delicacy of the instruments used in determining it. The stretching of a bar within the yield-point consists partly of an elastic extension and partly of a permanent set, and it is this permanent set which makes it so extremely difficult to determine the true elastic limit.

Professor Bauschinger has shown that these artificially raised yield-points are extremely unstable, and may be lowered considerably by hammering the test-bar on the end and reloading it; and that, moreover, the yield-point cannot be raised in tension without at the same time lowering the yield-point in compression. When a bar is subjected to stresses alternating between tension and compression the elastic limit cannot be raised, and the yield-point settles down to the true limit of elasticity. Professor Bauschinger further points out that ordinary materials of construction have their yield-points artificially raised in the process of manufacture, and proves by a most elaborate series of experiments that the true elastic limit-which he still defines as the stress beyond which the strains cease to be proportional to the stresses producing them -can be correctly ascertained by first subjecting the bar to a series of stresses alternating between tension and compression; the limit then decreases to a value not differing appreciably in tension and compression, and below the initial elastic limit or yield-point. The elastic limit found in this way is about 8 tons for wrought iron, and 9 tons for mild steel. The stretching which occurs at the yield-point for hard and soft steels does not differ materially, from which it is inferred that hard and soft materials may be relied upon to work together in a built-up structure, under ordinary working stresses. The same has also been observed in the case of iron.

It is very desirable, in all important tests of materials, to have a record automatically registered by the machine itself; such an apparatus is called an autographic stress-strain apparatus, because it draws a diagram which shows the strain produced by stresses which vary from nothing to that required to break the bar. Various forms of this apparatus exist, but the one designed by Professor Kennedy produces very perfect diagrams, although it is not the most convenient to handle.

The form of the diagram for a piece of mild steel is shown in the woodcut, Fig. 4, from which it will be seen that the extension produced by a given load is represented as an abscissa,

while the load itself is represented as a curved ordinate. The diagram represents the behaviour of the specimen during the test, and shows clearly the limit of elasticity, the maximum load, and the elongation. The curve not only indicates the yield-point, and the amount of extension which occurs at this point, but it is seen by inspection that the local extension which occurs at the breaking-point is measured by drawing ordinates at the commencement and termination of the curve drawn during the time that the specimen is undergoing local extension. Again, the area of the diagram represents the gross mechanical value of the material, as it represents the work done in breaking the bar, which of course depends upon its breakingstrength and ductility.

The principle of the apparatus is as follows: The test-piece is placed in the machine with a stronger bar, which is called a spring-piece. The material of this bar must be ascertained by previous experiments to be perfectly elastic, so that its extensions are strictly proportioned to the pull on the test-piece; and, moreover, it should be of such an area that its limit of elasticity occurs only at a load greater than that which will break the test-piece. By a simple arrangement a very light pointer is made to swing about an axis through an angle proportional to the pull on the test-bar. The end of this pointer in its motion always touches a piece of smoked glass, to which is given a travel in its own plane proportional to the extension of the testpiece. In this way the diagram is drawn. After the test the

glass is varnished to fix the black, and the necessary particulars about the test are written on it with it with a scriber. The glass is then used as a negative, and copies produced by photography.

Professor Unwin's autographic stress-strain apparatus consists of a revolving drum, whose angular displacement is proportional to the position of the poise-weight which denotes the load on the specimen. The extension produced by the load is recorded by means of a wire passing over pulleys and connected with the test-piece; a pencil attached to this wire draws the diagram.

Mr. Wickstead and others, including the author, have devised autographic apparatus which, like Professor Unwin's, show the limit of elasticity, ultimate strength, and total extension; but the portions of the diagrams recorded by Kennedy's apparatus from a to b and c to d, Fig. 4, is much more perfect than in any of the others.

It is well known that the form and dimensions of the testpiece have a very marked effect upon the results obtained in testing (see Hackney, "Forms of Test-pieces," Proc. Inst. C.E., vol. 76). High percentages of elongations may be obtained from short or thick test-pieces; long and thin test-pieces give much lower percentages of elongation for the same material.

