339 



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 



