"In an article in the Annales d'u Génie civil, March, 1879, on the “Resistance of Tubes subjected to an External Pressure,” by Théodore Belpaire, an attempt has been made to deduce a new formula for the collapsing strength of tubes. ...The writer ... considers the case of a tube with ends rigidly fixed, and supposes that under an external pressure it changes its form in such a manner that its generatrix becomes the arc of a circle, the centre of which lies on a perpendicular erected in the centre of the generatrix; and, neglecting, the elastic forces due to flexure or elongation of the fibres—which are very small as long as the curvature is slight—he investigates the shearing stresses; these attain their greatest value at the fixed ends. Calling S the greatest shearing stress, p the pressure in pounds per square inch, t the thickness of the tube in inches, L the length of the tube in inches, he deduces the following approximate formula for the external pressure which a given tube can bear with a degree of safety depending on the value attributed to S—viz.:p = \frac{2tS}{L}. { VI.}The writer deduces then a general value S from two experiments made by Fairbairn with elliptical tubes, because the uncertain and variable elements of strength due to the cylindrical form and to homogeneity of the material do not enter here. When the factor of safety in the foregoing equation is to be four, the value of S becomesS = 428,394 \frac{t}{D} - 7,111,550 (\frac{t}{D})^2;...With reference to those cases where the factor of safety exceeded four greatly, the writer claims that the high pressures necessary to produce collapse indicate merely the great increase of strength derived in the particular instances from the uncertain element of circular form."