135. It would appear from experiments by Mr. Parsons, of Her Majesty's dockyard service, on treenails used in shipbuilding, that the force required to shear English oak across the grain was 4000 lbs. per square inch, or about one-fourth of the cohesive force in the direction of the fibres.

136. When a pillar or other piece of timber is compressed in the direction of its length, the manner of yielding differs according to the proportion which the length bears to the least thickness or diameter. If the length be Considerable as compared with the diameter, the pillar will bend, and ultimately fail by breaking at the middle, in the same manner as it would under a cross strain. A portion of the section at fracture will be found to have been compressed and another portion extended.

When the pillar is very short in proportion to the diameter, it cannot be bent by any force, however great, but will fail by crushing alone.

No satisfactory theory has ever been adduced which will embrace these extremes. Euler, Lagrange,* Poisson,f and others, who have treated the subject, have for the most part confined their attention to cases where the length greatly exceeded the diameter, and they assumed the law in these cases to follow that relating to transverse strains. Hodgkin-son has shown that Euler's formula is true only on the supposition that failure takes place by bending, and not by the crushing of the material. It will be found, however, sufficiently near for practice when the length exceeds about

* 'Acad, de Berlin,' 1769; 'Collection Acad, de Turin,' vol. v. † Poissou,' Mecanique,' 2nd edit.

30 diameters, as in that case the load which would cause the pillar to end is a small proportion of that which would crush a short column of the same sectional area.

In pillars of medium length, or those shorter than 30 diameters, the load required to produce flexure is so considerable a portion of the crushing weight that the elasticity of the material is destroyed. In this case Euler's formula, to be at all applicable, would require considerable modifications, and it would altogether fail in the case of very short pillars, or those where the length is less than about 5 diameters, which yield wholly by crushing.

Euler's theory assumes the resistance to flexure to be directly as the fourth power of the diameter, and inversely as the square of the length. It is to be remarked that so high a power as 4 for the diameter or 2 for the length has not been obtained in any of the experiments which have been made on the resistance of wood to compression. In those of Lamande on pillars of oak, the power of the diameter deduced from pillars of 6 and 12 diameters in length is 2.186, and for pillars of 24 and 36 diameters in length it is 3.351. The powers of the length for the same pillars are .108 and 1.177. And Hodgkinson's experiments on Dantzic oak of 17 and 35 diameters in length, show the power of the length to be very much less than the square.

137. The following Tables give the results of experiments made by various authorities on the rosistance of wood to compression. But it is to be observed that in addition to the causes of variation in the resistance of timber referred to in Art. 75, a great difference is caused in the results according to the part of the tree from which the specimen is cut. The heart being stronger than the sapwood, and the butt stronger than the top, as shown by Fincham's experiments (Tables IX., X., and XIII.).