POINTS FROM WHICH THE PROPORTIONS ARE STUDIED. 379 



being granted that the angular relations of the osseous levers have an 

 immediate influence upon the development of speed (we think that we 

 have shown this a propos of the regions), is it possible to estimate these 

 relations ivith more accuracy than a single glance of the eye would give, 

 and, this being so, are the centres of rotation obtained by the process 

 indicated above sufficiently precise to allow comparative observations to 

 be made upon different subjects and afterwards to reason in a general 

 manner upon the results obtained f 



Well, there is no doubt but the question, brought down to these 

 limits, is susceptible of a positive solution ; and however approxima- 

 tive this solution may be, it will always be better than the state of 

 ignorance in which the observer was previously, or than the often 

 erroneous appreciations suggested by our senses. Let us see, besides, 

 the criticisms of M. Neumann, which, without contradiction, we our- 

 selves would have presented if our colleague had not previously 

 formulated thera.^ 



First, it is certainly not demonstrated that the articular angles are 

 always of the same geometrical kind for the same bone ; that they 

 possess a centre and only one; that the position of this centre is 

 always the same in relation with the external surface of the bone ; 

 finally, that the supposed axis of rotation is perpendicular to a cross- 

 section of the latter. Nor is it established, either, that the axes pass- 

 ing through the centres of rotation, perpendicularly to the plane of 

 movement, invariably meet the same anatomical points of the external 

 surface of the bones. All this is true, but the variations among dif- 

 ferent animals are less marked than M. Neumann seems to believe. 

 We will go further, for we have sought to determine it, and say that 

 these variations, a^lready so minute in the hybrids (mule, hinny), or in 

 subjects of the same genus (ass), are recognized with extreme difficulty 

 and are even unappreciable, so feeble are they, among the representa- 

 tives of the same species. Therefore, although these objections are 

 applied to possible and even probable errors, they are of little value as 

 concerns definite results, and may be neglected without great incon- 

 venience. 



This is not the case in the search for the points of external data, 

 or location of the axes of rotation in the living animal. Errors of 

 one, two, or three centimetres, either above or below the point indi- 

 cated, are easily committed, which lead without a doubt to solutions 



1 G. Neumann, Quelques observations sur la mecanique animale, a propos des recherches 

 de M. Alexis Lemoigne, in Recueil de medecine veterinaire, annee 1877, p. 489. 



