18 Design for a Bridge [Jan. 



Fig. 11, diagram to show the distribution of the weight and 

 strain on one half of the road or bridge. 



By (dynamics, or) a well-known law in mechanics,* if the 

 road were suspended from a catenarian arch (the tangent of a 

 curve giving the direction of the motion, &c), and its total 

 weight between the fulcrums represented by the line A, D, B, 

 the total strain on each fulcrum will be as the side of the 

 parallelogram A, C, or nearly 2i the weight of the road. 



By" the same law, if in the small parallelograms 1,2, 3, &c. 

 to 13, the short side represent the weight of that portion of the 

 bridge destined to be supported by each rod, the long side of 

 the parallelogram will represent the strain on the fulcrum from 

 which the rod is suspended, and the diagonal line the strain on 

 the abutment, or, in this case, the drawing power in the line of 

 the road. 



The circumstance of the suspending rods being delineated as 

 straight lines in these figures, instead of being represented in 

 the catenarian, or other nondescript curves which they will 

 assume in natme, is of little practical consequence, as the 

 tangents to such curves, would on the whole indicate rather 

 less strain than is here given. 



Fig. 12, a diagram to show the ratio of the increase of strain 

 on the different rods as it increases from the fulcrums toward* 

 the centre of the bridge and the abutments, the use of which is 

 to give the exact diameters of the rods at all the different points 

 of suspension. 



e, e, the ratio of the suspending rods. f,f, the ratio of the 

 longitudinal basement rods under the road, g, g, the ratio of 

 strain on the diagonal rods s, z, in Fig. 8, owing to the diver- 

 gency of the rods towards the fulcrums'. This ratio of strain is 

 found from Figs. 14 and 15. h, h, ratio of the increase of 

 strain on the cross rods of Fig. 8, from the same cause. (See 

 Figs. 14 and 15, &c. on a larger scale.) 



Fig. 13, Supposing the road to be formed of timber laid on 

 iron rods, instead of cast-iron, &c. in that case this represents 

 a mode which might be advantageously adopted in the centre 

 of the middle opening, as saving suspending rods, and tending 

 to lessen resiliency. 



Figs. 14 and 15. (See Fig. 12, h, h.) 



Fig. 16, cast-iron plate, three feet by 20, as a basis to the 

 road in Fig. 17. 



Fig. 17, a design preferable to Fig. 1, but constructed on the 

 supposition that the data are altered, and permission given to 

 rest one pier in the middle of the river, and to remove the other 

 two, each 50 or 100 feet towards the shores. At the spot where 

 the bridge would pass, the bed of the river might be widened,. 



* Young's Nat. Phil, sec, II,— RobjWs Eleiaeutu of Mechanical Philosophy, 

 part I. 



