PREFACE. 



* 



THE observations and calculations contained in this 

 Book have occupied my leisure hours during 

 the past ten years ; and they are now offered to the 

 public, with the view of showing the mutual advan- 

 tages obtainable by Anatomists and Geometers from 

 a combination of the Sciences which they cultivate. 

 Anatomists will gain by the increased precision which 

 numerical statements must give to their observations, 

 and Geometers will find in Anatomy a new field of 

 problems opened out to their investigation. I may 

 be allowed to call attention, from this point of view, 

 to the problem of the equilibrium of an elliptical 

 muscular dome, and to the use which I have made of 

 the hyperboloid of one sheet, of Ptolemy's Theorem, 

 and of some curves of the third order. 



In the course of my investigations, I have met 

 with numerous instances, in the muscular mechanism 

 of the vertebrate animals, of the application of the 

 principle of least action in Nature ; by which I mean 

 that the work to be done is effected by means of the 

 existing arrangement of the muscles, bones, and joints, 



