BY MEANS OF LONG STEEL RIBANDS. . 35 
APPENDICES. 
I.— Determination of Constant ‘00000779 Chain. 
Three steel ribands, each 5 chains long, and each in one piege, 
weighing 140625 tb., 1:25 b., sf ‘984375 tb., tested through a 
range of 15 %b., viz., from o 25, gave as the extension in 
1 chain, produced by a tension of 1 bb. ‘02200 inch, 02480 inch, 
vely. 
Multiplying these quantities by the weight of 1 chain of each 
riband gives the values ‘00618750, 00620000, and -00611625 
inch. The mean 00616792, reduced to a decimal of a chain, is 
00000779, and this quantity ‘will represent the extension ager 
by a tension o in 1 chain of riband weighing 1 Ib. It will be 
very approximately true for the light steel ribands now in use. 
The area of the transverse section of the riband, which is 
directly ah eet to its weight; is that upon which the tension 
ted, and the effect of the latter a aga sare 
decreases in the same ratio as the area increas 
h e of arriving at the equation L=/ re + 2) is too 
obvious ‘i ve illustration. 
TI.—Correction for Curved Form of the Suspended Riband. 
The Catenary Curve. 
If the riband were perfectly flexible, the curve in which it would 
hang would be very nearly y the | common sere ice (its elasticity 
f that curve). As, however, 
the method of using the riband snes the spationgiihs of a great 
horizontal tension, as com ared with its weight, the curve, although 
the riband is not perfectly flexible, will yet so closely approach the 
ordinary catenary that even the exact method of solution, viz., that 
which takes into account both the elasticity and the force requisite 
to bend the riband, will not give results appreciably differing from 
those given by the equations to that curve. Nor indeed will the 
as an arc of a circle, differ practically from the exact method. 
Notation. 
L=\length of curve, unit 1 chain. 
Ce teeth of cho 
s=length of curve from point «=0, y=c. 
h=horizontal tension, unit 1 hb. 
c =~ length of riband equal in weight to h. 
€= em Napierian Logarithms = 2°71828183 + ke. 
2,2’ =any ordinates to curve parallel to axis x reckoned from 
the lowest point of curve. 
yy =any. ordinates to curve reckoned from the saps c 
below the lowest point of curve. 
