326 REPORTS ON THE STATE OF SCIENCE, ETC. 
couple. It follows that the impressed conditions must approximate closely to Class I, 
the approximation being closer the less the deviation from proportionality within 
the fatigue limits. In the case of thin hollow test-pieces, the approximation will not 
be so close, owing to the greater proportion of overstrained to elastically strained 
material. 
In the Haigh electro-magnetic machine, as mentioned above, the impressed con- 
ditions fall in Class III. 
In the Stromeyer alternating torsion machine, the test-piece is fixed to a flywheel 
at one end, and the system is caused to execute forced vibrations by means of a small 
alternating rotation impressed on the other end, The torque range is varied by varying 
the running speed, which is below the speed of resonance. In this machine any increase 
in the amplitude of twist in the test-piece must be accompanied by an increase in the 
amplitude of the flywheel, and, therefore, by an increase in the torque. If thin hollow 
test-pieces are used, they must be under practically uniform stress at any instant of 
time, whence it follows that any increase of strain must involve an increase of stress, 
so that the impressed conditions fall in Class IV. 
If, however, solid test-pieces are used, the conditions are quite different, and are 
determined principally by the torque twist curve of the piece and the proportion of 
overstrained to elastically strained material. If only an infinitesimal skin is suffering 
overstrain, the conditions clearly fall in Class I. (unless the machine is running at the 
critical speed). At the other extreme the conditions may, perhaps, reach Class III. 
In most cases, however, it will probably be safe to assume that the Stromeyer machine 
using solid test-pieces yields impressed conditions falling within Class IT. 
In practice, the precise specification of impressed conditions is of considerable 
importance. In some tests recently made by Gough at the National Physical Labora- 
tory, on soft iron and low and medium carbon steels, it was found that the nominal 
limiting fatigue stresses were lower in the Haigh machine than in the Wohler (in the 
latter, there was practically no difference between the results obtained with solid 
and hollow test-pieces), while in the Stromeyer machine, solid and hollow test-pieces 
always gave different results. In thelatter case, the hollow test-pieces gave nominal 
fatigue limits from 12 per cent. to 16 per cent. lower than the solid ones ; in conformity 
with the theory, the difference was greater for the more ductile materials. 
As an instance of the importance of impressed conditions, as revealed by the above 
figures, suppose that it is desired to discriminate experimentally between Guest’s law 
of specific shear stress and Haigh’s law of specific strain energy, as applied to fatigue 
limits. According to the former law, the ratio of the fatigue range in pure shear to the 
fatigue range under tension-compression should be 0-5; according to Haigh’s law it 
should be about 0-62. Now, the difference between these two figures is not much 
greater than the variations of nominal fatigue limiting stresses already obtained by 
Gough ; itis clear, therefore, that no tests capable of discriminating between the two 
laws can be made unless precautions are taken to secure, in both cases, impressed 
conditions substantially equivalent to specific stress. 
IV. The Influence of Circular Holes on the Fatigue Strength of Hard 
Steel Plates. 
By Professor B. P. Hatau, D.Sc., M.Inst.C.H., and Mr. ALBERT Bray, Whitworth 
Senior Scholar. 
A small hole drilled in a plate subject to pulsating stresses, weakens itin a degree 
which depends on the nature of the metal and on the mode of pulsation of the stresses. 
Thus, a comparatively small hole drilled through the flange of a high-tensile steel 
chassis-frame may reduce the fatigue strength by one-half or more, on account of the 
concentration of stress round the hole ; while, on the other hand, rivet holes in a mild 
steel tension member of a bridge may have little effect, beyond reducing the strength 
in the same proportion as the cross-sectional area. 
This paper has as objects; (1) To describe experiments, illustrating the dangerous 
effects of holes drilled in hard-drawn steel plates, and (2) to develop a working rule 
which will allow for the effect of redistribution of stress due to‘:primary hysteresis. 
The concentrations of stress induced by discontinuities of circular or elliptic profile, 
in uniform plates stressed in one direction by pull or push, have been investigated 
mathematically by Suyehiro,' Inglis,? and others. On the hypothesis that the metal 
behaves elastically and isotropically, the intensities of the complex stresses acting at 
