LATERAL FACES OF THE BODY. 



153 



may be their service. In explaining tlie reasons for this, we will show 

 the inconveniences resulting from their flatness, their nearness to each 

 other, and their want of length. 



Fig. 42. 



1st. The normal curvation of the ribs is in direct ivlation with a 

 large transverse diameter of the thoracic cavity, and, consequently, with 

 the development of the respiratory apparatus. 



Before proceeding flu-ther, let us determine 

 what is understood by the convexity of a curve. It 

 is the relation which exists between the height of 

 its arch and the length of its chord, supposing, 

 be it well understood, that we are speaking of 

 a regular curve. In other words, a curve is much 

 more convex when it forms a greater projec- 

 tion upon a shorter chord. Thus, the two arcs 

 ADB, A'D'B' (Fig. 42), although belonging to two 

 circumferences of the same radius {OA = O^A^), have 

 not the same convexity relatively to the choVd which 

 unites them, for the arcs and their chords are difFer- 



CD CD' 



ent, and their relations, 



are not equal. 



Fig. 43. 



AB A'B' 



Again, the curve AOB (Fig. 43) is more convex 



than the curve J. C, although its height be equal, 



. OR . , , . DE 



because the ratio — r^ is greater than the ratio -773 



AB ^ AC 



Therefore, because two curves have the same projection upon their chord, 

 it must not be concluded that their convexity is the same, this condition being 

 realized only when the chords are equal. 



What we have just applied to the arcs can be extended to the ribs, although 



