LAWS OF BONE ARCHITECTURE 269 



section. By roforring to figure 16, it will be seen from the 

 ''Curve of vertical shear" that the shearing forces are a mini- 

 mum between sections 16 and 18, and for all points distal to the 

 latter section the shearing force is the same as at section 18. 

 Hence, for all points in the femur below this section the shearing 

 stresses will also be very near a minimum. It is clear that a 

 minimum amount of material will be required to resist the shear- 

 ing stresses distal to section 18. As horizontal and vertical shear- 

 ing stresses are most efficiently resisted by material placed near 

 the neutral plane, in this region a minimum amount of material 

 will be needed near the neutral axis. Referring to Plates 2 and 

 3, sections 20-52, it will be seen that the cross sections have little 

 if any material in the central space in the shaft, practically the 

 only material near the neutral plane being in the compact bone, 

 but lying at a distance from the neutral axis. This conforms 

 to the requirement of mechanics for economy, as a minimum of 

 material is provided for resisting shearing stresses where these 

 stresses are a minimum. The load of 100 pounds on the femur- 

 head produces horizontal and vertical shearing stresses on the 

 neutral plane of — 11 pounds per square inch in all the sections 

 distal to section 18 (table 6, cols. 12, 13). These stresses are 

 amply provided for by the compact bone lying in the neutral 

 plane. 



2. Eco7io7ny for resisting bending moinent. In figure 16, the 

 "Curve of bending moments" shows that the amount of the 

 bending moment increases from a minimum at section 4 to a 

 maximum between sections 16 and 18, then gradually decreases 

 almost uniformly to near section 75. The measure of the re- 

 sistance of a section to bending moment is the section modulus. 

 To resist bending moment stresses most effectively the material 

 should be as far from the neutral axis as possible. For equal 

 areas the section moduli vary directly as the distance at which 

 the entire area may be considered as concentrated. Hence the 

 farther the material lies from the central axis the more effective 

 its resistance to bending moment stresses. It is evident that the 

 hollow shaft of the femur is an efficient structure for resisting 

 bending moment stresses, all of the material in the shaft being 



