972 ON FORM AND MECHANICAL EFFICIENCY [ch. 



a diagram, or "graph," of the bending-moments from one point to 

 another along the length of the bone. 



The second point requires a Uttle more explanation. If we 

 imagine our loaded beam to be supported at one end only (for 

 instance, by being built into a wall), so as to form what is called 

 H i j a "bracket" or "cantilever," then we can 



see, without much difficulty, that the lines of 

 stress in the beam run somewhat as in the 

 accompanying diagram. Immediately under 

 the load, the "compression-lines " tend to run 

 ■ ^ vertically downward, but where the bracket is 



^^' ' fastened to the wall there is pressure directed 



horizontally against the wall in the lower part of the surface of 

 attachment; and the vertical beginning and the horizontal end of 

 these pressure-lines must be continued into one another in the form 

 of some even mathematical curve — which, as it happens, is part 

 of a parabola. The tension-lines are identical in form with the 

 compression-lines, of which they constitute the "mirror-image"; 

 and where the two systems , intercross they do so at right angles, 

 or "orthogonally" to one another. Such systems of stress-lines as 

 these we shall deal with again; but let us take note here of the 

 important though well-nigh obvious fact, that while in the beam 

 they both unite to carry the load, yet it is often possible to weaken 

 one set of lines at the expense of the other, and in some cases to do 

 altogether away with one set or the other. For example, when we 

 replace our end-supported beam by a curved bracket, bent upwards 

 or downwards as the case may be, we have evidently cut away 

 in the one case the greater part of the tension-hnes, and in the 

 other the greater part of the compression-hnes. And if instead of 

 bridging a stream with our beam of wood we bridge it with a rope, 

 it is evident that this new construction contains all the tension-hnes, 

 but none of the compression-hnes of the old. The biological interest 

 connected with this principle Hes chiefly in the mechanical construc- 

 tion of the rush or the straw, or any other typically cylindrical 

 stem. The material of which the stalk is constructed is very weak 

 ,to withstand compression, but parts of it have a very great tensile 

 strength. Schwendener, who was both botanist and engineer, has 

 elaborately investigated the factor of strength in the cylindrical 



