_A._--In the case of malleable iron bars it has been found that no very perceptible damage was caused by 10,000 deflections, each deflection being such as was due to half the load that produced a large permanent deflection.
78. _Q._--The power of a rod or pillar to resist compression becomes very little when the diameter is small and the length great?
_A._--The power of a rod or pillar to resist compression, varies nearly as the fourth power of the diameter divided by the square of the length. In the case of hollow cylindrical columns of cast iron, it has been found, experimentally, that the 3.55th power of the internal diameter, subtracted from the 3.55th power of the external diameter, and divided by the 1.7th power of the length, will represent the strength very nearly. In the case of hollow cylindrical columns of malleable iron, experiment shows that the 3.59th power of the internal diameter, subtracted from the 3.59th power of the external diameter, and divided by the square of the length, gives a proper expression for the strength; but this rule only holds where the strain does not exceed 8 or 9 tons on the square inch of section. Beyond 12 or 13 tons per square inch of section, the metal cannot be depended upon to withstand the strain, though hollow pillars will sometimes bear 15 or 16 tons per square inch of section.
79. _Q._--Does not the thickness of the metal of the pillars or tubes affect the question?
_A._--It manifestly does; for a tube of very thin metal, such as gold leaf or tin foil, would not stand on end at all, being crushed down by its own weight. It is found, experimentally, that in malleable iron tubes of the respective thicknesses of .525, .272, and .124 inches, the resistances per square inch of section are 19.17, 14.47, and 7.47 tons respectively. The power of plates to resist compression varies nearly as the cube, or more nearly as the 2.878th power of their thickness; but this law only holds so long as the pressure applied does not exceed from 9 to 12 tons per square inch of section. When the pressure is greater than this the metal is crushed, and a new law supervenes, according to which it is necessary to employ plates of twice or three times the thickness, to obtain twice the resisting power.