LAWS OF BONE ARCHITECTURE 215 



PART III. THE MATHEMATICAL ANALYSIS OF THE FEMUR 



Introduction 



The work of Wolff in developing the theory of the functional 

 form of bone has been of immense value and marks a great 

 advance in the sui'gery of the bones. His theory was based 

 on the study of the femur in great detail, the anatomical rela- 

 tions being carefully described, and the deductions based on the 

 normal structure were supplemented by a large number of path- 

 ological specimens of bone which were considered in much less 

 detail than the normal femur. 



1 . The Culmann model. The foundation for his whole theory, 

 however, was the mathematical analysis which Culmann made 

 of a model of the head and neck of the femur. This model 

 (fig. 13) had a circular cross section and the diameter varied 

 gradually from a maximum at the head to a minimum in the 

 shaft as shown. The analysis of this model was made for a 

 load of 30 kilograms placed on the head which acted in a direc- 

 tion parallel to the shaft. The lines of maximum stress in this 

 model were calculated on the supposition that the model was 

 a solid body. Under the assumed conditions the analysis of the 

 lines of maximum stress in the model is correct. But it must 

 be pointed out that the assumed model does not resemble the 

 normal femur, except remotely, and therefore the assumption 

 that the lines of stress in the model explain the position of the 

 trabeculae in the head of the femur is not warranted. 



2. Mathematical objections to Cidmann's conclusions. With- 

 out disparagement of Wolff's or Culmann 's work the following 

 objections may be fairly urged against the soundness of their 

 mathematical analysis of the head of the femur: 



1. Only a small part of the femur was analyzed and the rela- 

 tion of this part to the whole bone as a structure was not shown. 



2. The direction in which the assumed load on the femur 

 acted was taken parallel to the shaft of the femur. This point 

 will be considered in greater detail under the heading, Loading, 

 in Part III. 



