220 REPORTS ON THE STATE OF SCIENCE.—1913. 
material employed. The elastic limit im compression enters into the 
problem when the thickness is considerable, and also when the length is 
short. ‘The precise influence of the ultimate strength is not known, and 
the uncertainty in regard to its value would render futile any attempt to 
introduce it. 
Tn conclusion, it may not be out of place to make a few general remarks 
in regard to the practical side of the question. Few problems in engineer- 
ing have given rise to a larger number or greater variety of formule, and 
it is not surprising that in actual practice the design of tubes to withstand 
external pressure is based upon previous experience obtained from failures 
of tubes of the same material and dimensions rather than upon theory or 
even systematic general experimental work. In the case of boiler flues, 
the rules formulated by the Board of Trade * and Lloyds’ ** differ, but are 
based upon the same tests carried out upon flues of the same form as those 
to which they are intended to be applied, and are admittedly inapplicable 
beyond the range of these tests. In these formule, which stipulate the 
safe working pressure, and not the collapsing pressure, allowance is made 
for effects such as corrosion, associated with the particular purpose for 
which the tubes are used. 
The case of long, thin, plain tubes, such as are employed for smoke tubes 
in locomotive boilers, appears to be the only one for which it is possible 
to propose a general and useful formula. The most convenient appears to 
be that obtained by introducing into the rational formula a constant 
depending only upon the material and mode of manufacture, and not on 
the absolute size. It has been suggested by Slocum" that the most useful 
purpose likely to be served by further experimental work is the determina- 
tion of the factor for different kinds of tubes. This was proposed some 
four years ago, but the difficulty and expense of systematic experimental 
work of this character has limited the investigation to three classes of 
tubes only. 
BIBLIOGRAPHY. 
1 Basset, A. B. 1892 On the Difficulties of Constructing a Theory of the 
Collapse of Boiler Flues. ‘Phil. Mag.,’ 1892, vol. 
200, p. 221. 
2 Belpaire, T. 1879 Note on the Resistance of Tubes to External Pressure. 
‘ Annales du Génie Civil,’ March 1879. 
The formula 
2 9 t? B 
p = 3,427,15 ld 56,892,400. 
is given as representing the results of Fairbairn’s tests. 
3 Bridgman, P. W. 1912 The Collapse of Thick Cylinders under High Hydrostatic 
Pressure. ‘ Physical Review,’ vol. xxxiv., No. 1. 
Jan. 1912. ‘Sci. Abs.,’ 1912, No. 427. 
4 Bryan, G. H. 1888 Application of Energy Test to Collapse of Long, Thin Pipe 
under External Pressure. ‘ Proc. Camb. Phil. Soc.,’ 
vol. vi., p. 287. 1888. 
Gives the derivation of rational formula 
2E ii 
5 Carman, A. P. 1906 Resistance of Tubes to Collapse. ‘ Physical Review,’ 
vol. 21, Dec. 1905, pp. 381-387. ‘Sci. Abs.,’ 1906, 
No. 239. 
Describes a series of tests on small brass tubes, diameters ranging from 
