TISSUES AND SIMPLE ORGANS. 65 



T. The fibres and tissue-layers of a beam supported at both ends 

 having a weight in the middle are so influenced that the uppermost 

 fibres are most strongly pressed together and the lowermost fibres 

 are pulled. In the middle of the beam in cross-section there is an 

 imaginary " neutral" fibre in which the pressing tension passes into 

 a pulling tension. In this region pushing and pulling are at a 

 minimum. From this it follows that in order to have an appropriate 

 distribution of material in such a beam it must, in general, have the 

 form (in cross-section) of two capital T's, one of which is inverted, 

 thus (S3), since the mass of material must be distributed at the 

 points of greatest tension. In following out this idea one can 

 readily understand that a hollow cylinder would represent a type of 

 structure adapted to resist a bending tension from all sides. The 

 combination of many double-T supports will give us a polygon 

 whose sides are represented by the cross-lines of the T's. These 

 ' cross-lines, as already stated, indicate the strongest parts of the sup- 

 port (" girth ") ; the radial connecting lines (" filling ") may be 

 much weaker; when the " girth" becomes continuous, the " filling" 

 may be entirely omitted. 



II. In the determination of the equilibrium of a prismatic staff 

 bent to one side by some lateral force we must first of all find the 

 "modulus of elasticity." This maybe found as follows (it must 

 be remembered that in the rational construction of this formula no 

 fibre is to be stretched or elongated beyond the limit of elasticity) : 

 If we let A represent the area, in cross-section, of the tissue to be 

 tested, W the maximun weight which can be supported without 

 permanent elongation, then the supporting power within the limit 



W 



of elasticity per unit of surface U= -j. By dividing U by the 



specific elongation due to W, that is, y, in which A equals the elonga- 

 tion due to the tension and I the original length, the modulus of 

 elasticity is found E = U. -i-. 1 



A 



III. Besides the modulus of elasticity, there is still another 

 factor which enters into the determination of the equilibrium of a 

 bent twig or staff. 



1 In normal well-developed bast 1000 units (in length) of I equal about 13 units 

 of A, U = 20, hence E= 1540. 



