THE TRANSVERSE STRENGTH OF BEAMS AND TUBES. 447

We have seen in the last experiment that the meanbreaking-weight of an inch bar of cast-iron 1 inch long is13 - 6 tons, and for a bar 12 inches long it is therefore 1T3tons. Moreover, the ultimate deflection of bars 3 feet long 1was ‘78 inch, and the section being constant the deflectionof a bar will vary directly as the weight, and inversely asthe cube of the length. The ultimate deflection of a cast-iron bar 12 inches long would therefore be ^ x ’78 = *086inch.

Now, with this same weight the deflection of the wrought-iron bars was ‘080 inch. If, therefore, we estimate the usefulstrength by the amount of deflection, the wrought-iron barsappear but little stronger than cast-iron, and hence theusual constant for the strength of wrought-iron is very littlegreater than for cast-iron bars. But the cast-iron wasactually broken, whereas the wrought-iron carried more thandouble this weight before it was sufficiently bent to fallthrough the bearings, and its deflection is nearly propor-tionate to the weight close up to this limit. Hence thedifficulty of giving any constant for the ultimate strength ofthis material in this form, unless we define the limit to whichits deflection may be carried.

Experiment 53.

A bar 1| inch square, and 4 feet 6 inches long, with3 feet clear between the bearings, was then broken. Thisbar had been used as a rail for the trucks, and was some-what damaged and altered in texture by th6 constant ham-mering of the wheels, and it consequently cracked on thelower side with 1 ton 18 cwt. 2 qrs., its deflections beingas follows: —