_BY MEANS OF LONG STEEL RIBANDS. si. 
It is a this elastic —. se the ribands that the 
in the length between their ends, arising from their 
paspeiinion, 1 may be eliminated by increase of tension ; the increase 
diminishing the ordinates, and at the same time lengthening the 
chords of the curves in which the hang. In other words, the 
tensiéns applied to the suspended ribands may be so increased that 
the chords of the lengthened ribands will equal their normal 
lengths ; that is, their lengths at standard tension. A fuller con- 
sideration of this part of the subject will appear in ri Appendices. 
In order to avoid errors arising from slight bends or curves in 
- ribands, it is gr oman to apply a considerable Leica to them, 
n when using them upon a plane surface, or when testing at a 
Pandard This tension will hereafter be called the standard 
tension. 
The suspended riband hangs in a curve, which, unless acted 
u by wind, lies wholly in a vertical plane. This curve is 
approximately the common eatenary, and from its equations the 
When the ends of the suspended riband are in tha same 
horizontal plane, and, 
= tension at the lowest point in curved riband, 
¢ =the standard tension, 
w= Weight of 1 chain of riband, 
Pw 
2 
i - thé — — DAR =O. 
From this equation # may be readily found with the aid of a 
table of squares and ee and / will be the — to apply at 
either end of the nd; for conditions of accuracy render it 
imperative that ¢ should be large compared with w; and when 
hi ; 
not appreciably _— from the tangential tension at the end. 
The proportion ~ — = 30 to 35 has been found suitable to the 
necessities - satis 
ends of the riband are not in the same horizontal 
plane, and {- the angle between the chord of the riband and the 
zenith. 
7" =the tension to be applied to the upper end. 
7’ =the tension to be applied at the lower end and r= 
aA hoe g es 
1+T 
2 
P—tr— 
jw cost 
Pet 
Tere 
Scent 
2 
F 
