breadth taken flatwise, so we must divide four into sixteen and find that our net gain in stiffness is in this case four-fold. [Illustration: Telegraph poles under compression. Wires under tension.] Girders. Here let us for a moment dwell upon the two opposite ways in which strength may be brought into play, as either compression or tension is resisted. An example presenting both is a telegraph pole, with well-balanced burdens of wires. Its own weight and its load of wires, compress it, as we can prove by measuring the pole as stretched upon the ground before being set in place, and then after it is erected and duly laden. Should this downward thrust be excessive, the pole would be crushed and broken down. The strung wires are not in compression, but in the contrary case of tension, and are therefore somewhat lengthened as they pass from one pole to the next. Now observe a mass first subjected to compression, and next to tension. In bearing a pound weight a rubber cylinder is compressed and protrudes; when the weight is suspended from this cylinder, the rubber is lengthened by tension. In each case the effect is vastly greater than with wood or steel, because rubber has so much less stiffness than they have. [Illustration: Rubber cylinder. Flattened by compression. Lengthened by tension.] Both tension and compression are exhibited in our little rubber joist, which illustrates the familiar wooden support beneath the floors of our houses. This form in giving rise to the girder has been changed for the better. Let us see how. As the rubber joist sags between its ends, we observe that its upper half is compressed, and its lower half extended, the two effects though small being quite measurable. As we approach the central line, A B, this compression and tension gradually fall to zero; it is clear that only the uppermost and undermost layers fully call forth the strength of the material, the inner layers doing so little that they may be removed with hardly any loss. Hence if we take a common joist and cut away all but an upper and lower flange, leaving just web enough between to hold them firmly together, we will have the I-beam which among rectangular supports is strongest and stiffest, weight for weight. In producing it the engineer has bared within the joist the skeleton which confers rigidity, stripping off all useless and burdensome clothing. An I-beam made of rubber when laid flatwise over supports at its ends will sag much; when laid edgewise it will sag but little, clearly showing how due form and disposal confer stiffness on a structure. [Illustration: Rubber joist in section, compressed along the top, extended along the bottom.] [Illustration: Girder cut from joist.] [Illustration: Rubber I-beam suspended flatwise, and edgewise.] [Illustration: Simple girder contours.] [Illustration: Girder contours simple and built up.] [Illustration: Girder forms in locomotive draw-bars.]