THE MEASUREMENT OF STRESS BY THERMAL METHODS. 247 
7 THE VARIATION OF CoMPRESSION STRESS IN A LONG CoMPRESSION MEMBER. 
The stresses in any but a short bar are always influenced by bending, and if we 
assume, in pillars of rectangular section, that the lateral deflection is proportional to 
the square of the length /, and inversely as the thickness ¢, it is easy to show, with the 
usual assumptions of technical elasticity, that the maximum stress in a long column is 
greater than the stress in a short specimen of the same section, by an amount Che, 
where ¢ is a factor depending upon the fixing of the ends. The value of ¢ for the case 
of a pillar with fixed or squared ends is often taken as z,/59, where / and ¢ are expressed 
in the same units. For technical applications this formula is widely used in the 
slightly modified form proposed by RaNnKINE, viz. :-— 
where p is the allowable working stress, f is the safe working stress in direct com- 
pression, and r the least radius of gyration of the section, the constant ¢ being 
adjusted to agree as closely as possible with experimental values. As an example of 
the ease with which the stresses at different parts of the same column may be compared 
by thermal methods, the following result on a specimen with squared ends 15 inches 
long and 1°375 by ‘625 inches in section may be quoted. The load was applied at the 
rate of 4000 pounds in 25 seconds, and the galvanometer showed no lag with the rate 
of loading. The thermopile was a linear one, and it was pressed against the broad 
face of the specimen in the direction of the breadth. The maximum deflections for 
different positions of the thermopile were as follows :— 
TaBLe IX. 
Distance of Pile from | Time of appli- : Deflection cor- 
Expt. the top end of the | cation of Load, Load, pounds. Maximum rected to 70 - 
specimen in inches. seconds. Deflection. 4000 lbs. 
1 1:38 25 70-4000 2°65 2°65 
2 3°88 25 70-4000 3°00 3°00 
3 7°50 25 | 70-4000 3°05 3°05 
4 11-25 25 | 70-3900 2-95 3-03 
5 13°38 2 | 100-4000 2:90 2-90 
Notes.—Linear pile, long connecting leads. 
Distance of scale from galvanometer mirror= 10’ 54”. 
As the maximum deflections differed very little from one another, and there was no 
perceptible lag of the galvanometer, no correction for radiation was necessary. The 
actual readings obtained are plotted as ordinates on fig. 10, the distances along the bar 
