560 CABLE 



reciprocal proportion. But, in every case, it is impossible to effect this contraction 

 of one sido 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 consi- 

 dering what passes in the portion of the link which surrounds CD (fig. 308), whose 

 length is 4$ inches outside and 2^th inside. The segments MP and NO (Jig. 307), 

 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 cur- 

 vature or one of shorter radius than 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 fink is an extremely faulty one. 



Leaving matters as we have supposed in fig. 307, but suppose that G is a rod intro- 

 duced into the link, hindering its two opposite points A B from approximating. 



309 ^ This circumstance makes a remarkable change in the results. The 



link, pulled as above described, must assume the quadrilateral form 

 shown in jig. 309. 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 con- 

 struction of cables which are to be exposed to very severe strains. 



Supposing still the link to be circular, if the end 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 etill 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, stretched 30 feet, when put to the trial strain, and drew 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. 



Twisted cables are not now made, and but little of twisted chain. They were made 

 to give the familiar form of rope to the chain, to please the sailors' prejudice. 



Prom 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. 



Let us suppose that by some accident the link fig. 308 should have its two ex- 



310 x'iXX tremities pulled towards Y and z, whilst an obstacle x, placed right 



opposite to its middle, resisted the effort; The sido of the link 

 which touches x would be bent inwards; but if, as in fig. 310, there 

 is a stay, A G B, the two sides would be bent at the same time ; the 

 link would notwithstanding assume a faulty shape. 

 In thus considering the vicious forms, we are naturally directed to that which has 

 had at one time the preference, as is shown in fig. 311 ; but this form of link and 

 stay-pin is so faulty, as to give place now to the general 

 use of the simple link of parallel sides (see fig. 312) 

 and with a very different stay-pin, as will be shown 

 hereafter. This old link has a cast-iron stay with large 

 " 312 ^" ^*"'*311 en< k; i fc presents in all directions a great resistance to 



c ' every change of form ; for let it be pulled in the direction 



a b against an obstacle c, it is evident that the portions d e and df, which are supported 

 by the parts g e and gf, cannot get deformed or be broken without the whole link 

 giving way. As the matter composing ge and ^/cannot bo shortened, or that which 

 composes de and dfbo lengthened, these four sides will remain necessarily in their 

 relative positions, by virtue of the large-ended stay h, whose profile is shown in 

 fig. 314. Wo have examined the strength of a link in every direction, except that 

 perpendicular to its plane. Fig. 313 represents the assemblage of three links in the 



