288 JOHN C. KOCH 



Ihimiltoii, respectively, are shown to agree very closely with the 

 proiiortionate distribution of fractures accoi-ding to the laws of 

 probability, as applied by the writer to the femur. 



General conclusions 



The e^'idence presented in this paper is believed to warrant 

 the following conclusions : 



1. The normal external form and internal architecture of 

 the human femur results from an adaptation of form to the 

 normal static demands, or normal function of this bone. 



2. The proportions of the femur are everywhere such as to 

 show a definite mathematical relationship between the body 



'weight, and the internal structure of the bone: there is a defi- 

 nite relation between the structure and the stress at every 

 point. 



3. Spongy bone is homogeneous with compact bone as a struc- 

 tural material and differs from it mechanically only in possessing 

 smaller strength approximately in proportion to its density as 

 compared with compact bone. 



4. The femur has a factor of safety of 5.68 for the stresses 

 due to running, 11.36 for the stresses due to walking, and 30.30 

 for the stresses due to standing. The weakest section for re- 

 sisting the stresses due to loads on the femur-head is in the 

 neck of this bone. 



5. The structure of the femur is based upon the mathematical 

 requirements of mechanics and the inner architecture is such 

 as to produce great strength with a small amount of material 

 and the disposition of the material at all points corresponds to 

 the stress requirements at those points. 



6. The general law of bone, the adaptation of form to function, 

 holds true mathematically and mechanically in the normal 

 human femur, and therefore for all other normal human bones. 



Special conclusions 



1. A foundation is laid for the study and mechanical analysis 

 of the spongy bone entering into the structure of other parts of 

 the skeleton, by the application of the principle that spongy 



