_——— ——rF 
RESISTANCE OF TUBES TO COLLAPSE. 219 
the data of one experiment and those arrived at by actual collapse, will 
be seen to be very slight, and within the limits of error which might be 
anticipated. 
Ill. Strength as affected by the Thickness.—It is found that the tubes vary 
in strength according to a certain power of the thickness, the index of which, 
taken from the mean of the experiments, is 2°19, or rather higher than the 
square. 
Combining the above laws into a general expression, we get as the formula 
for the strength of tubes subjected to a uniform external force, 
R219 
L.D- 
where P is the collapsing pressure, & the thickness of the plates, L the length 
of the tube, which should not be less than 1°5, or greater than 10 feet; D 
the diameter, and C a constant to be determined from the experiments. For 
tubes of greater length than above specified, a variable quantity dependent 
upon the length must be introduced ; and the value of this has yet to be 
determined. 
For ordinary practical calculations the following formula will probably 
afford the needful accuracy, 
P=Cx 
2 
LxD 
Thus, for instance, take a flue 10 feet long, 2 feet in diameter, and com- 
posed of }-inch plates. Here the collapsing pressure 
P=806,300 x 
25° 
P= 3 
806, 00% a4 
=210 Ibs. 
per square inch nearly. 
Some experiments have also been made upon elliptical tubes; and the 
results have been most conclusive as to the weakness of this form in resisting 
_ external pressure. No tubes in use for boilers should ever be made of the 
elliptical form. 
With regard to cylindrical flues, the experiments indicate the necessity of 
an important modification of the ordinary mode of construction, in order to 
render them secure at the high pressures to which they are now almost con- 
stantly subjected. If we take a boiler of the ordinary construction, 30 feet 
long, 7 feet in diameter, and with one or more flues 3 feet or 3 feet 6 inches 
in diameter, it will be found that the outer shell is from three to three and a 
half times as strong in resisting an internal force, as the flues which have to 
resist the same external force. This being the case, it is evident that the 
excess of strength in those parts of the vessel subjected to tension, is actually 
of no value, so long as the elements of weakness are present in the other parts 
subjected to compression. To remedy these defects of construction, it is pro- 
posed that strong rigid rings of angle-iron should be riveted, at intervals, along 
the flue,—thus practically reducing its length, or in other words, increasing its 
strength to uniformity with that of the exterior shell of the boiler. This 
alteration in the existing mode of construction is so simple, and yet so 
effective, that its adoption may be confidently recommended to the attention 
of those interested in the construction of vessels so important to the success 
of our manufacturing system, and yet fraught with such potent elements of 
disaster when unscientifically constructed or improperly managed. 
