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weight of this casting corresponded to 228.65 lbs. in strength. The strength given by each pound weight of metal in this beam was, therefore, 138-73 lbs. less than that given by each pound of the other.
Mr. Hodgkinson's experiments had hitherto been confined to castings of the same depth and length. His inquiries were now directed to the comparison of castings of different depths and lengths. Collaterally with this inquiry, he directed his attention more particularly to the amount of deflexion, produced by a given load, and to the different stages of deflexion and pressure, under which the elasticity is destroyed, or under which the metal is technically said to take a set. This inquiry may be characterized as one into the stiffness of the casting. It is a most important one; for although beams, cast on the new principle, might resist ultimate fracture more successfully than those of the old form, yet if they deflected more under a given pressure, or if under such deflections they more readily fixed themselves in those forms into which they had been deflected, partaking thus in a degree of a quality analogous to flexibility, there might result from these causes inconveniences more than counterbalancing the increase of ultimate strength. It
may be mentioned in the outset, that these suppositions were in themselves improbable, and anomalous; it was to be expected that the difficulty which attended the ultimate fracture would in a degree characterize all the stages of approach to it, and such in reality was found to be
The beams were now cast 7 feet 6 inches long, and the props placed 7 feet asunder. The ratio of the upper and lower flanches was, in each experiment, that of 1 to 6, which had been ascertained to belong to the best form of section, and they were all of the same size, being, indeed, cast from the same model, which was only varied by increasing in each experiment the distance of the flanches, or the depth of the rib which joined them. The following diagrams represent the sections of fracture, each as before one-fourth its real size.
In the first of these experiments (diagram 10), the depth of the beam was 4:1 inches. The beam was loaded with 2764lbs., when the deflection was 0.25 parts of an inch, and on the removal of this load it returned to its original form, showing that the elasticity had not been strained. The load was then gradually increased up to 3339 lbs., and the deflexion to 0·28 inches, and still the beam recovered its form; 3454lbs. were then put upon it, and there was now a perceptible set, or permanent deflexion, but of exceeding small amount. With a load of 3914, this permanent deflexion became 0:05 inches. The load was then further increased until it became 6215 lbs., and the deflexion 0.51, and throughout the whole of this increase no further set was apparent, the beam returning, when the load was removed, always to its first permanent deflexion of 0.05. When, however, the load was made 6971 lbs., a new set became apparent, and when it was increased to 8637lbs., this set was measured to 0.03 more than the first, or the whole permanent deflexion was now made 0:08 with a load of 11,397lbs., this
permanent deflection became 0·09, with each further increase of weight; the permanent deflexion began now rapidly to increase, until with 12,815 lbs. it became 0:14, and with 13,543lbs. the beam broke.
Similar circumstances characterized the other experiments. In the second (see diagram 11), the depth of the beam was 5.2 inches—the first perceptible set took place under a load of 7257lbs., with 7947lbs. it was 0.08, and the deflexion 0:35. It bore 12,087lbs. with a deflexion of 0-63, and broke by extension with a weight of 15,129 lbs. In the third experiment (see diagram 12), the depth of the beam was 6-0 inches, and the first perceptible set took place under a weight of 13,543lbs., and a deflexion of 0.49 inches. The beam broke with 15,129 lbs. In the fourth experiment (diagram 13), the depth of the beam was 6.93 inches, and the first perceptible set took place with a load of 14,271 lbs., and a deflexion of 0:35. The beam broke with 22,185 lbs. These results may be tabulated as follows:
From these experiments, the first conclusion to be drawn is, that other things being the same, the ultimate strength is, in beams of this form, nearly as the depth, but in a somewhat lower ratio.
The second, that the stiffness of the beam rapidly increases with its depth, a weight nearly twice as great being required to produce the
same deflexion in the fourth experiment as in the first, although the depths were only in the ratio of 3 to 4.
The third, that the quality of elasticity as distinguished from flexibility, or the difficulty of giving a set to the beams was in a much higher ratio than is assigned to it in ordinary beams, requiring in experiments 2 and 4, more than one-half the breaking-weight. Experiment (1)
( presents in reality no exception to this remark, because the depth there is exceedingly small, and the first set which is that given in the table was exceedingly small, and did not affect the elasticity of the material, being followed by no other set until the weight was nearly doubled.
Now in ordinary beams, it appears (Tredgold, page 79), that there is a sensible injury of the elastic force with one-third the breakingweight.
Mr. Hodgkinson concludes, therefore, that in these beams the elasticity remains perfect under loads greater in comparison with those under which they break than in the ordinary beams.
Various other experiments were made after the first publication of these on a considerably larger scale; for the details of them the reader is referred to the fifth volume of the Transactions of the Manchester Phil. Society. It need only here be stated, that these experiments on a larger scale have in every way supported the conclusions drawn from those on a less scale. In conclusion, we shall give the very simple rule which Mr. Hodgkinson has deduced from these experiments to estimate the strength of beams cast on his construction.
RULE. If a be the area of a section of the bottom rib in the middle of the beam, and if d be the depth of the beam there, and I the length or distance between the points of support, all these dimensions being in inches, then will the ultimate strength of the beam in tons, when it is cast erect, be represented by the formula,
26 X A XD
And when it is cast on its side by
25 X A XD
That is, if taking the dimensions in inches, we multiply the area of the middle section of the lower rib by the depth of the beam, and divide this product by the length of the beam, then 26 times this product will represent the number of tons weight which will just break the beam when it is cast upright, and 25 times the product when it is cast on its side.
