LAWS OF BONE ARCHITECTURE 183 



or meeting the lines of the first system at an acute angle and 

 stopping: the third system consisted of numerous short cancelli 

 which bound the two preceding groups together. These obser- 

 vations on the two first groups are correct and in general accord 

 with the facts, but the description and explanation of the 

 position and action of the third group is entirely erroneous. 



The earliest German writer on this subject seems to have been 

 Engel ('51), an anatomist of Prague, who made remarkably 

 good observations bringing out some points previously over- 

 looked. He comments on the occurrence in the inner structure 

 of the femur and tibia of the pointed arch, the elliptic arch in 

 various combinations with vertical and inclined buttresses. 

 But the significance of the various geometrical figures he so 

 accurately described was never grasped by him. 



In 1858 the English anatomist, Humphry, pubUshed his ob- 

 servations on the inner architecture of bone, contributing two 

 very important additions to the knowledge of the inner structure 

 of the head of the femur; that in the frontal section of this bone 

 the lines of cancelli arising from the articular surface of the 

 head are perpendicular to the articular surface at all points; 

 that the two principal groups of cancelli intersect each other 

 at right angles. The importance of these two observations was 

 not recognized for almost a decade, although upon them an 

 important part of the theory of the mathematics of bone archi- 

 tecture depends. 



In 1867 Hermann von Meyer demonstrated before a meeting 

 of naturalists held at Zurich a collection of preparations of hu- 

 man bones and discussed the significance of the arrangements 

 of the cancelli in many of the bones. By chance it happened 

 that Culmann, the great Zurich mathematician and engineer, 

 attended the meeting and became much interested in the struc- 

 ture of the bones. He observed that the cancelli of many of the 

 bones were arranged in forms similar to those which he had 

 computed as the lines of maximum internal stress in similar 

 bodies or structures when carrying similar loads. This led to 

 his calculation of the lines of maximum internal stress in a 

 Fairbairn crane having a form which was assumed to approxi- 



