with great patience and admirable skill, and at a very considerable cost. Mr. Hodgkinson's position among the manufactories of Man- chester, together with the unlimited command over the resources of one of the largest engineering establishments, which he obtained through the liberality of its proprietor Mr. Fairbairn, enabled him to direct his inquiries to the forms of pillars which are found most useful in practice. The results of his labours he has reduced to em- pirical formulae, peculiarly adapted for application to the purposes of mechanical art.
Among the most useful of the practical conclusions to which he has arrived, the following are more particularly deserving of notice.
Mr. Hodgkinson has found, that in all long pillars of the same di- mensions, the resistance to crushing by flexure is about three times greater when the ends of the pillars are flat, than when they are rounded. A long uniform cast-iron pillar, with its ends firmly fixed, whether by means of discs or otherwise, has the same power to re- sist breaking as a pillar of the same diameter, and half the length, with the ends rounded, or turned so that the force would pass through the axis. The strength of a pillar with one end round and the other flat, is the arithmetical mean between that of a pillar of the same dimensions with both ends round, and one with both ends flat. Some additional stnmgth is given to a pillar by enlarging its diameter in the middle part.
The strength of long cast-iron pillars with relation to their dia- meter and length is also made the subject of Mr. Hodgkinson's in- vestigations ; and the result he deduces from them is, that the index of the power of the diameter, to which the strength is proportional, is 3*736. He has also determined, by a comparison of experimental results, the inverse power of the length to which the strength of the pillar is proportional. The highest value of this power he finds to be 1*914, the lowest 1*537, and the mean of all the comparisons 1*7117. He thus deduces, first, approximate empirical formulae for the break- ing weight of solid pillars, and afterwards, more correct methods of determining their strength. From experiments on hollow piUars of cast-iron, formulae representing the strength of such pillars are, in like manner, deduced.
The strength of pillars of wrought iron and of timber, in relation to their dimensions, is made the subject of another series of experi- ments. The result for wrought iron is, that the strength varies in- versely as the square of the length of the pillar, and directly as the power 3*75 of its diameter, the latter being nearly identical with the result obtained for cast iron ; while in timber, the strength varies nearly as the fourth power of the side of the square forming the sec- tion of the pillar. In like manner, the power of cast-iron pillars to resist long-continued pressure, and the relative strengths of long pil- lars of cast iron, wrought iron, steel and timber, are determined.
The inquiry which constitutes the subject of this paper is not, however, the first of the kind in which Mr. Hodgkinson has been engaged ; several series of experiments and papers on the strength of iron, in various forms, have been published by him at different
