184 JOHN C. KOCH 



mate that of the upper fourth of the femur. Basing his calcu- 

 lations upon this crane having no hollow spaces he found that 

 the lines of maximum internal stress in this model had similar 

 shapes and positions to the caricelli in the upper femur as shown 

 in frontal section. The conclusion was that these cancelli lie 

 along the paths of maximum internal stress within the bone 

 and thus transmitted a maximum load in the bone with a mini- 

 mum of material. This discovery of Culmann is the mathe- 

 matical basis of the modern theory of the functional form of 

 bone. 



Von Meyer ('67) published an article describing in great 

 detail the inner structure of various bones together with Cul- 

 mann's discovery, but incorrectly described the intersections of 

 the cancelli in the head of the femur as obtuse or acute and his 

 illustrations show the cancelli rising from articular surfaces in 

 nearly all cases inaccurately, at an acute or obtuse angle. 



Wolff ('69) improved on the technique of his predecessors by 

 using the ivory-worker's saws for making extremely thin sec- 

 tions of bone which were very easily photographed when placed 

 against a dark back-ground. In this manner and with abso- 

 lute accuracy the detailed structure of the bone could be repro- 

 duced and studied. He emphasized the importance of the 

 right angle crossing of the cancelli in the upper femur, which 

 was first observed by Humphry, and called attention to the 

 significance of the analogy between the directions of the cancelli 

 of the upper femur and the tensile and compressive lines of 

 maximum stress, as demonstrated by Culmann's calculations 

 for the Fairbairn crane. 



Shortly after appeared a large number of studies and in- 

 vestigations of the subject by numerous writers. It is impos- 

 sible to review here all the valuable contributions and the ex- 

 tensive controversial literature on the subject. Various writers 

 took up in detail the study of the different bones almost alto- 

 gether from a morphological point of view, rather than a mathe- 

 matical or analytical one. Important work was contributed by 

 Zaiijer ('71), Wolfermann ('72), Aeby ('73), Engelmann ('73), 

 Merkel ('74), Langerhans ('74), Bardeleben ('74), Dwight ('75), 



