2()S JOHN C. KOCH 



The effect of vertical shearing force, as explained in Part II, 

 {50), in such a structure as the femur, is to produce maximum 

 horizontal shearing stresses and maximum vertical shearing 

 stix^sses on the neutral plane. The magnitude of these maxi- 

 immi shearing stresses on the neutral plane is about 1.4 times 

 as great as the average vertical shearing stress on the entire 

 cross section. Referring to table 5, column 6, it is seen that 

 the equivalent area of the spongy bone, converted into terms of 

 compact bone in the upper femur, varies from a maximum of 

 0.S16 square inch at section 4, to a minimum of 0.022 square 

 inch at section 18. This gradual and consistent diminution of 

 the spongy bone parallels the diminishing intensity of the ver- 

 tical shear. Hence it may be concluded that one of the func- 

 tions of the spongy bone in the upper femur is to resist the 

 shearing forces and that the amount of the spongy bone in this 

 region varies with the amount of the shearing stresses. 



Conclusions. It may therefore be concluded from the fore- 

 going that: 



1. The trabeculae of the upper femur, as shown in frontal sec- 

 tions are arranged in two general systems, compressive and ten- 

 sile, w^hich correspond in position with the lines of maximum 

 and minimum stresses in the femur determined by the mathe- 

 matical analysis of the femur as a mechanical structure. 



2. The thickness and spacing of the trabeculae vary with the 

 intensity of the maximum stresses at various points in the upper 

 femur, being thickest and most closely spaced in the regions 

 where the greatest stresses occur. 



3. The amount of bony material in the spongy bone of the 

 upper femur varies in proportion to the intensity of the shearing 

 force at the various sections. 



4. The arrangement of the trabeculae in the positions of 

 maximum stresses is such that the greatest strength is secured 

 with a minimum of material. 



Significance of the inner architecture of the shaft 



1. Economy for resisting shear. The detailed description of 

 the inner architecture of the femur has been given in a preceding 



