159. When the length of a pillar is less than 30 diameters, the resistance to direct crushing becomes a considerable portion of the strength, and must therefore be taken into account in all calculations of the breaking weight.

160. The formula adopted for the most part by the engineers on the Continent is due to M. Love, who applied it to steel and other pillars; * it is similar to that introduced to the notice of English engineers by Professor Gordon, which is of the form

CS/1+fR2 = W , [23] where C is the 'weight in pounds that will crush a short prism 1 inch square (Table XXI.); S the area of a cross section of the pillar in square inches; R = L/T the ratio of the length to the diameter or least thickness; f, a constant which

* ' Memoire sur la Loi de Resistance des Piliers d'Acier.' will depend upon the elasticity of the material; and W the weight in pounds that would break the pillar.

This formula, though apparently correct in theory, requires to be modified to accord with the result of experiments, thus:

CS/1.1+L2/2.9 T2 = W for square or rectangular pillars. [24]

In which L is the length of the pillar in feet, and T the least thickness in inches.

161. When the pillar is cylindrical, find the breaking weight as if it were square, and divide the result by 17.

162. The following Table shows the application of the formula to the mean results of the experiments of Lamande and Hodgkinson. The crushing strength of French oak being taken at 6336 lbs. to the square inch, and that of Dantzic oak at 7731 lbs. to the square inch:

Table XXIV. - Showing The Agreement Of The Formula With Experiment

163. Though the factor f in the formula would vary with the elasticity of the material, it has been taken at the constant value 2.9 for all kinds of wood, the strength of which is supposed to vary directly as C, or as the resistance to direct crushing per square inch.