mathematical theory of suspension bridges . 205 
T, the tension at P, being obviously equal to Va 7 - + z* , 
is equal (Eq. A. No. 2.) to \/~a Z + 2d X + X 2 a + X. 
The angle of suspension is derived from the common ana- 
logy of the incremental triangle, and of the forces corres- 
ponding with it. 
Tables I. and II. are constructed from these theorems, and 
their use will be best explained by an example. 
Let the span proposed for a suspension bridge be 800 feet, 
and let the adjunct weight of suspension rods, road-way, &c. 
be taken at one-half of the weight of the chains ; then, if the 
full tenacity of iron is represented by the modulus of 14800 
feet, the virtual modulus for the whole weight must be re- 
duced in the proportion of 2 -|- 1 : 2, or to 9867 feet ; and let 
it be determined to load the chains at the point of their 
greatest strain, that is at the points of suspensions, with one- 
sixth part of the weight they are theoretically capable of 
sustaining. 
Then, since the semi-span is 400 feet, and y in Table I. is 
taken at an hundred measures, each of these measures must 
be four feet, and the weight expressed in the same measures 
to be sustained at the points of suspension will be 9867 -f- 6 x 4 
— 411,125. Now it appears from Table I. where y is uni- 
formly an hundred, that when T = 412 
a == 400 measures or 1600 feet. 
x— 12.565 - - 50.260 
z= 101.045 - 404.180 
< the angle of suspension 75 0 49'. 
Having now determined a, the modulus, latus rectum, or 
parameter of the curve. In Table II. will be found all the 
respective quantities for each measure of y. But as a is in 
mdcccxxvi. E e 
