made with those experiments; but from the evidence in chief given by Mr. Stephenson on the subject, on the 5th May following, it appears that the idea which prevailed in his mind was that of a bridge with openings of 450 feet (afterwards increased to 460 feet); with a roadway formed of a hollow wrought-iron beam, about 25 feet in diameter, presenting a rigid platform, suspended by chains. At the same time, he expressed the confident opinion that a tube of wrought iron would possess sufficient strength and rigidity to support a railway train running inside of it without the help of the chains. While the bill was still in progress, Mr. Fairbairn proceeded with his experiments. He first tested tubes of a cylindrical form, in consequence of the favourable opinion entertained by Mr. Stephenson of the tubes in that shape, extending them subsequently to those of an elliptical form. {329b} He found tubes thus shaped more or less defective, and proceeded to test those of a rectangular kind. After the bill had received the royal assent on the 30th June, 1845, the directors of the company, with great liberality, voted a sum for the purpose of enabling the experiments to be prosecuted, and upwards of £6000 were thus expended to make the assurance of their engineer doubly sure. Mr. Fairbairn’s tests were of the most elaborate and eventually conclusive character, bringing to light many new and important facts of great practical value. The due proportions and thicknesses of the top, bottom, and sides of the tubes were arrived at after a vast number of trials; one of the results of the experiments being the adoption of Mr. Fairbairn’s invention of rectangular hollow cells in the top of the beam for the purpose of giving it the requisite degree of strength. About the end of August it was thought desirable to obtain the assistance of a mathematician, who should prepare a formula by which the strength of a full-sized tube might be calculated from the results of the experiments made with tubes of smaller dimensions. Professor Hodgkinson was accordingly called in, and he proceeded to verify and confirm the experiments which Mr. Fairbairn had made, and afterwards reduced them to the required formula.