ON THE STRENGTH OF PILLARS. 
423 
bars upon which most of the experiments on wrought iron were made. But we 
have seen (Art. 59.) that 21187 lbs., and 21355 lbs. produced a great change in the 
strength of the pillars 30| inches long ; it was, therefore, obvious that incipient crush- 
ing was the cause of the great falling off in the strengths of these pillars, and indeed 
of those in all the preceding experiments (Art. 6.) ; and a knowledge of this fact pre- 
pared me for attempting to adapt the formula used for long pillars to the case of short 
ones (Art. 41.). 
61. It was shown (Art. 12.) from the experiments upon cast iron, that a uniform 
pillar, with its ends flat, had the same strength as one of equal lateral dimensions, 
and half the length, with the ends rounded. Making a similar comparison between 
the wrought-iron pillars, in Table XII., or in the preceding abstract (Art. 58.), we 
obtain an approximation to the same result ; and that even when the pillars, from 
their shortness, are much crushed by the breaking weight, which we have seen was 
the case with the shortest wrought-iron pillars. 
Strength of Pillars of Wrought Iron and Timber, as dependent upon their dimensions. 
62. On this subject I have laboured under considerable difficulty, for want of expe- 
riments of a sufficiently comprehensive character to furnish all the data that were 
required. The complete determination of the constants for the purpose would require 
experiments upon pillars, whose lengths, compared with their diameters, were nearly 
as various as those upon cast iron in this paper. 
I trust, however, that the experiments in Tables XII. and XIII., and the analogies 
derived from the results on cast iron, will supply the deficiencies so far, as, in some 
measure, to meet the wants of practice. 
Length . — To find the inverse power of the length to which the strength of wrought- 
iron cylindrical pillars, of a constant diameter, is proportional, I shall follow the mode 
used for cast-iron pillars (Art. 26. 27-) ; and confining the inquiry to pillars suffi- 
ciently long not to have been crushed (Art. 6. 60.) with the breaking weight, we have 
as below : 
Lengths of which the strengths 
are compared. 
Description of pillar. 
Inverse power of the length. 
ft. ins. ft. ins. 
7 6| 2 6L 
7 6| 5 o| 
7 6f 5 0| 
Rounded ends. 
Rounded ends. 
Flat ends. 
1*9546 ~| 
1*9199 >Mean 2*0316. 
2*2203 J 
Whence it appears that the strength is as the inverse square of the length nearly. 
Diameter. — To find the power of the diameter, or of the side of a square, to which 
the strength of wrought-iron pillars of a given length is proportional. For this pur- 
pose we have, from Table XII., the following results : 
In the pillars 2 feet 6^ inches long, rounded at the ends, from a mean between 
three experiments, one of *52 inch diameter had its greatest resistance overcome with 
