216 REPORTS ON THE STATE OF SCIENCE.—1913. 
and therefore the maximum pressure which could be applied to the tube 
without permanent deformation is theoretically 
ee ae oe 
p= 7} a? 5 
where /, = direct compressive stress at yield. How far the strength of the 
material in compression does actually enter into the problem does not 
appear to have been satisfactorily determined. It is probable that for a 
c el 
certain range of the ratio 7 Upwards from -025 the tube does not fail either 
by simple buckling or by direct crushing, but by a combination of both. 
Tt is found that the results of tests on tubes of this form may be con- 
veniently expressed by the relation 
reals) 
where a and 6 are constants depending on the material. 19 The upper 
t 
d 
but its maximum value in the tests upon which it is based was about :07. 
limit of the ratio for which this relation holds has not been determined, 
A question of some interest is the value of 5 for which collapse in the 
form of buckling ceases to occur. Recent experiments by Bridgman 3 
have shown that the effect of the application of high hydrostatic pressure 
to tubes of ductile materials in which the ratio of thickness to external 
diameter is greater than 0:27 is to close up the hole in a uniform manner, 
without any departure from the circular form. 
Length. 
Very little experimental data are available in regard to the influence of 
the length upon the strength of a tube to resist collapse. Indeed, the 
attention paid to this point has not been in any degree commensurate with 
its importance. 
Recent experimental work has shown that when the length is suffi- 
ciently great 1t ceases to have any appreciable effect upon the strength. 
An attempt has been made to define the length below which the strength is 
materially increased, and the term ‘ critical length’* has been applied to 
this quantity by Love and Carman. Such a term suggests a point of dis- 
continuity, the existence of which, in the above sense, is hardly conceivable. 
An investigation by Love,}* based partly on analysis, and partly on analogy 
to simpler problems, leads to the result that, for thin tubes of different 
lateral dimensions, the influence of the length becomes negligible to the 
same order when it is greater than some multiple of the mean proportional 
of the diameter and thickness ; 7.¢., when 
L> ar/dt ; : : : (2) 
where a is a constant. 
An important contribution to the theory of this subject recently made 
by Southwell !7) 18 has pointed to the desirability of a modification in the 
meaning attached to the term ‘critical length.’ It is a well-known fact 
that the number of lobes into which a tube collapses is dependent upon the 
