On the Strength of Cylindrical Steam Boilers. 69 
separating it along two lines, on opposite sides, would be represented 
by multiplying the diameter by the force exerted on each unit of sur- 
face, and this product by the length of the cylinder. But even with- 
out regarding the length, we may consider the force requisite to rup- 
ture a single band, in the direction now supposed, and of one linear 
unit in breadth; since it obviously makes no difference whether the 
cylinder be long or short in respect to the ease or difficulty of sepa- 
rating the sides. The divellent force, in this direction, is therefore 
truly represented by the diameter multiplied by the pressure per unit 
of surface. ‘The retaining or quiescent force. in the same direction, 
is se the strength or tenacity of the two opposite sides of the sup- 
and. Here also, at the moment when a rupture is about to 
occur, ‘the divellent must exactly equal the quzescent force. 
3. In order to estimate the augmentation of divellent force, conse- 
quent upon an ‘increase of diameter, we have only to consider that as 
the diameter is increased, the product of the diameter and the force 
per unit of surface, is increased in the same ratio. But unless the 
thickness of the metal be increased, the quiescent force must remain 
unaltered. The quiescent forces, therefore, | ee the 
divellent increase with the diameter. 
. Again, as the diameter of the cylinder is cncresnadl the area of 
its ig is increased in the ratio of the square of the diameter. 
divellent force is therefore augmented in this ratio. But the retain- 
ing force does not, as in the other direction, remain the same, since 
the circumference of a circle increases in the same ratio as the diam- 
eter. The quiescent force will consequently be augmented im the 
simple ratio of the diameter, without any additional thickness of 
metal, so that on the whole the total tendency to rupture in this di- 
rection will increase only in the simple ratio of the diameter. 
-§. Since we have seen that the. tendency to rupture, in both di- 
rections, increases in the simple direct ratio of the increase of diam- 
eter, it is obvious that any position of the sheets which is right for 
one diameter, must be right for all. Hence, there can never bea 
condition, in regard to mere magnitude, which will require the sheets 
to be reversed. 
6. The foregoing considerations being once admitted, we may 
proceed to ascertain what is the true direction of the greatest tena+ 
City in the sheet, if any difference exist, and to what that difference 
might amount, consistently with equal safety of the boiler im both 
