1848.] Construction of Iron Tension Bridges. 425 



And angle C A B— angle C A D=25°— 21°-32 / =3°.28, or angle of first 

 resultant A F with the horizon. Thus the magnitude and direction of 

 the first link are found, and the link is a true resultant of the two 

 forces acting at its lower extremity. In like manner can each link be 

 ascertained till the series is complete, and thus a perfect system of links 

 and auxiliaries will be obtained in equilibrio, under the maximum strain 

 to which the structure can be exposed. 



30. By reference to annexed Fig. 16, the formation of the chain 

 will be readily understood from the mechanical construction, as, shown 

 in the dotted lines, which are the forces taken from a scale of equal 

 parts, and correspond with the results obtained by the mode of calcula- 

 tion above referred to. (See Fig. 16.) 



The points of attachment, e, e, e, of the oblique rods and platform, 

 are originally known, the span being divided into a number of equal 

 parts ; the length of the links or points d. d. d. are found by the annex- 

 ed formulae (Drewry, p. 172). 



>v/ (deflection -f- deflection) 2 -+• semichord 2 = semilength of chain, which 



3 

 must be computed independent of the centre link. The semi-length 



thus obtained is to be divided into as many links as are required, which 

 will of course depend on the number of spaces of the platform upheld 

 direct from the standards (Fig. 17). The deflection may be assumed 

 any proportion of the chord line from a 10th to a 15th. In small 

 bridges the latter is the best as affording greater rigidity, with but little 

 extra material ; in large spans, perhaps a medium, or -^th wm " De found 

 most practicable. In the above Fig. 16, a c, a c, represent the strains 

 on the main chains, a d, a d, the tensions on the oblique rods, and 

 c d, c d, the resultants. 



31. In a bridge on the resultant system of 500 feet span and 24 

 feet width of roadway, if the chain were made to taper at the centre 

 b to ith the section of the link at the point of suspension, which in this 

 case would be equivalent to the tension of 1014 tons, the central link 

 would have 9 times the strength, that in the extreme, or Dredge's taper- 

 ing system, would have been assigned to it, whilst from the position of 

 the resultant link, and collateral oblique rods, the iron in the centre, does 

 not hang as dead weight tending to produce vibration by the slightest 

 cause, as in the uniform system, but is kept under the dominion of tension 

 drawn in the direction of its length, and thus preserved steady and rigid. 



