Report on ike Progress and State of Applied Mechanics. 215 



34. The Mathematical theoex of Steength is a branch of the 

 general theory of elasticity; and when that general theory is strictly 

 applied to such problems as occur in practice, the mathematical expres- 

 sions arrived at are so complex, that they have been exactly solved in 

 but a few cases, and are in general too elaborate for practical use. It 

 therefore becomes one of the functions of mathematicians who study 

 this branch of mechanics, to seek for approximate solutions of the 

 problems that it presents, which shall be sufficiently simple to be used 

 as practical rules, without incurring too great a sacrifice of exactness. 

 A remarkable example of success in this, is furnished by M. de St. 

 Veuant's investigations upon the torsion of bars, other than circular in 

 Bection. 



35. Amongst recent experiments on the strength of stone which have 

 been made generally public, are those of Messrs. Wheatstone and 

 Daniell, on specimens of stone prepared for the building of the Palace 

 of Westminster. It is the practice of many architects and engineers — 

 and it ought to be the practice of all — to test, by experiments, the 

 stone proposed to be used in every building of importance. Mr. Alex- 

 ander J. Adie's experiments on the expansion of stone and brick by 

 heat, published some years ago in the Transactions of the Royal Society 

 of Edinburgh, furnished data which are indirectly of importance as 

 regards the strength of structures. 



36. The principal sources of information respecting the strength of 

 timber, and especially of those kinds which are most commonly employed 

 in Europe, continue to be the experiments of Professor Barlow, as re- 

 corded in his work on tlie Strength of Materials, and (with the addition 

 of some experiments by Tredgold and others), in TredgokVs Princijdes 

 of Carpentry. The most important additions recently made to the 

 information afforded by these works, have been the experiments of Mr. 

 Hodgkinson on the resistance of timber to crushing, — those of Captain 

 Fowke, on the specimens of timber at the Paris Exhibition of 1855, — 

 and those of Mr. Adrian Mendis, on the Timber Trees of Ceylon. 



37. The information collected in the standard work of Tredgold, on 

 the Stbenoth op Ieon, received, a few years ago, most valuable 

 additions from the experiments of Mr. Hodgkinson, who ascertained 

 the great difference which exists between the strength of cast iron to 

 resist direct crushing and direct tearing — the former being about six 

 times the latter — a fact of the highest practical importance. Mr. 

 Hodgkinson also ascertained the mode of variation of the resistance of 

 cast and wrought iron pillars to a vertical load, and represented its law 

 by a formula. Mr. Lewis Gordon has since shown, in a paper read to 

 the Philosophical Society of Glasgow, that the results of Mr. Hodgkin- 



