ON THE STRENGTH OF PILLARS. 
397 
60| inches long, rounded at the ends, comparing together the strengths of the pillars 
whose sides are 
'77 16 and 1*0275, gives n — 3*9830 ; 
77 16 and 1*540, gives n — 3'6789 ; 
1*0275 and 1*540, gives n — 3'4698 ; 
Mean n = 37105. 
24. From the two preceding inquiries, as to the value of n, we see, that whether the 
pillar be circular or square, the power of the thickness to which the strength is pro- 
portional is nearly the same. We may therefore conclude, that the same value of n 
would be obtained from any other form of section. 
In the values obtained from the circular pillars, which include specimens varying 
in length from twenty times the diameter to one hundred and twenty times, the values 
of n do not differ so widely, but that they may be considered as constant. They in no 
case rise so high as four, the power according to Euler ; but in pillars, so long with 
respect to their diameter that the breaking weight is very small, they approach nearly 
to it. We may, therefore, say that four is the power to which they would arrive if the 
breaking weight was so small that it produced no compression in the pillar. 
Long Pillars with the Ends jlat. 
25. We will determine the values of n, the power of the diameter to which the 
strength is proportional, in these pillars, in the same manner as was done in the former. 
In the cylinders 60| inches long (Table II.), comparing the strength of that of 
77 inch diameter with that of *997, gives n = 3'606 ; 
77 inch diameter with that of 1*29, gives n — 3'641 ; 
77 inch diameter with that of l - 56, gives n — 3*495 ; 
*997 inch diameter with that of 1*29, gives n — 3*670 ; 
*997 inch diameter with that of 1*56, gives n = 3*428 ; 
Mean n = 3*568 * 
The pillars of the same length, with discs upon the ends, in Table IV., if we make 
the same comparison of strength, give as below : 
Comparing that of 
*51 inch diameter with that of 1*00 diameter, we have n — 3*922 ; 
*51 inch diameter with that of 1*28 diameter, we have n — 3*820 ; 
*51 inch diameter with that of 1*53 diameter, we have n = 3*775 ; 
*775 inch diameter with that of 1*53 diameter, we have n = 3*568 ; 
*775 inch diameter with that of 1*28 diameter, we have n — 3*578 ; 
1*00 inch diameter with that of 1*53 diameter, we have n = 3*412 ; 
Mean = 3*679. 
* In my earlier experiments the mean obtained was 3'55, and that number will be used in the computations 
further on in this paper. 
