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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.

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NOTE. The diameter at the top should be ths of the diameter at the base.

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(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).

Mp × D316 ÷ L2.

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√(Fx L2 M1).

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In which F the breaking weight on the pillar in lbs., tons, &c., by flexure, dependent on Mɲ.

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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.

P

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 Mp 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, P1 = F × Cp÷(F+3 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

TABLE 44.-Of the STRENGTH of SOLID CYLINDRICAL PILLARS of WROUGHT IRON and CAST STEEL.

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the experiments is to a great extent due to the correct value of C 19 tons.

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As an illustration of the rules in (197) and (164), we may take Nos. 13, 14, in Table 44: then 95848 × 1·005 ÷ 1·262 61470 lbs., the value of F, or the breaking weight by flexure, as in col. 9. This requires correction for incipient crushing (163):-to find Cp we have 1.0052 × 7854 × 42560 = 33760 lbs. as in col. 10, hence Cp 25320 lbs., and the rule Po F × Cp (F+ Cp) becomes 61470 x 33760 (61470 + 25320) = 23910 lbs., the reduced breaking weight or value of Pc, as in col. 7.

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52.5)

Table 44 has been calculated in this way throughout the sum of all the + errors in col. 8 = 56 9 and of all the 52.5, giving on 15 experiments an average of (56.9 ÷15 = 0.293 per cent. only. The greatest + error 13.8 per cent., and the greatest 15.3 per cent. (959).

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42.79 ÷

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3·73 × 12

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(202.) Searching as in (165) for the length of wrought-iron pillars with which the correction for incipient crushing becomes nil, beyond which length the rule must not be applied for reasons given in (164); we find that a pillar 1 inch diameter crushes with ⚫7854 × 19 14.92 tons, the correction will therefore be nil when F 14.924 = 3.73 tons (169), which in a pillar with both ends pointed is due by the rule (199) to a length of 40.64 inches, or 40·64 times the diameter. With one end pointed and one flat 88.263.73 x 12 58.37 inches: with both ends flat 133.83.73 x 12 71.86 inches, &c. With cast-iron pillars (165) we obtained for the same diameter 16.64, 25.04, and 31.78 times the diameter respectively, which differs remarkably from 40 64, 58.37, and 71 86 as found for wroughtiron pillars.

These ratios vary with the diameter as we found to be the case with cast iron (166), and as shown by Table 39, which has been calculated by the rule:

(203.)

LD (MP X D36Cp) x 12 D.

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In which the letters have the same significance as in (167).

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