 
log (w+-a)+log n=k'— vlog (w+-a) -.------ (4) 
log (w+-a)+log n=hk—vlogw _..----------(5) 
These equations are of the form y= k-+-ve. 
where y and « can be determined from the observations. They 
are given in the table below : 
These values of x and y for eq. (4) and (5) are codrdinated oD 
the chart and a straight line, drawn as nearly as possible through 
the points, shows the functions to be linear in each case. ¥ 3 
