186 JOHN C. KOCH 



t 



curved trabeculae in bone are like the parabolic lines formed 

 by the tiny jets of water which cross each other at random in a 

 water-fall. Biihr ('97) on solely mathematical grounds, with- 

 out respect to anatomy or clinical studies, denies that the femur 

 acts as a crane at all, and asserts that the Culmann analysis is 

 entirely wrong! 



To enumerate all the more or less fanciful theories proposed 

 to account for the form of the inner architecture of bone would 

 be both tedious and confusing. In spite of the general accept- 

 ance, at least in part, of Wolff's doctrines, there is still strong 

 opposition to his theories of bone transformation and the func- 

 tional form of bone, and the soundness of the mathematical basis 

 of these theories has been assailed with numerous mathematical 

 arguments. 



The development of Roentgenology has given a new interest 

 to the subject of bone architecture, by permitting comparative 

 studies of the inner architecture to be made upon the living in 

 whom the transformation processes can be readily followed. 

 Such studies made by Sudeck, Gallois and Bosquette ('08), 

 and many other investigators have tended to confirm the sound- 

 ness of the doctrine advanced by Wolff, although all such stud- 

 ies lack the precision required for the mathematical demonstra- 

 tion of the theories under discussion. 



Additional work by Solger, von Recklinghausen ('93), Roux 

 ('80, '93, '96), Graf ('94), Schmidt ('98), Maas ('01), and Fuld 

 ('01) tend to confinn, in a general way, the observations of 

 Wolff. The work of Gebhardt ('01) will be briefly discussed in 

 another section. 



PART II. SUMMARY OF MATHEMATICAL PRINCIPLES 



Introduction 



A fundamental idea of mechanics is necessary to an under- 

 standing of the application of mechanics to the problem pre- 

 sented in the analysis of the femur. It will be manifestly im- 

 practicable to explain these principles of mechanics, which are 

 applied to this problem, in great detail and only the essentials 



