488 



NA TURB 



{April 22, 1875 



On the " Law of Fatigue " regulating Muscular 

 Exertion ' 



With regard to Mr. Nipher's new series of experiments pub- 

 lished in Nature (vol. xi., p. 276), in Table II., I shall make 

 only two observations : — 



I. That they appear to me to be subjected to too much of 

 reduction and discussion, a process which does not always 

 improve experiments, and that the intervention of an assistant 

 who lifts the weight from the experimenter appears to introduce 

 new sources of error, both as regards the work done and the 

 punctual observance of time of lift. 



, 2. That the formula (cubical hyperbola) objected to by Mr. 

 Kipher, which is derived from the "Law of Fatigue," repre- 

 sents his new series of experiments quite as well as the compli- 

 cated empirical formula which he has employed, and which has 

 no theoretical meaning. 



I simply give the following table, taken from Mr. Nipher's 

 Table II., and calculated from the formula — 



n (a/ -1- a)2 = ^ 

 where A = 469-2, o = — 1-276. 



Comparison 0/ Nifher and Ham^hton's CalcuUUii»minth Nipliei's 

 Oisci-vations. 



I also give a diagram (No. 3), showing to the eye the agrce- 



nitnt Ltlwetn the shape of the cubical hyperbola and Mr. 

 Nipher's obseivations. In fact it is plain, either from the table 

 or the diagram, that my foimula, derived from the " Law of 

 Fatigue," represents his observations fully as well as his own 

 empirical formula. 



In Mr. Nipher's former experiments already given, the value 

 of o comes out to be -f i -094, and in the present experiments it 

 is a negative quantity and equal to - I '276 ; whereas, according 

 to direct observation, it ought to be + 1-50. According to the 

 Law of Fatigue, the value ol a should be half the weight of the 

 aim, and a negative value of a is absurd. 



The absurdity, however, is easily explained, and is not in the 

 "Lawof Fatigue." The "Law of Fatigue" asserts that the total 

 work done by a group of muscles tired fairly out is inversely pro- 

 portional to the rate at which they are condemned to act ; but it 

 tacitly supposes that the group of muscles in question is not aided 

 by other muscles in any way. This is very difficult to prevent, 

 and it can only be accomplished by a careful ttudy uf the muEcles 

 used, and by devising a rigorous posture and movement during 

 * Continued from p. 4G6. 



the expermienls, such as shall c(mipel the group of muscles to do 

 their work and prevent oiher groups from helping them, which they 

 endeavour to do, from the strong animal instinct of avoiding pain. 

 In the experiments made by myself. Dr. Macalister, and Mr. 

 Gilbert Haughton, the muscles used were two — 



1. Supraspinatus 



2. Deltoideus Acromialis : 



and the palms were supinated, and the plane of motion was the 

 transverse plane. 



In Mr. Nipher's expeiiments (if I understand his description 

 correctly) the plane of motion was 45° in advance of the trans- 

 verse plane, and the hand was probably pronated. These cir- 

 cumstances would allow the muscles already named to be aided 

 in an irregular manner by the following muscles ; — 

 I 3. Deltoideus clavicularis 



4. Trapezius scapularis (anteiior fibres) 



5. Pectoralis major (supeiior fibres). 



The assistance supposed given to the group of muscles which are 

 tired out is not sufficient to fatigue the muscular fibres called into 



