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ANNUAL REPORT SMITHSONIAN INSTITUTION, 1918. 



T> 1 is the outer diameter of the cross section of the hollow cylinder ; 

 and 



d is the diameter of the cross section of the inner area of the hollow 

 cylinder. 



Utilizing these two formulae we may get, by aid of the most ele- 

 mentary algebraic calculations, which need not be made here, the 

 following two interesting conclusions : 



1. If we assume that an extremity with the central skeleton (lower 

 left figure) has the same cross section as an extremity with an outer 



B. C. 



Fig. 1.— Graphs of cross sections of skeletons, of limbs for instance. A, exoskeleton with diameter of 

 internal area (d)=4/5 of the external diameter (D). B and C, endoskeletons. 



skeleton (upper figure), the areas of the cross section of the skeleton 

 and muscles being equal in both figures, then the extremity with the 

 central skeleton will appear to be almost three times (2 and 11/15) 

 weaker than the one having a peripheral skeleton. 



2. If we calculate the diameter that the cross section of the central 

 skeleton should be in order that, with the same outer diameter of the 

 extremity, it should be equally strong in both cases, we will get the 

 third figure (lower right figure). It turns out that the skeleton has 

 to be colossal : Its diameter must be 84 per cent of the diameter of 

 the whole cross section, so that only an insignificant peripheral layer 



