The relation of models to machines, as to strength, deserves the particular attention of the mechanic. A model may be perfectly proportioned in all its parts as a model, yet the machine, if constructed in the same proportion, will not be sufficiently strong in every part; hence, particular attention should be paid to the kind of strain the different parts are exposed to; and from the statements which follow, the proper dimensions of the structure may be determined.

If the strain to draw asunder in the model be 1, and if the structure is 8 times lager than the model, then the stress in the structure will be 8 3/4 equal 512. If the structure is 6 times as large as the model, then the stress on the structure will be 6 3/4 equal 216, and so on; therefore, the structure will be much less firm than the model; and this the more, as the structure is cube times greater than the model. If we wish to determine the greatest size we can make a machine of which we have a model, we have.

The greatest weight which the beam of the model can bear, divided by the weight which it actually sustains equal a quotent which, when multiplied by the size of the beam in the model, will give the greatest possible size of the same beam in the structure.

Ex. - If a beam in the model be 7 inches long, and bear a weight of 4 lbs. but is capable of bearing a weight of 26 lbs.; what is the greatest length which we can make the corresponding beam in the structure ? Here

26 ÷ 4 = 6-5, therefore, 6-5 X 7 = 45-5 inches.

The strength to resist, crushing increases from a model to a structure in proportion to their size, but, as above, the strain increases as the cubes; wherefore, in this case, also, the model will be stronger than the machine, and the greatest size of the structure will be found by employing the square root of the quotient in the last rule, instead of the quotient itself; thus,

If the greatest weight which the column in a model can bear is 3 cwt., and if it actually bears 28 lbs., then, if the column be 18 inches high, we have

√ (336/28) = 3-564; wherefore 3-464 X 18 = 62-352 inches, the length of the column in the structure.

[From AdcocK's Engineer.]

List of metals, arranged according to their strength. - Steel, wrought-iron, cast-iron, platinum, silver, copper, brass, gold, tin, bismuth, zinc, antimony, lead,

According to Tredgold's and Duleau's experiments, a piece of the best bar-iron 1 square inch across the end would bear a weight of about 77.373 lbs., while a similar piece of cast-iron would be torn asunder by a weight of from 16,243 to 19,464 lbs. Thin iron wires, arranged parallel to each other, and presenting a surface at their extremity of 1 square inch, will carry a mean weight of 126,340 lbs.

List of woods, arranged according to their strength. - Oak, alder, lime, box, pine (sylv.), ash, elm, yellow pine, fir.

A piece of well-dried pine wood, presenting a section of 1 square inch, is able, according Eytelwein, to support a weight of from 15,646 lbs. to 20,408 lbs., whilst a similar piece of oak will carry as much as 25,850 lbs.

Hempen cords, twisted, will support the following weights to the square inch of their section:

1/4 inch to 1 inch thick, 8,746 lbs.; 1 to 3 inches thick, 6,800 lbs.; 3 to 5 inches thick, 5,345 lbs.; 5 to 7 inches thick, 4,860 lbs.

Tredgold gives the following rule for finding the weight in lbs. which a hempen rope will be capable of supporting: Multiply the square of the circumference in inches by 200, and the product will be the quantity sought.

In the practical application of these measures of absolute strength, that of metals should be reckoned at one-half, and that of woods and cords at one-third of their estimated value.

In a parallielopipedon of uniform thickness, supported on two points and loaded in the middle, the lateral strength is direcly as the product of the breadth into the square of the depth, and inversely as the length. Let W represent the lateral strength of any material, estimated by the weight, b the breadth, and d the depth of its end, and

I the distance between the points of support; then W=f d2b / 41. If the parellelopipedon be fastened only at one end in a horizontal position, and the load be applied at the opposits end, W = f d2b / 41.

It is to be observed that the three dimensions, 6, d, and I, are to be taken in the same measure, and that b be so great that no lateral curvature arise from the weight; f in each formula represents the lateral strength, which varies in different materials, and which must be learnt experimentally.

A beam having a rectangular end, whose breadth is two or three times greater than the breadth of another beam, has a power of suspension respectively two or three times greater than it; if the end be two or three times deeper than the end of the other, the suspension power of that which has the greater depth exceeds the suspension power of the other, four or nine times; if its length be two or three times greater than than the length of another beam, its power of suspension will be 1/2 1-3 respectively that of the other; provided that in each case the mode of suspension, the position of the weight, and other circumstances be similar. Hence it follows that a beam, one of whose sides tapers, has a greater power of suspension if placed on the slant than on the broad side, and that the powers of suspension in both cases are in the ratio of their sides; so, for instance, a beam, one of whose sides is double the width of the other, will carry twice as much if placed on a narrow side, as it would if laid on the wide one.

In a piece of round timber (a cylinder) the power of suspension is in proportion to the diameters cubed, and inversely as the length; thus a beam with a diameter two or three times longer than that of another, will carry a weight 8 or 27 times heavier respectively than that whose diameter is unity, the mode of fastening and loading it being similar in both cases.

The lateral strength of square timber is to that of a tree whence it is hewn as 10: 17 nearly.

A considerable advantage is frequently secured by using hollow cylinders instead of solid ones, which, with an equal expenditure of materials, have far greater strength, provided only that the solid part of the cylinder be of a sufficient thickness, and that the workmanship be good; especially that in cast metal beams the thickness be uniform, and the metal free from flaws. According to Eytelwein, such hollow cylinders are to solid ones of equal weight of metal as 1.212: 1, when the inner semi-diameters is to the outer as 1: 2; according to Tredgold as 17: 10, when the two semi-diameters are to each other as 15: 25, and as 2: 1, when they are to each other as 7: 10.

A method of increasing the suspensive power of timber supported at both ends, is, to saw down from 1/8 to 1/2 of its depth, and forcibly drive in a wedge of metal or hard wood, until the timber is slightly raised at the middle out of the horizontal line. By experiment it was found that the suspensive power of a beam thus cut 1-3 of its depth was increased l-19th, when cut 1/2 it was increased l-29th, and when cut 3-4th through it was increased l-87th.

The force required to crush a body increases as the section of the body increases; and this quantity being constant, the resistance of the body diminishes as the height increases.

According to Eytelwein's experiments, the strength of columns or timbers of rectangular form in resisting compression is, as

1. The cube of their thickness (the lesser dimension of their section). 2. As the breadth (the greater dimension of their section). 3. inversely as the square of their length.

Cohesive power of Bars of Metal one inch square, in Tons.

Relative Strength of Cast and Malleable Iron.

It has been found, in the course of the experiments made by Mr. Hodgkinson and Mr. Fairbairn, that the average strain that cast iron will bear in the way of tension, before breaking, is about seven tons and a half per square inch; the weakest, in the course of 16 trials on various descriptions, bearing 6 tons, and the strongest 9 3-4 tons. The experiments of Telford and Brown show that malleable iron will bear, on an average, 27 tons; the weakest bearing 24, and the strongest 29 tons. On approaching the breaking point, cast iron may snap in an instant, without any previous symptom, while wrought iron begins to stretch, with half its breaking weight, and so continues to stretch till it breaks. The experiments of Hodgkinson and Fairbairn show also that cast iron is capable of sustaining compression to the extent of nearly 50 tons on the square inch; the weakest bearing 36 1/2 tons, and the strongest 60 tons. In this respect, malleable iron is much inferior to cast iron. With 12 tons on the square inch it yields, contracts in length, and expands laterally; though it will bear 27 tons, or more, without actual fracture.

Rennie states that cast iron may be crushed with a weight of 93,000 lbs., and brick with one of 562 lbs. on the square inch.