( 11 )

and loaded as in No. 1, whose length in feet is L,depth in inches d, and breadth in inches h, and it berequired hence to find the strength of a beam of thesame material, but of different dimensions, it may befound by the proportions stated above; namely, that itis directly as the breadth and square of the depth,and inversely as the length. But for the convenienceof practical men, all experimental results, in what fol-lows, are reduced to the case in which the breadth,depth and length are each unity; and it thereforeonly requires that the tabular S should be multipliedby the square of the given depth in inches by thebreadth in inches, and the product divided by thelength in feet, and this again multiplied by the propercoefficient belonging to the particular mode of fixingand loading; or in other words,

Let L be the length of any beam in feet;d its depth in inches;b its breadth in inches;

C the coefficient belonging to the given mode offixing and loading, or multiples of S in thepreceding page;

Then the weight, W, required to break it will beW = C- t x S.

Jj

This formula is general, and all that is required isthe value of S for different materials, of which the fol-lowing table contains, it is believed, all that are everlikely to be required in practice. The first part (Tab.III.) is reduced from a series of experiments made byMr. Barlow on pieces 6 feet long and 2 inches square,each result being the mean of two or more experiments.