On the Strength of Cylindrical Steam Boilers. 71 
tenacity by the greatest force per unit of surface, which the boiler + as 
ever to sustain. 
10. When, knowing the absolute tenacity of a metal or other ma- 
terial reckoned in weight, to the bar of a given area, in its cross sec- 
tion, we would determine the thickness of that metal which ought to 
be employed in a boiler of given diameter and to sustain a certain 
Br i ” 
force, we may use the formula ion and, dividing the latter mem- 
ber of this equation by the strength of the square bar, which we may 
_ Calls, we obtain the thickness demanded z the direction of the curve, 
which we may denominate p, so that p= Ee ; this will give the thick- 
ness of the boiler plate, either in whole numbers or decimals, Thus, 
suppose the diameter of a cylindrical boiler is to be 36 inches,—that 
it is to be formed of iron which will bear 55000 lbs. to the square 
inch, and is to sustain 750 lbs. to the square inch ;—what ought to 
be the thickness of the metal? Here «=36, f=750, 2s=110,000; 
36 X 750 
consequently, p=F T0000 = 72454 or a little less. ae 908. SE 
of an inch. 
11. It must, however, be evident that the minimum cannéity; of 
any particular description of metal, is that-on which all the calcula- 
tions ought to be made, when there is any probability that the actual 
pressure will, in practice, ever reach the limit assigned as the value 
of f in the calculation. 
If we had plates of different metals, or of different known degrees 
of tenacity in the same kind of metal, and were desirous of ascer- 
taining how strong a kind we must employ under a limited thickness, 
diameter and pressure, we should decide the point by transforming 
the formula p= into pene and then into s=5>- In other terms, 
in order to know the strength of the metal required, or the direct 
strain which an inch square bar of the same ought to be capable of 
sustaining, we must multiply the diameter of the boiler in inches by 
the pressure per square inch in pounds, and divide the product by 
twice the intended thickness in parts of an inch. Thus, how strong 
a metal ought to be employed to sustain a pressure of 1000 Ibs. to 
the square inch, in a boiler 30 inches in diameter agd one quarter of 
