Let A B [fig. 215.] be a circular link or ring, of one inch rod iron, the outer circumference of the ring being 15 inches, and the inner 9. If equal opposite forces be applied to the two points of the link C D, pulling C towards E, and D towards F, the result will be, when the forces are sufficiently intense, that the circular form of the link will be changed into another form with two round ends and two parallel sides, as seen in [fig. 216.] The ratio of the exterior to the interior periphery which was originally as 15 to 9, or 5 to 3, is no longer the same in [fig. 216.] Hence there will be a derangement in the relative position of the component particles, and consequently their cohesion will be progressively impaired, and eventually destroyed. In [fig. 215.] the segment M N of the outside periphery being equal to 3 inches, the corresponding inside segment will be 3⁄5 of it, or 14⁄5 inches. If this portion of the link, in consequence of the stretching force, comes to be extended into a straight line, as shown in [fig. 216.], the corresponding segments, interior and exterior, must both be reduced to an equal length. The matter contained in the 3 inches of the outside periphery must therefore be either compressed, that is, condensed into 14⁄5 inch, or the inside periphery, which is only 14⁄5 inch already, must be extended to 3 inches; that is to say, the exterior condensation and the interior expansion must take place in a reciprocal proportion. But, in every case, it is impossible to effect this contraction of one side of the rod, and extension of the other, without disrupture of the link.
Let us imagine the outside periphery divided into an infinity of points, upon each of which equal opposite forces act to straighten the curvature: they must undoubtedly occasion the rupture of the corresponding part of the internal periphery. This is not the sole injury which must result; others will occur, as we shall perceive in considering what passes in the portion of the link which surrounds C D, [fig. 216.], whose length is 41⁄2 inches outside, and 21⁄10 inside. The segments M P and N O, [fig. 215.], are actually reduced to semi-circumferences, which are inside no more than half an inch, and outside as before. There is thus contraction in the interior, with a quicker curvature or one of shorter radius in the exterior. The derangement of the particles takes place here, in an order inverse to that of the preceding case, but it no less tends to diminish the strength of that portion of the link; whence we may certainly conclude that the circular form of cable links is an extremely faulty one.
Leaving matters as we have supposed in [fig. 215.], but suppose that G is a rod introduced into the mail, hindering its two opposite points A B from approximating. This circumstance makes a remarkable change in the results. The link pulled as above described, must assume the quadrilateral form shown in [fig. 217.] It offers more resistance to deformation than before; but as it may still suffer change of shape, it will lose strength in so doing, and cannot therefore be recommended for the construction of cables which are to be exposed to very severe strains.
Supposing still the link to be circular, if the ends of the stay comprehended a larger portion of the internal periphery, so as to leave merely the space necessary for the plan of the next link, there can be no doubt of its opposing more effectively the change of form, and thus rendering the chain stronger. But, notwithstanding, the circular portions which remain between the points of application of the strain and the stay, would tend always to be straightened, and of consequence to be destroyed. Besides, though we could construct circular links of sufficient strength to bear all strains, we ought still to reject them, because they would consume more materials than links of a more suitable form, as we shall presently see.
The effect of two opposite forces applied to the links of a chain, is, as we have seen, to reduce to a straight line or a straight plane every curved part which is not stayed; whence it is obvious that twisted links, such as Brown first employed, even with a stay in their middle, must of necessity be straightened out, because there is no resistance in the direction opposed to the twist. A cable formed of twisted links, for a vessel of 400 tons stretches 30 feet, when put to the trial strain, and draws back only 10 feet. This elongation of 20 feet proceeds evidently from the straightening of the twist in each link, which can take place only by impairing the strength of the cable.
From the preceding remarks, it appears that the strongest links are such as present, in their original form, straight portions between the points of tension; whence it is clear that links with parallel sides and round ends, would be preferable to all others, did not a good cable require to be able to resist a lateral force, as well as one in the direction of its length.
