424 A Resultant System for the [Oct. 



the tension on c. b. will be a maximum when a. c. b. are in one line, 

 and a minimum (Fig. 14.) when a. c. d. are in one line. The minimum 

 of the central angle has however been practically determined to be 25°, 

 with a view to the equilization, as far as practicable, of the strains on 

 the entire series of oblique rods. 



28. We have thus the means of assigning to the centre link any 

 amount of power ; its direction, (horizontal) is known as well as the 

 tension and direction of the central oblique rods, we have therefore two 

 forces, the magnitude and direction of which, with reference to each 

 other, are known, from which to obtain a resultant, which shall be the 

 first link from the centre. And here it must be borne in mind, that the 

 height of the point of suspension and consequently deflection of the 

 chain depend on the power of the centre link, for the resultant, or first 

 link from the centre will form a greater or less angle with the horizon 

 as its direction approaches less or more to that of the centre link, and 

 the resultants arising therefrom, as the series of the chain draws nearer 

 to the standards, will all be similarly affected. 



29. The first resultant from the centre link and oblique rod is 



obtained from the following expression, (Fig. 15.) 



Suppose given A B=200 centre link. "j The actual forces in 



A C=: 33 centre oblique rod. I the bridge designed 



(for the "Jumna" at 

 /_ A C E or C A B= 25° J Agra. 



to find the magnitude and direction of A. D. 

 By Trigonometry, 

 A D 2 =A C 2 +A B 2 — 2 A C. A B. Cos : A B D 

 =A C 2 +A B 2 + 2 (A C. A B Cos : A B) 

 =1089 +4000 0+(1320Q+ 906) 

 A D= v / 53048=230.32=magnitude of A D. 

 Again, 



A D : sin. B A C : : { £ B } : sin * C A D * 



Sin. B A C=25° log. 9' 625948 



AB=200 2- 301030 



11- 926978 

 A D=230'32 2- 362332 



AngleCAD=21°.32 / 9' 564646 



