“If the shell plate of a cylindrical boiler is 1⁄2 inch thick, there is one inch section of metal to be broken before the boiler can be divided into two pieces, that is to say there is 1⁄2 inch on each side of the shell, as shown in [Fig. 3237], and the two together will make 1 inch. If we take a ring an inch broad, as, say, at a in [Fig. 3238], we shall obviously have a section of 1 square inch of metal to break before the ring can be broken into two pieces.
“The next consideration is, what is the average strength of a plate of boiler iron? Now suppose we have a strip of boiler iron 2 inches wide and 1⁄2 inch thick, or, what is the same thing, a bar of boiler iron 1 inch square, and that we lay it horizontally and pull its ends apart until it breaks, how many lbs. will it bear before breaking? Now for our present purpose we may assume this to be 47,040 lbs., and if this number of lbs. be divided by the diameter of the boiler in inches, it will give the bursting pressure in lbs. for any square inch in the ring, or any other square inch in the cylindrical shell of the boiler.
“The reason for dividing by the diameter of the boiler is as follows:
Fig. 3239.
“Of course the steam pressure presses equally on all parts of the interior surface of the shell, and may be taken as radiating from the centre of the boiler, as in [Fig. 3239], which represents an end view of a strip an inch wide, of one half of a boiler. Now leaving the riveted seam out of the question, and supposing the shell to be truly cylindrical, and the metal to be of equal quality throughout, it will take just as much pressure to burst the shell apart in one direction as it will in another, hence we may suppose that the boiler is to be burst in the direction of arrow a, and it is the section of metal at b b that is resisting rupture in that direction.
“Now suppose we divide the surface against which the steam presses into six divisions, by lines radiating from the centre c, and to find the amount of area acting on each division to burst the shell in the direction of arrow a, we drop perpendicular lines, as line e, from the lines of division to the line b b, and the length of the line divided off (by the perpendicular) on the diameter represents the effectiveness of the area of that division to burst the boiler in the direction of arrow a; thus for that part of the boiler surface situate in the first division, or from b to line e, the area acting to burst the boiler in the direction of a is represented by the length of the line k, while the general direction of the pressure on this part of the shell is represented by arrow m.
“Similarly, for that part of the shell situate between vertical line e and vertical line f, the general direction of the steam pressure is denoted by the arrow l, while the proportion of this part that is acting to sever the boiler in the direction of a is represented by the distance n, or from the line e to line f measured on the line b b.