It is manifest that the principles which Mr. Hodgkinson has established for the best sections of girders, are applicable, with the proper modifications, to every form under which cast-iron is employed to sustain a transverse strain of the material.
INSTANTANEOUS LIGHTS. The tinder-box has been employed from time immemorial for the purpose of obtaining a light: it is now, however, nearly expelled from our dwellings by a host of ingenious chemical contrivances, called “ Instantaneous Lights.” A popular account of some of these may, perhaps, be acceptable to the readers of this Magazine.
About the year 1673, phosphorus was discovered, and its singular inflammability was taken advantage of, as a refined chemical method of getting a light quickly. A small portion of phosphorus, rubbed between the folds of brown paper, instantly bursts into a flame, which will kindle a common brimstone match. This method was eagerly adopted by all such persons as could procure so great a chemical curiosity; for phosphorus was by no means plentiful until the year 1680, when Godfrey Hanckwitz manufactured and sold it in large quantities at his laboratory, in Southampton-street, Strand. [This laboratory, and much of its curious apparatus, is yet in existence.] The marvellous properties of phosphorus excited much attention in this country, and Godfrey set out on his travels abroad, to exhibit and vend the article; he, therefore, has the merit of generally introducing the first chemical method of getting a light.
Improvements were, of course, soon made upon it; one of which was to coạt the wicks of small wax-tapers with phosphorus, in glass tubes, hermetically sealed; thus constituting what were called “phosphoric tapers.” When a light was required, one end of the tube was cut off with a file, and the taper being quickly drawn out, it took fire upon touching the air; but this plan, although ingenious, was not so simple as the original method of friction; it was inconvenient, sometimes even dangerous, and never came into general use. It was succeeded by placing a bit of phosphorus in a small phial, and then stirring it about with a hot iron-wire, thus partially burning it in a confined portion of air, and covering the interior of the phial with oxide of phosphorus: it was then corked up tightly after removing the wire, and preserved for
When a light was wanted, a common brimstone-match was put into the bottle, and a small portion of the phosphoric compound withdrawn upon its brimstone tip; flame instantly resulted, from the strong affinity of the sulphur for the phosphorus. This method, from its simplicity and durability, had a long run, and may even now be met with. Another plan with phosphorus was, to take a small bit of it on the point of a brimstone-match, and then to rub it on a cork or piece of soft wood; the friction caused the union of the phosphorus and sulphur, with the evolution of flame.
These methods with phosphorus were succeeded by a substance called pyrophorus: it was a black powder, produced by the calcination of flour, sugar, and alum, and having the singular property of taking fire upon mere exposure to air. A small bottle of pyrophorus, well prepared, lasted a considerable time, and was a good method of getting a light. The theory of its action was long a mystery; but we now know, that the fire of the pyrophorus, or fire-bearer, results from the attraction of oxygen for potassium, which inflammable metal is elicited from the
potash of the alum by the action of the charcoal of the flour and sugar. “Homberg's pyrophorus," for so it was named, had a long day, but chiefly with scientific curiosos. The invention which first bore the name of “ Instantaneous Light Machine," was the “inflammable air-lamp of Volta;" an extremely elegant and scientific apparatus, consisting of a glass reservoir filled with hydrogen-gas (or inflammable air, as it was then called), which could be subjected to the pressure of a column of water upon turning a stop-cock. The pedestal upon which the reservoir was placed, contained an electrophorus (a variety of the electrical machine), the apparatus being so adjusted by connecting wires, that upon turning the cock a small stream of hydrogen rushed out, and met with a spark of electric fire, which caused its combustion; and this flame kindled a wax-taper, placed directly against it. This machine was soon modified into a variety of ornamental forms, and quickly found a place in the study of almost every scientific man. One fatal objection to its general introduction was, its tendency to explode,-a most disagreeable tendency certainly, especially if the light-seeker was in a great hurry to seal a letter, to say nothing of the squirting of the acid-water over papers, books, and furniture, and perchance the fracture of a looking-glass or window, by a flying fragment of the gas-reservoir. Such an accident often happened, and the Light Machine was denounced as an “ Infernal Machine."
The researches concerning the evolution of heat, by the compression of air, led to the introduction of its agency for obtaining a light.
A small stout brass tube, about six inches long, and half an inch in diameter, closed at one end, and fitted with a hollow air-tight piston, containing in its cavity a scrap of amadou or German tinder, constituted the apparatus which was called, “The Pneumatic Tinder-box, or Light Syringe," and which was used as follows:-The piston was suddenly driven into the tube by a strong jerk of the hands; the air in the tube thus compressed, had its capacity for heat diminished, and therefore parted with it in sufficient quantity to cause the ignition of the tinder; and upon quickly drawing out the piston, the glowing tinder would, of course, kindle a match*.
The Light Syringe is even now frequently used on the continent, although we very seldom see it here, unless upon the lecture-table of the chemist. Considerable practice is required to learn the right method of using it, and a novice has to undergo sundry abrasions of the knuckles, fingers, sprains of the hands, &c., before he lights upon the proper knack of suddenly and successfully compressing the air. The agency of Voltaic electricity was next pressed into the “light company;" it was found that a plate of zinc, and a double plate of copper, when dipped into a dilute acid, evolved sufficient electricity to ignite a fine platina-wire connecting them. This apparatus, being very simple and scientific, was adopted by many, but more especially by philosophers. It took up very little room, as a single pair of plates, two inches square, and a little cistern of acid, about the size of a snuff-box, was quite adequate to the ignition of a fine
* This apparatus, somewhat modified, was employed by the French as a substitute for the gun-lock on fire-arms, before the introduction of percussion-caps.