On the Strength of Cylindrical Steam Boilers. 71 



tenacity by the greatest force per unit of surface, which the boiler is 

 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- 

 lion, we would determine the thickness, of that metal which ought to 

 be employed in a boiler of given diameter and to sustain a certain 



xf 

 force, we may use the formula ^ = ^' and, dividing the latter mem- 

 ber of this equation by the strength of the square bar, which we may 

 call s, we obtain the thickness demanded in the direction of the curve, 



^/ . . . 

 which we may denominate p, so that p=^ i 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 a? = 36,/=750, 25 = 1 10,000; 



36x750 

 consequently, p= . iriQrvr) =.2454, or a little less than one quarter 



of an inch. 



11. It must, however, be evident that the mznmMm tenacity, 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 ^ 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 



^f . ^f . ^f 



the formula p=n' into ps=-^> and then into s=-^' 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 jjarts of an inch. Thus, how strong 

 a metal ought to be employed to sustain a pressure of 1000 lbs. to 

 the square inch, in a boiler 30 inches in diameter and one quarter of 



