248 PROFESSOR E. G. COKER ON 
being used as abscissee, and the corrected maximum readings of column are plotted in 
the same way to show the variation of thermal effect. 
It will be seen that the corrected readings are not symmetrical with regard to the 
centre of the length of the pillar, so that we may infer that the ends were not in exactly 
the same condition as regards fixture, and therefore it would be difhcult to draw any 
definite conclusions ; but the experiments serve to demonstrate the value of the method, 
and it appears probable that further experiments in this direction will be fruitful of 
results. Asa further example of the application of the method, we may quote some 
experiments on the variation of thermal effect in beams. 
8. THe VARIATION OF STRESS IN THE Cross SECTION OF A Bram. 
The assumptions of the Bernouilli-Kulerian hypothesis for beams lead to the simple 
result that there is a neutral plane perpendicular to the plane of symmetry, and that 
the stress at any point of the section varies as the bending moment and as the distance 
from the neutral plane. The assumptions of the above theory have been shown to be 
false by PEarson,* who has proved that for a beam of circular cross section, subject to 
a surface load perpendicular to the axis of the beam, the stress does not vary according 
to the distance from a neutral axis, nor according to the bending moment. ‘The varia- 
tion of stress at the surface of a beam has been determined by more than one 
experimenter, chiefly by observations of the strains ; and in order to establish the value 
of the thermal method for determinations of this kind, a steel I beam was chosen of the 
section shown in fig. 11, and this was subjected to a uniform bending moment by apply- 
ing equal loads at two points, each distant 4 inches from the central section of a span 
of 5 feet. In this way the bending moment at the central section was made as uniform 
as possible. The thermopile was pressed against the beam at five different places in — 
succession, and the deflections of the galvanometer were noted for approximately the 
same loading applied at a uniform rate. The value of the correction factor for each 
experiment was determined in the usual manner, and its value was found to be very 
constant, except in the last set of readings. The observed and corrected readings are 
plotted in place upon fig. 11, and from them a curve has been drawn, the ordinates of 
which represent to a reduced scale the maximum readings for a total load of 5000 
pounds. ‘The variation of thermal change is seen to be proportional to the distance 
from a point slightly above the centre line, and (fig. 11) to obey a linear law almost 
exactly. These results agree in general with those obtained by Professor Bovey, F.R.8.,7 
who used a very delicate roller extensometer. He found an approximately linear relation 
for the strains, and in most cases the neutral axis was somewhat above the centre of 
gravity of the section towards the compression side, a result which may be expected, 
having regard to the probable distortion of the section by the bending moment. The 
* “Qn the Flexure of Heavy Beams subjected to Continuous Systems of Load,” Quart. Jour. Math., 1889. 
+ “A New Extensometer,” Trans. Roy. Soc. Canada, 1901. 
