PRESIDENTIAL ADDRESS. 497 
cylindrical hole in a tension member trebles the stress intensity. If the hole 
is elliptical the increase of stress may be still greater, and Inglis has shown, 
among other interesting cases, that if the minor axis of the ellipse is parallel 
to the direction of the applied load in a tension member, the stress intensity 
is increased by an amount measured by twice the ratio of the axis of the ellipse. 
A crack, considered as the limiting case of an elliptical hole, is thus seen to 
give extremely great stresses at the ends, tending towards infinite values for 
an extremely fine crack. 
Optical experiments afford an independent means of examining the alterations 
of stress intensity produced by discontinuities, and the results are found to agree 
remarkably well with those obtained from the theory of elasticity. The stress at 
the boundary of a small cylindrical hole in a plate has been found to be almost 
exactly three times the stress in the full plate, and the effects of holes com- 
parable with the width of the tension member have also been examined in some 
detail. 
In the case of a rivet just filling the hole and exerting no tangential effect 
at the boundary, there is a lessened tension stress across the minimum section 
at the boundary hole, accompanied by a marked radial tension. These effects have 
been recently confirmed in a mathematical discussion by Suyehiro. Other cases 
give satisfactory agreement with calculation, and we may therefore feel some 
confidence that experimental investigation will prove useful in some of the very 
complicated cases arising out of engineering practice where analysis is difficult, 
if not impossible. 
The effects of overstress in materials may also be examined by optical means, 
and although the laws relating to stress distribution in overstressed transparent 
material are not known, the general effects observed in simple cases are fairly 
evident. If, for example, a tension member of glass is stressed, there is no 
ductile yielding of the material, and the stress will therefore rise very rapidly 
at the boundary of a small hole, and fracture will therefore occur with a 
moderate load. If, however, a ductile transparent material is employed, and 
the material shows signs of failure at the hole, the break-down of the structure 
spreads outwards as the load is increased, until we may have a condition in which 
within the elastic limit the curve of stress intensity at the minimum section 
accords with calculation, but at the overstressed part the stress tends to equalise, 
and the curve of intensity tends to become horizontal near the hole. The mean 
value of this part of the stress distribution may be inferred from the difference 
between the total load and the measured values below the region of failure; 
but the true distribution of the overstress has not been accurately determined, so 
that the shape of this peak is largely conjectural. 
The effects of groups of rivets such as occur in bridges, boilers, and struc- 
tural members of all kinds, afford ample scope for further inquiry; but before 
more exact knowledge can be gained of the condition of stress in a complicated 
riveted joint it appears necessary to examine thoroughly the very simple cases. 
Mr. Scoble and I have examined the case of the load applied by one rivet to 
a plate with various amounts of overlap, and the stresses around the rivet holes 
have been measured with fair accuracy. 
Other interesting cases of discontinuity in structure are afforded by the 
engine hatchways, gun-turrets, funnel openings, and the like, in ships’ decks, and 
some progress in this direction has been made by experiments on model decks, 
subjected to loads like those produced when a vessel meets the waves due to a 
head sea. 
Even if the utility of transparent models is left out of account, it is generally 
acknowledged that many engineering problems are often simplified by the use of 
models of machines and structures on a small scale, where circumstances forbid 
experimental examination of the actual work. No defence of their use is, I 
think, necessary, since the employment of models is a characteristic feature of 
British methods, not limited to engineers. Kelvin did not disdain their use, and 
his successors, who have done so much to advance knowledge of the ether and the 
atomic dust, have freely employed their great ingenuity in the construction of 
mechanical models and diagrams to explain their views, as in the Lodge cog-wheel 
diagrams of the ether, the planetary systems of atoms of J. J. Thomson and 
Rutherford, and the grouping of elements by Soddy. 
1914. K K 
