228 



• pillars with relation to their diameter and length. He concludes 

 that the index of the power of the diameter, to which the strength 

 is proportional, is 3'736. He then proceeds to determine, by a 

 comparison of experimental results, the inverse power of the length 

 to which the strength of the pillar is proportional. The highest 

 value of this power is r914, the lowest, 1*537, the mean of all the 

 comparisons, 1*7117. He thus deduces, first, approximate empirical 

 formulae for the breaking weight of solid pillars, and then proceeds 

 to deduce more correct methods of determining their strength. 



Experiments on hollow pillars of cast iron are then described, 

 and formulse representing the strength of such pillars are deduced 

 from these experiments. 



After giving some results of experiments still in progress for 

 determining the power of cast-iron pillars to resist long-continued 

 pressure, the author proceeds to determine from his experiments^ 

 the strength of pillars of wrought iron and timber, as dependent 

 on their dimensions. The conclusion for wrought iron is, that the 

 strength varies inversely as the square of the pillar's length, and 

 directly as the power 3*75 of its diameter, the latter being nearly 

 identical with the result obtained for cast iron ; for timber, the 

 strength varies nearly as the 4th power of the side of the square 

 forming the section of the pillar. Experiments for determining the 

 relation of the strength to the length in pillars of timber, were not 

 instituted, as, from the great flexure of the material, it was consi- 

 dered that no very satisfactory conclusions on this point could be 

 derived experimentally. 



In conclusion, the author gives the relative strengths of long 

 pillars of cast iron, wrought iron, steel, and timber. 



