27-t M. Girard on the Resistance of' Cast-iron. 



10 or 11 times greater than that which the steam commonly 

 exerts in steam engines of that kind where the tension is equal 

 to about 6 or 7 atmospheres. 



INIr. Girard next states that he has in the above calculation 

 omitted the effect of the ends of the boiler, and supposing them 

 to be separated in the direction of their diameters at the same 

 tune as the cj'linder, and to be of the same thickness, the cy- 

 linder being 2 metres in length, each of them woidd be capable 

 of resisting a pressure of steam equal to about 450 atmospheres. 



And in general, he observes, we may regard the resistance 

 of boilers at their ends as infinite in regard to their resistance 

 according to their length ; and that they ought not to break in 

 the plane of the axis, but accoi'ding to a line of double curva- 

 ture traced on the cylindric surface*, of such a nature that, 

 the line of rupture being of a constant length, the sum of the 

 products of the radius of the cylinder supposed to be horizon- 

 tal by the vertical ordinates of the ciu've sought may be a maxi- 

 mum ; these vertical ordinates being measured from the origin 

 of a plane, which is a tangent to the cylinder and parallel to its 

 axis, and that sum of the products being taken from the middle 

 of the boiler to each of its extremities. The solution of this 

 problem depends on an useful application of the methotl of va- 

 riations-]-; and he concludes that with the thicknesses it is usual 

 to give to the boilers of high pressure engines, they are capable 

 of resisting a pressure from fifty to sixty times greater than 

 they are exposed to in the ordinary operation of the engine : 

 he therefore attributes the failure of boilers in England to air 

 bubbles or other defects in casting them, and imagines that 

 were they j^rovecl, by a hydraulic press, to a pressure fifteen or 

 twenty times greater than they were destined to resist, such 

 accidents would be avoided:]:. These proofs, which present no 



* Considering the pressure exerted in the direction of the axis of the 

 boiler, in more favourahlc circumstances than ever have place in a boiler, the 

 strength in the example above quoted is only 15 times that which is barely 

 safe. 



■\- A little skill in conducting this inquiry will bring the problem within 

 the reach of a less refined branch of anal)^sis. 



J Our practical readers will observe that the trial by the hydraulic press 

 is a proof only of its resistance to pressure ; and therefore the excess of 

 strength will be far short of that which appears on a comparison of the 

 pressure in the working state, and that indicated by the press; in conse- 

 quence of the heat, the inequality of the heat, and pressure, &c. It is also 

 important to remark, '.hat the pressure in proving a boiler should never be 

 equal to that which produces permanent alteration of structure in the ma- 

 terial (see Tredgold on Cast Iron, art. 180. J, or the boiler will be irrepara- 

 bly injured by the trial, and yield to perhaps a less pressure than the [)roof. 

 In questions of such importance, the real state of the problem cannot be too 

 closely studied, 



difliciihy, 



