a = (190.) “ Connecting-rods of Steam-engines.”—The strength of cast-iron connecting-rods of the ordinary + sectional form cannot be calculated satisfactorily by the ordinary rules ; in practice it is necessary to provide for extraordinary strains arising from forces in motion, &c., which the ordinary rule does not contemplate. The safer course is to use a theoretical formula with a constant multiplier derived from experience: the rule may then take the following form :(191.) B = V (H x L = 42). In which H = the reputed or nominal horse-power of the engine; L = the length of the connecting-rod between centres in feet; and B = the breadth of the rod at the centre in inches. Thus, for a 60-horse engine with a rod 14 feet 6 inches, or 14:52 feet between centres, we have 14.522 = 210.8; then 60 x 210.8 •:42 = 30114, the log of which, or 4.478773 · 4 = 1.119693, the natural number due to which or 13.17, say 13] inches, is the breadth at the centre. We should obtain the same result by finding the square-root of the square-root of 30114: thus, the square-root of 30114 = 173-5, and the square-root of 173.5 = 13.17 inches as before. Table 41 gives the proportions of connecting-rods from cases in practice, col. 4 being calculated = TABLE 41.-Of the PROPORTIONS of CAST-IRON CONNECTING-RODS of + SECTION for STEAM-ENGINES : Cases in Practice. 100 60 42 35 30 22 12 ft. in, 195 14 61 13 5 13 39 11 61 9 111 17.3 13) 11 11 91 8 8 52 41 (6) (1) 23 (7) (2) (4) (8) (9) by the rule: the particulars of the bearings at the two ends are added as useful memoranda. It should be observed that the rule supposes that the thickness of the ribs and the heavy mouldings with which the corners are filled in, are of the proportions usually adopted in practice and as shown in Fig. 37. (192.) “ Cast-iron Pillars of I Section.”—This form of pillar is sometimes used for stanchions: their strength may be calculated on the same principles as those of + section. Mr. Hodgkinson made an experiment on the pillar of the section shown by Fig. 39, the length was 7.562 feet, both ends pointed, and the breaking weight 29,571 lbs., the pillar breaking by flexure in the direction of the arrow C. Neglecting the middle web, as having very little influence on the result (187), we have simply to calculate for a rectangular pillar 3 x .7 inches forced to fail by flexure in the direction of its larger dimension, hence, using the rule in (178) t = 3 inches and b = .7 inch, and 326 being 17:4, we obtain 56100 x 17•4 x .7 - 31:17 = 21925 lbs., which is 25.8 per cent. less than 29,571 lbs., the experimental breaking weight. It should be observed that the thickness of the metal in Fig. 39 has been calculated. Mr. Hodgkinson did not give that dimension unfortunately, but he states that the area of the crosssection was the same as that of the + pillar in (189); if we assume the thickness to be uniform all over, we obtain of necessity •35 inch, as in the figure. It is possible that the thinness of the metal in these cases (931) may be the reason for the excess of strength shown by the experiments; this appears to be the more probable from the fact that the casting .35 inch thick gave a greater excess than the one • 48 inch thick. The difference although considerable is not of practical importance, being covered by the “ factor” of safety (880); moreover the error is on the side of safety, calculation giving in both cases, the breaking weight less than by experiment. (193.) “Cast-iron Steam-engine Columns.”—A common arrangement for beam engines is shown by Fig. 41, in which a crossentablature A is built into the side walls, and is supported by = two columns. The strain on these columns is comparatively small, and the proper sizes cannot be calculated by the ordinary method, but may be found by the following empirical rules : (194) D= V (H X L2 X 2.2). (195.) d = D X 5 = 6. In which H = the reputed, or nominal horse-power of the engine; L = the length of the column in feet; D = the diameter at the base, and d = the diameter at the top, both in inches. Thus for an engine of 100 nominal horse-power, and columns 16 feet long, we have 162 256, giving by the rule 100 x 256 x 2.2 56320, which is the fourth power of D: then the log. of 56320 or 4.750663 - 4 = 1.187666, the natural number due to which is 15·4, or say 153 inches, the diameter of the column at the base, from which we obtain 15.4 x 5 = 6 12.83, or say 127 inches, the diameter at the top. The actual diameters were 153 and 13 inches respectively, as shown by Table 42, which gives the sizes of engine columns from cases in practice with the corresponding sizes calculated by the rule. It should be observed that we might have found the 4th root of 56320 without the use of logarithms, for the square-root of the squareroot of a number is the 4th root of that number; thus, the square-root of 56320 = 237.3, and the square-root of 237.3 = 15·4, or the same as found direct by logarithms. TABLE 42.-Of the DIAMETER of COLUMNS to BEAM ENGINES with CROSS-ENTABLATURE between the Walls—Two Columns to each Engine (Fig. 41). From Cases in Practice. Table 43 has been calculated by the rule, and the approximate depth of the cross-entablature is given as calculated by the rule in (953). TABLE 43.–Of the APPROXIMATE SIZES of COLUMNS and DEPTH of Cross-ENTABLATURE for BEAM ENGINES: two columns to each Engine, as in Fig. 41. NOTE.—The diameter at the top should be ths of the diameter at the base. (196.) “ Wrought-iron Cylindrical Pillars.”—The strength of pillars of wrought iron is directly proportional to the 3.6 power of the diameter or side of square pillars, and inversely as the square of the length, this latter being the theoretical ratio as shown by (145). For solid cylindrical sections we have the following general rules for long pillars failing simply by flexure :-short pillars require correction for incipient crushing by the rules in (163). (197.) F = Mp x D96 ; L2. X (198.) D = 3 (F x L2 = My). Mp. (199.) L = y(Mp * D*6 = F). X (200.) Mp = F x L2 = 18-6. 9.6/ P In which F = the breaking weight on the pillar in lbs., tons, &c., by flexure, dependent on Mp. D the diameter of the pillar at the centre, in inches. L the length in feet. Mp = constant multiplier, the value of which is given in Table 34. Table 44 gives the result of 27 experiments on solid cylindrical pillars of wrought iron by Mr. Hodgkinson; col. 9 has been calculated by the rules, the value of Me taken from Table 34 was 95,848 lbs. for pillars with both ends pointed ; 197,700 for those with one end pointed and the other flat; and 299,620 lbs. for those with both ends flat. (201.) Comparing cols. 9 and 7, it will be seen that many of these pillars require correction for incipient crushing by the rule (164), namely, Po = F x Cp = (F + Cp). It is a matter of considerable difficulty to determine the crushing strain for wrought iron, or indeed for any very malleable metal (133). The ordinary method of crushing a small specimen is quite inapplicable in such a case :—by experiments on the transverse strength in (520) we found it to be 24 tons per square inch. But the only satisfactory course is to find by trial the resistance to crushing, or value of C, which when used in the rule for incipient crushing (164) will bring the calculated strength into agreement with the experimental strength. The result of a laborious application of that tentative method is that the value of C in wrought-iron pillars is 19 tons, or 42,560 lbs. per square inch, which, multiplied by the area of the pillar, will give the value of Cp in the rule for incipient crushing. This value of C has been used for solid cylindrical pillars in Table 44; for solid rectangular pillars in Table 53; for hollow cylindrical pillars of thin plate-iron in Table 52; and for rectangular pillars of thin iron in Table 55; and its correctness is proved by the general agreement of the calculations with the experiments as shown by (958) and Table 150. The mean average error of those 4 tables is only 0.293, 0:0, 0:461, and 2.25 per cent. respectively :-of 99 experiments, 85 were reduced by the rule for incipient crushing, and the near agreement with |