ON THE STRENGTH OF PILLARS. 
399 
29. Pillars with their Ends fiat. 
Diameters considered 
Lengths of which the 
Values of x. 
Mean value of x. 
equal. 
strengths are compared. 
inch. 
inch. 
inches. 
inches. 
•77 
•77 
60-5 and 30-25 
1-8431 
•77 
•777 
60-5 
20-1666 
1-682 
1-625 
•77 
*775 
60-5 
15-125 
1-550 
r 
•77 
•785 
60-5 
12-100 
1-424 
•997 
1-01 
60-5 
30-25 
1-691 ’ 
1-587 
•997 
1*022 
60-5 
20-1666 
1-483 J 
> 
30. The value of x, as exhibited in the preceding abstracts from Tables I. and II., 
is not constant. Taking pillars of any particular diameter, we see that x decreases 
according as we decrease the length of the pillar ; and consequently increase the press- 
ure necessary to break it. Thus, in pillars with rounded ends, taking those of *50 
inch diameter, and comparing the strengths of those of 60| inches long with those 
of 30-25, 15-125, 7'5625, 3-78125 inches, we have x = T914, T867, 1'734, 1*681. In 
pillars with flat ends, taking those of which the diameter is '77 inch nearly, and com- 
paring those of 60^ inches long with those of 30*25, 20-1666, 15-125, 12-1 inches, we 
obtain successively, x — T843, T682, T550, T 424. This decrease in the value of x 
also takes place in the comparison between the different lengths of the pillars *99 inch 
diameter ; and it is evident that it would do so in all cases where the diameter was 
% 
the same, whatever that diameter might be. The falling off in the strength of pillars, 
whose length is less than twenty-five to thirty times the diameter, in those with flat 
ends ; and about one-half that length, in those with rounded ends, as before observed, 
is not the sole cause of this diminution in the value of x, though it is a part of it. 
Indeed, we may perhaps say that both depend in some degree upon the same cause, 
the compressibility of the material. The increasing weight alters the position of the 
neutral line in the pillar, and consequently lessens the part subjected to tension. By 
this means the flexibility of the pillar is increased, and its resistance decreased; because 
this resistance depends upon the transverse strength and the power to resist flexure. 
The position of the neutral line, on which this variation of the strength depends, has 
been obtained in several of the cases of Tables I. and II. ; and indeed many others. 
31. In the abstract from Table I., just given, and in which the lengths vary as widely 
as sixteen to one, we find the highest value of x =■ 1-914, and the lowest = 1'537 ; 
and the mean from all the values = T7117. 
The abstract from the pillars with fiat ends, in Table II., is not pursued to the same 
extent as the former. In it, the highest and lowest values of x are T843 and T424 ; 
the mean from the whole of these being 1*6 12. 
32. The pillars compared above comprise a much greater range of lengths than 
those in general use ; and as the shortest pillars do not come within the simple rules 
applicable to the longer ones, I shall adopt 1'7 in the future calculations as an ap- 
proximate value of x, applicable to most of the pillars used in practice. 
