On the Rupture of Materials under Combined Stress. 81 
in the upper part o£ the diagram. These are of various 
length so that the longest at the top is shown with the 
segments corresponding to its seventh natural tone. Passing 
down the series, we reach the last pipe, the shortest of all, 
with one segment only as when emitting its fundamental. 
The antinodes are indicated by small circles and the nodes by 
crosses. The equidistant positions midway between the anti- 
nodes are shown by dots. 
Experiments by Mr. D. J. Blaikley have shown the 
existence of these nodes in positions slightly displaced from 
equidistances, each node being moved towards the vertex 
from the corresponding equidistant position. Further, it 
was found by Blaikley that the displacement was the greater 
for those nodes which are nearer the vertex. Or, in other 
words, " the nodes in the cone are at increasing distances 
apart, reckoning from the open end, and at the apex of the 
cone is a node common to all the notes." These nodal 
positions were established by Blaikley with an experimental 
bugle made in sections. On taking this to pieces, thin 
metal diaphragms were inserted at the positions of the nodes 
for a certain note, and their presence was found not to 
prevent the production of the note in question. The dia- 
phragms had each a few small holes to admit the passage of 
the player's breath, but prevented all free vibration at the 
place. 
University College, Nottingham, 
June 7, 1907. 
VII. On the Rupture of Materials under Combined Stress : — 
Tension and Hydrostatic Pressure. By W. Ellis 
Williams, B.Sc, Research Fellow of the University of 
Wales*. 
THE connexion between the rupture of a solid body and 
the stress causing it is at present but vaguely under- 
stood, and a number of different theories have been put 
forward to enable the tendency to rupture to be calculated 
from the stresses acting on the body by the methods of 
elastic theory. The principal of these are f : — 
(1) Lame. — Rupture occurs when the greatest tension 
has reached a certain limit. 
(2) Poncelet and St. Venant. — Rupture occurs when 
the greatest extension has reached a certain limit. 
* Communicated by Prof. E. Taylor Jones. 
t Love, i Elasticity,' vol. i. p. 106. 
Phil. Mag. S. 6. Vol. 15. No. 85. Jan. 1908. G 
