VII. Account of experiments made on the strength of materials.

By George Rennie, jun. Esq. In a Letter to Thomas Young, M. D. For. Sec. R. S.


Read February 12th, 1818.

London, June 3, 1817. IN

N presenting you the result of the following experiments, I trust I shall not be considered as deviating from my subject, in taking a cursory view of the labours of others. The knowledge of the properties of bodies which come more immediately under our observation, is so instrumental to the progress of science, that any approximation to it deserves our serious attention. The passage over a deep and rapid river, the construction of a great and noble edifice, or the combination of a more complicated piece of mechanism, are arts so peculiarly subservient to the application of these principles, that we cannot be said to proceed with safety and certainty, until we have assigned their just limits. The vague results, on which the more refined calculations of many of the most eminent writers are founded, have given rise to such a multiplicity of contradictory conclusions, that it is difficult to choose, or distinguish, the real from that which is merely specious. The connections are frequently so distant, that little reliance can be placed on them. The Royal Society appears to have instituted, at an early period, some experiments on this subject, but they have recorded little to aid us. EMERSON, in his Mechanics, has laid down a number of rules,


and approximations. Professor Robison in his excellent treatise in the Encyclopædia Britannica ; Banks on the power of machines ; Dr. ANDERSON of Glasgow; Colonel Beaufov, &c. are those, amongst our countrymen, who have given the result of their experiments on wood, and iron. The subject, however, appears to have excited considerable attention on the continent. A theory was published in the year 1638, by GALILEO, on the resistance of solids, and subsequently, by many other philosophers. But however plausible these investigations appeared, they were more theoretical than practical, as will be seen in the sequel. It is only by deriving a theory from careful and well directed experiments, that practical results can be obtained. It would be useless to enumerate the labours of those philosophers, who in following, or varying from the steps of Galileo, have merely tended to obscure a subject respecting which they had no data to proceed upon. It is sufficient to enumerate the names of those who, in conjunction with our own countrymen, have added their labours to the little knowledge we possess. The experiments of Buffon, recorded in the Annals of the Academy of Sciences at Paris, in the years 1740 and 1741, were on a scale sufficiently large to justify every conclusion, had he not omitted to ascertain the direct and absolute strength of the timber employed. It however appeared from his experiments, that the strength of the ligneous fibre is nearly in proportion to the specific gravity. MUSCHENBROECK, whose accuracy (it is said) entitled him to confidence, made a number of experiments on wood and iron, which by being tried on various specimens of the same materials, afforded a mean result considerably higher than other previous authorities. Experiments have also been made by MARIOTTE, VARIGNON, PERRONET, RAMUS, RONDELET, GAUTHEY, NAVIER, AUBRY and TEXIER DE NORBECK, as also at the Ecole Polytechnique, under the direction of M. PRONY. With such authorities before us, it might be deemed presumption in me, to offer you a communication on a subject which had been previously treated of by so many able men. But whoever has had occasion to investigate the principles upon which any edifice is constructed, where the combination of its parts are more the result of uncertain rules than sound principle, will soon find how scanty is our knowledge on a subject so highly important. The desire of obtaining some approximation, which could only be accomplished by repeated trials on the substances themselves, induced me to undertake the following experiments; for which purpose I ordered an apparatus to be prepared, of which the two annexed plates (Plates VI. and VII.] are representations.

Description of the Apparatus. A bar of the best English iron, about 10 feet long, was selected and formed into a lever (whose fulcrum is denoted by f). The hole was accurately bored, and the pin turned, which suffered it to move freely. The standard (A) was firmly secured by the nut (c) to a strong bed plate of cast iron, made firm to the ground. The lever was accurately divided in its lower edge, which was made straight in a line with the fulcrum. A point, or division (D), was selected, at 5 inches from the fulcrum, at which place was let in a piece of hardened steel. The lever was balanced by the balance weight (E), 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 (t) fitting into a corresponding groove in the hole. So that, in order to preserve the level, we had only 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 attained. The scale was hung on a loop of iron, touching the lever in an edge only. I at first used a rope for the balance weight, which indicated a friction of four pounds, but a chain diminished the friction one half. Every moveable centre was well oiled. Of the resistances opposed to the simple strains which may disturb the quiescent state of a body, the principal are the repulsive force, whereby it resists compression, and the force of cohesion, whereby it resists extension. On the former, with the exception of the experiments of GAUTHEY and RONDELET, on stones, and a few others, on soft substances, there is scarcely any thing on record. In the memoir of M. LAGRANGE, on the force of springs, published in the year 1760, the moment of elasticity is represented by a constant quantity, without indicating the relation of this value to the size of the spring : but, in the memoir of the year 1770, on the forms of columns, where he considers a body whose dimensions and thickness are variable, he makes the moment of elasticity proportional to



the fourth

power of the radius, in observing the relations of theory and practice to accord with each other. This was admitted by EULER in his memoir of 1780, in his elaborate investigation of the forins of columns. Mr. COULOMB had however shown before that time, how inapplicable all these calculations were to columns under common circumstances; and you, Sir, have repeated the observation in your lectures on natural philosophy. The results of experiments have also been equally discordant; since it is deduced from those of REYNOLDS, that the power required to crush a cubic quarter of an inch of cast iron, is 4480oolbs. avoirdupoise, or 200 tons; whereas by the average of thirteen experiments made by me on cubes of the same size, the amount never exceeded 10392.53lbs, not quite five tons. This may be seen by referring to the tables. There were four kinds of iron used, viz. ist. 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. 2ndly. Iron taken from a small casting, close grained, and of a dull grey colour. 3rdly. Iron cast horizontally in bars of įth

8 inches long. 4thly. Iron cast vertically, same size as last. These castings were reduced equally on every side to 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


inches square,

* It is probable that Mr. REYNOLDS made his experiments on metal cast at the furnace of Maidley Wood, which is of a very strong and superior quality ; but this circumstance can have been but of little importance compared to the great dispror portion of the results.

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