319 



ends flat, was about three times as strong as a pillar of the same 

 length and diameter with its ends rounded in such a manner that the 

 pressure would pass through the axis, the ends being made to turn 

 easily, but not so small as to be crushed by the weight ; 2nd, that 

 if a pillar of the same length and diameter as the preceding had one 

 end rounded and one flat, the strength would be twice as great as 

 that of one with both ends rounded ; 3rd, if, therefore, three pillars 

 be taken, differing only in the form of their ends, the first having 

 both ends rounded, the second one end rounded and one flat, 

 and the third both ends flat, the strength of these pillars will be as 

 1 2 3 nearly. 



The preceding properties having been arrived at experimentally, 

 are here attempted to be demonstrated, at least approximately. 



The pillars referred to in my former paper were cast from Low 

 Moor iron No. 3 ; they were very numerous, but usually much 

 smaller than those used in the present trials. I felt desirous too of 

 using the Low Moor iron in the hollow pillars employed on this 

 occasion, not on account of its superior strength, but its other good 

 qualities. The pillars from this iron were cast 10 feet long, and 

 from 1\ to 4 inches diameter, approaching in some degree, as to size, 

 to the smaller ones used in practice. The results from the breaking 

 weights of these were moderately consistent with the formulae in the 

 former paper, with a' slight alteration of the constants, rendered 

 necessary by the castings being of a larger size, and therefore softer 

 than before, a matter which will be adverted to further on. 



The formulae for the strength of a hollow pillar of Low Moor iron 

 No. 2, where w is the breaking weight, in tons, of a pillar whose 

 length is I in feet, and the external and internal diameters D and d 

 in inches, the ends being flat and well bedded are as below : 



-ss ,73-55 

 ~ d 



from formula in Phil. Trans. 1840 ; 



from formula in present paper. 



To obtain some idea of the relative strengths of pillars of different 

 British irons, I applied, at Mr. Stephenson's suggestion, to Messrs. 



