A term derived from the Latin, implying the property or holding fast, firmness, etc.; some authors restrict its application to that force by which metals resist their being pulled, or torn asunder; as the action of a weight suspended to the end of a wire; and make a distinction between it, and the term cohesion, which of course implies that force by which the parts of bodies cohere. The real distinction, if any, is however so refined, that we may without much impropriety treat them here as the same force.
The tenacity or cohesion of solids is measured by the force required to pull them asunder; and authors on the subject in general agree, that it may be calculated from the transverse strength of the bar or rod, as near, or perhaps nearer to the real cohesion, than can be obtained by pulling the body asunder; but we find that this assertion, however correct it may apppear from abstract reasoning, is at variance with the most prominent facts derived from actual experiment, and given by the same authors. By the experiments of Emerson, it is stated that a wire of iron, one-tenth of an inch in diameter, requires a force of 450lbs. to pull it asunder; and according to Rumford, that an inch cylinder or rod of iron, required a pull of 63,320lbs. to break it. Now the area, or transverse section of the inch rod is 785; in other words, it contains 78 wires of one-tenth of an inch in diameter; therefore the aggregate strength of the 78 wires, ought according to the doctrine laid down, to be equal to 63,320lbs.; but 78 X 450, make only 35.100; and thus it appears that calculation by the transverse strength, taking the wire for our datum, gives us but little more than half the real tenacity of the inch rod; and if we were to take the inch rod for our datum of calculation, we find (78÷ 63.320 = 811 62/78); that each wire should sustain a force of 81 libs.
Indeed, rather more than this, for we are further told, (and we do notdispute its general accuracy,) that"the cohesive force of metals is much increased by wire-drawing, rolling, and hammering." Such illustrations of the correctness of a theory, we have thought it necessary to notice, as it might prove of very serious consequence, were an engineer (for instance) to construct a wire bridge, founded upon calculations of the given transverse strength of a rod of iron. His only security, it appears to us, would be to prove, himself, the actual tenacity of the identical material he employs, and not place much dependance upon the experiments of others; for, however judiciously the latter may have been conducted, or faithfully detailed, there is such a wide difference in the results of experiments made upon the same nominal material, that it is only by a great number of experiments that any useful approximation to the truth can be obtained. Mr. John Rennie, who has most laudably and ably exerted himself in this field of inquiry, found many such discordant results as those we have detected.
In a paper furnished to the Royal Society, that engineer states, that it had been deduced from the experiments made by Reynolds, that the power required to crush a cubic quarter of an inch of cast iron was 448,0001bs. avoirdupois, or 200 tons; whereas, by the average of thirteen experiments made by Mr. Rennie, in cubes of the same size, the amount never exceeded 10,3921bs.=not 5 tons!
The desire of obtaining some approximation, which could only be accomplished by repeated trials on the substances themselves, induced Mr. Rennie to undertake the following experiments.
The apparatus used for this purpose was a powerful lever of the second class; it consisted of a flat bar of the best English iron, about ten feet long, one of the extremities being formed into a rule-joint, by which it was attached to a stout and short standard of wrought iron, that was bolted to a massive bed-plate of cast iron; the hole in the centre of the joint, and the pin which formed the fulcrum, were accurately turned, so as to move slowly and freely. The lever was accurately divided on its lower edge, which was made straight in a line with the fulcrum. A point or division was selected, at five inches from the fulcrum, at which place was let in a piece of hardened steel. The lever was balanced by a weight, and in this state it was ready for operation. But, in order to keep it as level as possible, a hole was drilled through a projection on the bed-plate, large enough to admit a stout bolt easily through it, which again was prevented from turning in the hole by means of a tongue fitting into a corresponding groove in the hole, so that, in order to preserve the level, it was only necessary to move the nut, to elevate or depress the bolt, according to the size of the specimen.
But as an inequality of pressure would still arise, from the nature of the apparatus, the body to be examined was placed between two pieces of steel, the pressure being communicated through the medium of two pieces of thick leather, above and below the steel pieces, by which means a more equal contact of surfaces was obtained. The scale was hung on a loop of iron, touching the lever in an edge only. At first a rope was used for the balance weight, which indicated a friction of four pounds, but a chain diminished the friction one half. Every movable centre was well oiled.
In Mr. Rennie's experiments on the cohesive strength of cast iron, to resist compression, there were four kinds of iron used; viz. 1. Iron taken from the centre of a large block, whose crystals were similar in appearance and magnitude to those evinced in the fracture of what is usually termed gun-metal.
3. Iron cast horizontally, in bars of three-eighths of aninch square, eight inches long. 4. Iron cast vertically, same size as last. These castings were reduced equally on every side, to one quarter of an inch square; thus, removing the hard external coat, usually surrounding metal castings. They were all subjected to a gauge; the bars were then presumed to be tolerably uniform. The weights used were of the best kind that could be procured, and, as the experiment advanced, smaller weights were used.