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Postulate 1. — That the amoant of "Work done hj a muscle in a given 

 time is proportional to its weight; i. e., to the number of muscular fibres 

 in contraction. 



Postulate 2. — That the mean lengths of the ditferent muscles em- 

 ployed at each joint are proportional to the perpendiculars let fall from 

 the centre of motion of the joint upon the directions in which the 

 muscles act. 



In the statement of the first postulate there is, of course, a slight 

 error, arising from the different amounts of cellular tissue and fascia en- 

 tering into the composition of each muscle ; this, however, only intro- 

 duces an error proportional to the differences of the cellular tissue and 

 fascia in the different muscles, which may be regarded as small. So far 

 as my experiments have led me, I incline to the opinion, that such 

 muscles as the heart and psoas, composed nearly altogether of muscular 

 fibre of fine texture, are capable of giving out their work for a longer 

 time than muscles of an opposite character, such as the glutseus maxi- 

 mus and deltoid ; but that for an interval of time less than that requisite 

 to produce fatigue, the work given out is the same for both classes 

 of muscles, within small limits. 



The reasonableness of the second postulate may be shown from the 

 following considerations : — 



1. The distance through which the point of application of a muscle 

 is moved by its contraction is proportional to the mean length of the 

 muscle. 



2. It is geometrically evident that the perpendiculars let fall on the 

 directions of the muscles are proportional to the spaces moved through 

 by their points of application. 



3. The Divine Contriver of the joint has made a perfect mechanism, 

 and therefore employs a minimum expenditure of force. 



If the third of these considerations be admitted, Postulate 2 follows 

 from the first t-wo considerations ; for otherwise there would occur a waste 

 of force, some of the muscles having ceased to act before the others had 

 expanded their store of force. 



Professor Donders, of Utrecht, has indeed proved, by direct measure- 

 ment, that the lengths of the muscles acting on the human elbow are 

 nearly proportional to the distances of their points of application from 

 the joint ; and I believe that he would have found a still more exact 

 agreement, if he had used the perpendiculars instead of the distances. 

 The following corollary follows from the two postulates employed: — 



Corollary 1 . — The moment of each muscle, with respect to the centre 

 of the joint, is proportional to its weight. 



Let F be the force of the muscle, p the perpendicular let fall upon its 

 direction from the centre of the joint, x the space through which the 

 muscle contracts, and I its mean length. 



The work done by the muscle is Fx, which is proportional to Fl, and 

 therefore to Fp, by the second postulate ; but Fx is also proportional to 

 the weight of the muscle, by the first postulate; and therefore Fp, 

 which is the moment of the muscle with respect to the centre of the 



