compressions with the long bars, we find that the short cylinder of Ystalyfera iron gave 0083·0047242 = 1.76, and the Lowmoor 0161004742 3.4 times the compression given by the long bars. With 42 tons, which is nearly the mean crushing strain for British iron, the short cylinders of Clyde iron gave 0446·0243574 = 1.83, and the mixed irons 070243574 2.87 times the estimated (609) compression of the long bars.

=

In searching for a reason for this great discrepancy, we might at first be led to suppose that it was due to the fact that the short cylinders were free to expand laterally in proportion to the longitudinal compression, while the long bars, being confined in a guide-frame, were prevented from doing so; but the fit of the latter was presumably so slack that this reason seems inadequate to account for the differences observed.

Mr. Hodgkinson himself seems to have suspected that there were considerable errors in the observed compressions of the short cylinders due to the method by which they were taken; he says "they were crushed between two discs of steel inch thick, which were parallel to each other. Between the disc and the specimen, both at top and bottom, a very thin piece of lead was interposed to prevent irregular action against each other; but, notwithstanding the care taken, it is probable that the results of these experiments are not free from considerable errors arising from the following causes: the great weights applied, 20 or 30 tons per square inch of section, caused the ends of the cylinders to be driven into the surface of the discs to such a degree that the surface of the steel sometimes remained irregular and broken after the experiments, showing the form of the ends of the cylinder. From the same cause the discs of steel would become slightly incurvated, and their distances asunder would be decreased more than was due to the shortening of the cylinder by the quantity of its penetration into the discs, added to their approach through flexure."

(612.) The experiments on short cylinders must therefore be regarded as of doubtful accuracy, and in the present state of our knowledge the compressions given by Table 89 from experi

.

ments on long bars may be taken as approximately correct for all strains up to the crushing load. The shortening of a pillar under heavy strains is very considerable; thus, by Table 89, with 42 tons per square inch, a pillar 10 feet, or 120 inches, long is shortened 0243574 × 120 = 2.92, or nearly 3 inches. If we admitted the results given by Table 90 for mixed iron, we obtain 07 × 120 = 8.4 inches compression; even under ordinary strains, the amount of compression is much greater than most practical men are aware of; for instance, with the ordinary safe strain of one-third of the ultimate crushing load, or 14 tons per square inch, a pillar or series of pillars joined end to end, 50 feet, or 600 inches long, by col. 5 of Table 89 is shortened 002731 × 600 = 1.6386, or 1 inch, and when thus loaded, 1000 lbs., more or less, will, by col. 9, cause a further change of length =0000001049 x 1000 x 600 = 06294, or inch.

(613.) In Table 89, col. 6 shows that the compression is not simply proportional to the weight, but, on the contrary, is progressively increased from 0001744 with the first ton to ·0013156 with the last, or 42nd. The ratio of the compressions with equal weights is therefore 00131560001744 = 7.53 to 1.0; this being due to defect of Elasticity (604).

The rate of compression being thus variable, it becomes necessary, as we found to be the case with extension (604), to distinguish the mean compression between two given strains from that produced by a certain weight on a bar already loaded. This has been explained and illustrated for variable extension, and need not be repeated here. Cols. 8 and 9 have been obtained by analysis with the numbers given by the experiments: an illustration of their application will suffice; a pillar 1000 inches long, loaded with 20,000 lbs. per square inch, will, by col. 8, be shortened 00000008294 × 20000 × 1000 : = 1.659 inch, and when thus loaded, an extra strain of 1 cwt., or 112 lbs., will, by col. 9, give 00000008941 × 112 × 1000 = ⚫01, or Tooth inch compression, &c.

For moderate compressive strains, say under 15 tons per square inch, the compression of cast iron will be given with considerable accuracy by the Rules :—

=

(614.) C (·00017 × Wc) + (·0000018 × W¿).

C

(615.) Wc = {-0000018 + 2228 47.2.

In which C Compression in parts of the length.

=

We Crushing weight in Tons per square inch.

Wc =

Thus, to find the compression due to 15 tons per square inch, have 00017 × 15 = ⚫00255; and ·000405. Then ⚫00255 +000405 =

15 being 225, we

=

⚫0000018 × 225

002955, the compression sought.

Again; to find the compressive strain due to a compression = .002955, we have 0029550000018 = 1641; then (1641 + 2228) √ = 62·2, and 62·2 — 47·2 = 15 tons, the strain required, &c. Calculating in this way, we obtain the following results :

=

These compressions differ very little from those given by Table 89; with great strains it would seem that the compressions become too anomalous and irregular to be expressed by any ordinary practical rule. Thus, for 35 tons, Mr. Hodgkinson's rule in (608) gives 01064785, but the diagram, based on the experiments on long bars, and col. 5 of Table 89, gives 0159945, and the direct experiments on short cylinders, Table 90, from 026 to 0458. Except for the purposes of scientific research, cast iron is never strained beyond one-third of the ultimate crushing load, or beyond 14 tons per square inch; hence the uncertainty as to its compression under excessive strains is of little practical importance.

(616.) "Comparative Extension and Compression of Cast Iron."-We should have expected instinctively that all materials would resist compression with greater energy than extension.

but experiment has shown that with cast iron, and still more with wrought iron (628), the material yields more to a small compressive strain than to a tensile. Confining ourselves to the direct and unreduced experiments as given by cols. 4, 4, in Tables 88, 89, we obtain the results given by Table 91, which show that for strains below 2 tons per square inch the compressions exceed the extensions; with 2.355 tons they are equal, as shown by Table 92; with greater strains the extensions exceed the compressions, a fact which is due to defect of elasticity. The ultimate resistance of cast iron to compressive strains being six times that for tensile ones, and defect of elasticity increasing rapidly as the ultimate strain is approached, this fact tells more influentially on the extensions than on the compressions.

(617.) It should be observed that 2.355 tons is very nearly rd of 7.142 tons, the mean ultimate Tensile strength of cast iron, andth of 43 tons, the mean Crushing strength. Let Fig. 206 be the section of a bar 1 inch square and 1 foot long, loaded transversely until the tensile strain at B and crushing strain at C are both = 2.355 tons per square inch. The extension and compression with that strain being, as we have seen, equal to one another, it will follow that the neutral axis N. A. will be in the centre of the section. By Rule (639), the transverse load will in our case beth of the maximum strain at B or C, hence we have MT = 2.35518 = · 1314 ton, which is 4th only of 921 tons, its mean value for breaking load, as given by col. 6 of Table 66 (523).

We now have this remarkable fact: that the "Factor of Safety" varies greatly with the three great strains involved in the case; for the Tensile it is = 3, for the Crushing for the resulting Transverse strain = 7.

=

18, and

It will be evident from this that, if a flanged girder were loaded to 4th only of its Breaking weight, the proper form of section would be one with equal top and bottom flange. As the strain increases beyond th up to the breaking weight the neutral axis rises from the position in Fig. 206 until it becomes as in Fig. 168, when, as shown by Mr. Hodgkinson's experiments, the most economical form of section is with flanges