The tests intended to govern the quality of the material for a particular purpose will next be considered.

In testing wrought iron and steel intended to be used in engineering construction, it is at least necessary to determine the strength and ductility. The ductility is usually ascertained by measuring the percentage of elongation in the manner already described, or by the percentage of contraction of the fractured area. The contracted area is measured most conveniently by means of micrometer callipers. The strength alone, as first pointed out by Mr. Kirkaldy, is no indication of the quality of the material. "A high breaking-strength may be due to the iron being of a superior quality, dense, fine, and moderately soft, or simply to its being hard and unyielding. A low breaking-strength may be due to looseness and coarseness in the texture, or to extreme softness, although very close and fine in quality. The contraction of area at fracture forms an essential element in estimating the quality of a specimen, and by comparing the breaking-strength with the contraction of area

at fracture the respective merits of various specimens can be correctly ascertained."

The contraction of area can generally be measured with sufficient accuracy in round specimens, but in the case of flat specimens, especially very broad, thin strips, it cannot be measured with sufficient accuracy; and when the fracture is oblique, which is often the case, the difficulty is increased. The contraction of area is also largely influenced, as stated by Professor Unwin, by local conditions of hardness and homogeneity at point of fracture.

It is in consequence of the difficulty in measuring accurately the contraction of area at fracture, that many competent authorities have advocated its omission, in specifications of tests of materials, in favour of elongation; but here also a difficulty exists. The elongation consists of two parts-namely, general and local. The general extension in a specimen continues so long as it offers increased resistance to the force producing it, and is proportional to the length of the specimen; but the local extension commences after the general extension has ceased, and is most decided in all ductile materials, such as steel. It is confined to the portion immediately adjacent to the fractured area. The local extension is, in fact, proportional to the contraction of area of the specimen.

Although it is usual to measure the total extension on a specimen, and to express it in percentage of length, the more scientific way, which has been suggested by Professors Unwin, Barba, and Wickstead, is to separate the general extension from the local.

Mr. Wickstead described, at the meeting of the British Association for 1890, a method of doing this from the autographic record, and recommended a column in the test-sheet of "Percentage of General Extension," in addition to the usual columns-namely, Percentage of Contraction of Area," and "Percentage of Total Extension." The local extension can then be expressed by subtracting the general extension from the total extension.

The local extension is seen by dividing the test-piece before testing, over the length of say 10 inches, into ten equal parts, each 1 inch long; the elongation remeasured after testing will be much greater on the 2 inches or 3 inches which include the fracture than over equal lengths measured on the remaining portion of the 10 inches.

Local and General Extension of a Test-Piece; Drop Tests. 9

Figs. 5 and 5a show a bar 30 inches long, divided into thirty equal parts, with the remeasured lengths after testing. Here the local extension is very decided.

In autographic stress-strain diagrams, such as those produced by means of Professor Kennedy's apparatus, the local extension is easily separated from the general extension; and when this is done it is possible to eliminate the effect of different proportions in regard to the length and area of cross-section, on the percentage of total extension.

The ductility of a specimen can also be ascertained by bending round a bar of given radius. But here, again, the proportions of the test-piece exercise a decided influence on the angle bent through before fracture, which measures the ductility.

In order to secure a suitable material for railway axles, it is usual to specify, in addition to the ordinary tests for tensile strength and ductility made on specimens cut from the axle, that the axle itself should be tested to destruction by a series of blows produced by a falling weight, the axle being reversed after each blow. The results of the drop-test-which this test is called-on axles, when the experiments are carefully conducted, give a fairly close approximation to the endurance which may be expected from similar axles under the conditions existing in ordinary railway practice. The French make use of the drop-test, not only for axles, but for small samples of the materials used in the construction of guns.

In general it may be stated that the conditions under which a given material is tested should conform as nearly as possible with those existing in the structure, machine, rail, tire, axle, or gun of which it forms a part.

Cast Iron. There is no definite modulus of elasticity for cast iron; its apparent modulus