222 REPORTS ON THE STATE OF SCIENCE.—1913. 
Where C, = compressive strength, 
eé = ellipticity, 
d = diameter of circular tube of same circumference as ellipse. 
10 Lilly, W. E. 1910 The Collapsing Pressure of Circular Tubes. ‘ Proc. Inst. 
Civ. Eng. of Ireland,’ Feb. 2, 1910. 
The analogy of the problem of tube collapse to failure of columns is dis- 
cussed, and a formula similar to the Rankine-Gordon formula is derived, 
viz. 
eee) 
i) es 
t nE t 
where / = strength to compression, and 7 is a constant to be determined 
experimentally. 
The investigation is also extended to corrugated flues. 
11 Lorenz, R. 1911 Buckling of Thin-walled Cylinders. ‘ Phys. Zeitschr.’ n. 
12, pp. 241-260. April 1911. ‘Sci. Abs.,’ 1911, 
No. 978. 
12 Love, A. E. H. ‘ Mathematical Theory of Elasticity,’ p. 530. 
The theoretical formula 
p es 2H e 
1—m d 
is given, and it is shown that when the pressure exceeds this limit, any flue 
will collapse if its length exceeds a certain multiple of the mean proportional 
between the diameter and thickness. 
13 Love, G. H. 1859 Sur la résistance des conduits intérieurs 4 fumée dans 
les chaudiéres & vapeur. ‘Mémoires et Comptes 
Rendus,’ 1859, pp. 471-500. Todhunter and Pearson, 
* History of Elasticity,’ vol. ii., pt. 1, p. 667. 
The formula 
t? e t 
p = 5,358,150 + 41,906— 1,323— 
p= 5,3 ae + 41,90 7 + 1,3 q 
is given as representing the results of Fairbairn’s experiments. 
14 Nystrom, J. W. ‘ Treatise on Steam Engineering,’ p. 106 
Derives the formula 
t? 
= 692,000 —_ 
iy [93q 
as representing results of Fairbairn’s tests. 
15 Roelker, C. R. 1881 Experimental Investigation of Resistance of Flues to 
Collapse. ‘Van Nostrand’s Magazine,’ vol. 24, p. 
208. 
16 Slocum, 8. E. 1909 Collapse of Tubes under External Pressure. ‘ Engineer- 
ing,’ Jan, 8, 1909, vol. 87, p. 35. 
A discussion of Carman’s and Stewart’s experiments. Suggests that 
discrepancy between theoretical formula and experimental results due 
to imperfections in geometrical form. Proposes the introduction of a 
‘correction factor’ C in the formula, thus : 
—c _2E_ zy" 
ae 1— m* ( 
Following values of C are given : 
Lap-welded steel tubes C = -69. 
Solid-drawn weldless steel tubes C = -76. 
Solid-drawn brass tubes C = -78. 
17 Southwell, R.V. 1913 On the General Theory of Elastic Stability. ‘Phil. 
Trans,’ (A), vol. 213 (1913), pp. 187-244. 
Discusses the boiler-flue problem as an example to illustrate a proposed 
ee 
