284 JOHN C. KOCH 



If w{^ ('oiiibiiic these statistics of these two investigators we have 

 the following: 



COMBINED COMPUTED 

 PER CENT PER CENT 



Upper third 64 16.3 19.9 



Middle third 254 64.6 62.9 



Lower tliird 75 19.1 17.2 



393 100.0 100.0 



The close agreement of the actual distribution of breaks of the 

 femur with that determined by the application of the mechani- 

 cal principles and the laws of probability, as I have indicated, 

 is such as to be at least very suggestive as to the correctness of 

 the analysis. 



3. Suminary. My analysis of the femur is found to be in 

 agreement with the tests on longitudinal breaking and cross- 

 breaking tests on femurs made carefully by Messerer: the com- 

 puted maximum unit-stresses in the femur are closely parallel 

 to the ultimate strengths of compact bone as determined by Rau- 

 ber: the statistics of the location of fractures in the femur are 

 very near the calculated distribution based on this analysis of 

 the femur; and my ow^n breaking tests on one of the femurs 

 analyzed are in close agreement with Rauber's tests. 



These independent checks on the soundness of this analysis 

 of the femur, and the consistency of the quantitative relations 

 established throughout, afford the strongest confirmation of the 

 accuracy of the computations and the correctness of the appli- 

 cations of the principles of mechanics to this problem. 



General comments 



The doctrine of the functional form of bone, with its coral- 

 lary of the functional pathogenesis of deformity, advanced by 

 Wolff, and maintained by him with rare courage and persistence 

 for so many years, is confirmed mathematically for the first time 

 by the studies presented in this paper, for the structure of nor- 

 mal bone. To confirm the doctrine of the functional pathogene- 

 sis of deformity mathematically, there is needed only the appli- 

 cation of the principles and methods used in this paper to the 



