LAWS OF BONE ARCHITECTURE 201 



be very briefly considered. The strength of any column of 

 homogeneous material of whatsoever shape or size is dependent 

 upon the following factors: 



1. The materials of which it is built. 



2. The cross sectional area. 



3. The shape of the cross section. 



4. The ratio of the smallest diameter to total length of the 

 column. 



These factors are to a certain extent interdependent. It is 

 obvious that different materials will vary in strength depending 

 upon their physical qualities. If all other factors remain un- 

 changed, an increase in cross sectional area will give increased 

 strength. 



44- The shape of the cross section is of the greatest impor- 

 tance. For example, a flat piece of card-board of rectangular 

 form, if placed in a vertical position will carry only a very small 

 weight applied to the upper end without bending. But if this 

 same card-board be rolled into the form of a hollow cylinder, 

 with the edges fastened together, it will carry without bending 

 many times the weight previously carried by the flat sheet, 

 although there has been no increase in the amount of material 

 employed nor in the height of the column or sheet. 



45. If the ratio of least diameter to total length of column is 

 decreased, without decreasing the cross sectional area the stiff- 

 ness of the column is reduced and its load-carrying capacity is 

 reduced. In terms of mechanics the measure of stiffness of 

 any column is expressed by the ratio of its length to its least 

 moment of inertia. 



46. Determination of moment of inertia. In the case of irregu- 

 lar cross sections such as are encountered in the bones, the 

 determination of the moment of inertia can not be made by the 

 integration formulas of calculus, but the methods of calculus 

 may be applied graphically to the problem, and the moment of 

 inertia of any section may be very closely approximated. 



Jf.7. For such calculation an accurate drawing (tracing) is made 

 of the cross section whose moment of inertia is to be computed. 

 Then the principal axes, which are the axes of greatest and of 



