ON THE STRENGTH OF PILLARS. 
427 
to be one-fourth of c, the crushing weight of the section. We have, therefore, as 
before, 
b c 
y ~ bTfc 
where b = the computed value from the general formulae for long pillars of different 
kinds of woods in the last article, and y that for short ones. 
If there were no fixed pressure at which pillars in breaking suffered a marked di- 
minution of their strength, but that there was a regular falling off with all weights 
from the least necessary to break a long pillar up to such as would crush it, then d 
might be taken = 0, and the formula would be 
b c 
y b + c 
where b would have to be obtained from experiments upon the longest pillars only, 
and this formula must be used for all others but them. We see that the strength of 
short (and perhaps long) pillars to resist fracture by flexure depends upon their re- 
sistance to crushing. Before attempting, therefore, to calculate the strengths of the 
short pillars broken by Lamande,wc must know the crushing strength of the French 
oak, which fortunately is given by Rondelet*, who states that its strength, from a 
mean between his experiments, is 6336 lbs. per square inch. Whence we are enabled 
to obtain an approximation to the value of c, the crushing weight of the pillars which 
Lamande made use of. 
66. The following table contains the results of his experiments upon short pillars 
computed by the formula for y , from the value of b, deduced (Art. 64.) from his longest 
and slenderest pillars, which we may consider not to have been materially reduced in 
their strength by crushing, and which are placed the first in the Table. 
* Traite de l’Art de Batir, tome 1, p. 232, edit. 1838. 
3 I 2 
