_Answer._ The reason for multiplying by the diameter instead of by the circumference is because only a portion of the pressure on the inside surface of the boiler exerts a force to burst the shell at any one point. Thus, supposing the following diagram, fig. 50, to represent a section of a boiler, if we have a force acting on the shell in the direction of the line _a b_, at the point _b_, where it is exerted against the shell of the boiler, it would be composed of two forces, one acting in the direction _b e_, and tending to tear the boiler apart on the line _c d_, and the other acting in the direction _f b_, to tear it apart on the line _h g_. It is so with all pressure inside the boiler, excepting that, say _a h_, which acts exactly at right angles to the line of rupture _c d_, it is all composed of two forces, only one of which tends to tear the boiler apart at one point. It is therefore only a part of the pressure on the circumference which tends to burst the boiler at a given place, and that part is equivalent to the pressure on a surface whose width is equal to the diameter and not the circumference. [Illustration: Fig. 50.] [Illustration: Fig. 51.] This we know is a little difficult for those to understand who are not familiar with the principles of what is called the “resolution of forces,” and we will therefore try to make it clear in another way. To do this we will suppose that we have a boiler, _a b_, fig. 51, made in two halves and bolted together at _a_ and _b_ by flanges. It is evident that if we brought a pressure against the inside of the flanges in the direction of the darts _c_ and _d_, such a pressure would not have a tendency to tear apart the bolts _a_ and _b_. Some distortion of the boiler might in fact take place, if, for example, we put a jack-screw inside and forced out the flanges as indicated, without subjecting the bolts to a tensile strain. We see therefore that the forces acting in the direction _c_ and _d_ have no tendency to tear apart the bolts at _a_ and _b_, but it is only the forces such as _e_, _f_ and _g_, which act at right angles to _a b_, that exert a strain on the flanges.