282 JOHN C. KOCH 



3. Actual tests of the compact bone of the left femur analyzed 

 in this paper (shown in figs. 21, 24 and 25) were made by me 

 in the engineering testing laboratory of Johns Hopkins Uni- 

 versity. Pieces 1| inches long having a cross sectional area of 

 0.25-0.33 square inch broke at a maximum compression of 

 25,100 pounds per square inch. 



4. If we compare the calculated maximum stresses as shown 

 in figure 18 with the ultimate streng'li of compact bone in ten- 

 sion and in compression as determined by actual tests, a remark- 

 able agreement is found in the ratios of the maximum tensile 

 and compressive stresses. The ratio of the maximum tensile to 

 the maximum compressive stress at successive sections of the 

 femur (fig. 18) is everywhere less than 1.0 except at section 16 

 where the ratio is 1.010, at all other sections the ratio is be- 

 tween the limits of 0.926 at section 18 and 0.324 at section 60. 

 The average of all the ratios of maximum tensile to maximum 

 compressive stress is 0.652. The tests made by Rauber (1876) 

 showed the ultimate strength of compact bone from 13,200 to 

 17,700 pounds per square inch for tension, and 18,000 to 24,000 

 pounds per square inch for compression. The ratios of these 

 ultimate strengths are 0.733 to 0.738. The substantial agree- 

 ment of the ratios of these theoretical tensile and compressive 

 stresses with the ratio of the actual ultimate tensile and com- 

 pressive strengths is of considerable value in checking the ac- 

 curacy of the mathematical analysis quantitatively. 



2. Distribution of fractures of the fernur. Calculated proba- 

 bility of distribution of fractures of the femur. The theory of 

 probability may be applied to the femur for the purpose of 

 determining in what ratio fractures from blows should occur in 

 various regions. Without entering into detail, such a study 

 involves the assumption of the following rational premises: 



1. The tendency for a fracture to occur at any point varies 

 inversely as the least strength of the bone at that point. 



2. Blows of the same intensity are equally apt to be received 

 at any point along the femur. Although blows may vary in 

 intensity, they are equally distributed. 



