68 On the Strength of Cylindrical Steam Boilers. 
Art. XII.—Remarks on the Strength of Cylindrical Steam Boilerss z 
by Watrer R. Jounson, Professor of Mechanics and Navanel 
“Philosophy in the Franklin Institute, Philadelphia.* 
[Read before the Institute, at the stated monthly meeting, July 26, 1832.] 
Ir has been generally supposed that the rolling of botler-plate iron, 
gives to the sheets a greater tenacity in the direction of the length, 
than in that of the breadth. Supposing this to be correct, it has fre- 
quently been asked, how the sheets ought to be disposed in a cylin- 
drical boiler of the common form, in order to oppose the greatest — 
Strength to the greatest strain. It has also been asked, whether the 
same arrangement will be required for all diameters, or whether a 
magnitude will not be eventualby attained, — ay —— the di- 
rection of the sheets to be reversed ? % 
~ "To determine these questions in a —— fansner, rout irse must 
be had to patiathematical formulas, assuming such symbols et each of 
the elements as may apply to any given case of which the separate 
data are determined either by experiment or by the conditions of the 
case. The principles of the calculation require our first notice. 
1. ‘To know the force which tends to burst a cylindrical vessel in 
the longitudinal direction,—or, in other words, to separate the head 
from the curved sides, we have only to consider the actual area of 
the head, and to multiply the number of units of surface by the num- 
ber of units of force applied to each superficial unit. This will ee 
the total divellent force in that direction. 
To counteract this, we have, or may be eounacel - — the te- 
nacity of as many longitudinal bars as there are linear units in the cir- 
cumference of the cylinder. The united strength of these bars con- 
stitutes the total retaining or quiescent force, and at the moment when 
rupture is about to take place, the valle and = = eset ie@eeforces 
must obviously be equal. sili 
2. To ascertain the amount of force which tends to rupture the 
— along the curved side, or rather along two opposite sides, 
We may regard the pressure as applied through the whole breadth of 
the cylinder upon each linear unit of the diameter. Hence the total 
amount of force which would tend to divide the cylinder in halves by 
* From the Journal of the Franklin Institute. 
