(332.) No satisfactory results have been obtained either by theory or experiment respecting the laws by which solids resist compression. The power of a perpendicular pillar to support a weight placed upon it evidently depends on its thickness, or the magnitude of its base, and on its height. It is certain that when the height is the same, the strength increases with every increase of the base, but it seems doubtful whether the strength be exactly proportional to the base. That is, if two columns of the same material have equal heights, and the base of one be double the base of the other, the strength of one will be greater, but it is not certain whether it will exactly double that of the other. According to the theory of Euler, which is in a certain degree verified by the experiments of Musschenbrock, the strength will be increased in a greater proportion than the base, so that, if the base be doubled, the strength will be more than doubled. When the base is the same, the strength is diminished by increasing the height, and this decrease of strength is proportionally greater than the increase of height. According to Euler’s theory, the decrease of strength is proportional to the square of the height; that is, when the height is increased in a two-fold proportion, the strength is diminished in a four-fold proportion. (333.) The strain to which solids forming the parts of structures of every kind are most commonly exposed is the lateral or transverse strain, or that which acts at right angles to their lengths. If any strain act obliquely to the direction of their length it may be resolved into two forces (76.), one in the direction of the length, and the other at right angles to the length. That part which acts in the direction of the length will produce either compression or a direct pull, and its effect must be investigated accordingly. Although the results of theory, as well as those of experimental investigations, present great discordances respecting the transverse strength of solids, yet there are some particulars, in which they, for the most part, agree; to this it is our object here to confine our observations, declining all details relating to disputed points. Let A B C D, _fig. 186._, be a beam, supported at its ends A and B. Its strength to support a weight at E pressing downwards at right angles to its length is evidently proportional to its breadth, the other things being the same. For a beam of double or treble breadth, and of the same thickness, is equivalent to two or three equal and similar beams placed side by side. Since each of these would possess the same strength, the whole taken together would possess double or treble the strength of any one of them.