362 Kev. S. Haugliton. On some [Apr. 29, 



experiments into mean probable errors in percentages, we obtain the 



following results : — 



w. Mean probable error. 



975 lbs +171 per cent. 



775 „ ±1-36 



6-87 „ ±1-26 



5-87 „ ±1-13 



4-25 „ .. ±1-94 



3-19 „ ±1-48 



2-56 „ ±0-91 



0-00 „ +278 



This table shows the degree of credit attaching to the several groups 

 of observations, and proves (what I did not anticipate) that the fatigue 

 produced by small weights is as definite as that produced by large 

 weights. 



The interpretation of these observations by means of the Law of 

 Fatigue is thus found. 



When the arm is extended horizontally, the muscles of the shoulder 

 joint keep it in position ; and, at the same time, the scapula and its 

 muscles and surroundings are raised by the reaction; so that the arm 

 and scapula equilibrate by means of equal and opposite con pies acting 

 round the centre of the glenoid cavity. If, therefore, w denote the 

 weight held in the hand, and a denote the weight, which, if held in 

 the hand, would represent the sum of the couples of the arm and 

 scapula and surroundings about the centre of the glenoid ; then it is 

 plain that the total work done by the muscles before fatigue stops 

 the experiment must be proportional to (w + oc)t, where t is the whole 

 time of the experiment. The rate of work is evidently proportional to 



W + x 



Therefore, by the Law of Fatigue we have 



(w + *)H=A ... (1) 

 in which a, A are unknown constants to be determined by experiment. 



From the foregoing experiments, we have the eight following- 

 equations : — 



(2). 



+ 975) 3 x 64-5 = A. 

 0+775) 2 x 80-9=A. 

 + 6-87) 3 x 95-5=A. 

 + 5-87) 2 xll4-4=A. 

 O + 4-25) 2 xl39-0=A. 

 + 3-19) 2 xl58-5=A. 

 0+2-56) 2 xl87'3=A. 

 (« + 0-00) 2 x481-l=A. 



