678 ON FOKM AND MECHANICAL EFFICIENCY [ch. 



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 

 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-Unes " 

 tend to run vertically downward; but 

 Pig. 332. where the bracket is fastened to the 



wall, there is pressure directed horizon- 

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

 attachment; and the vertical beginning and the horizontal end 

 of these pressure-hnes 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-hnes are identical in form 

 with the compression-hnes, 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-hnes 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 

 always possible to weaken one set of hnes 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-lines, 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-Unes of the old. The biological interest connected 

 with this principle hes chiefly in the mechanical construction of 

 the rush or the straw, or any other typically cyhndrical 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 

 cyhndrical stem, which Gahleo was the first to call attention to. 



