208 
Mr . Davies Gilbert on the 
and that the column T has the whole pull which any build- 
ing or support may have to sustain in the direction of the 
tangent. 
In Table III. y being, as before, an hundred measures of 
four feet each, a must be sought =411,125, and by propor- 
tioning between 420 and 400 
x— 12.2904^ - - - - 49.1616- 
z = 101.0020 
£ = 102.0235 
- - - - 404.0080 
measures or i Feet. 
- - - - 408.0940 
T = 423.6019J - - - - 1694.4076 
< . 76° 3' 17". 
a, or the modulus of this curve being fixed at 411,125 mea- 
sures of 4 feet each, or at 1644,5 feet; and a in Table IV. 
being taken at 100 measures, each one will be 16,445 feet, 
and all the quantities are given for each gradation of y. 
Thus at 21 measures of y .z = 21,1564 £=21.3142 
20 measures of y . z= 20.1347 £ = 20.2710 
1,0217 1.04332 
1.0217 x 16.445 = 16.8019 feet the increase of z; 
1.0432 x 16.445 = 17.1410 feet the increase of material in £ : 
consequently ~~ =1.021, the quantity of matter in this 
part of the chain to maintain uniform strength, that at the 
apex being unity, and the adjunct matter should be in the 
proportion of 1 to 1,04332. 
Moreover x the versed sine, or the length of the suspen- 
sion rods to the level of the apex will be at 
21 measures of y . ^=2.2214 measures x 16,445 = 36,531 ft. 
20 measures of y . jc=2.oi 35 measures x 16.445=33.112 ft. 
