BY MEANS OF LONG STEEL RIBANDS. _ 39 
approximately. Dividing by 2, (r—#) :- Bei foe But the left- 
hand side of this last equation = Z—J, which is the correction in 
the direction of the chord. +r=f+ ho cos € according as the tenison 
is applied at the lower or the upper end of the riband. Therefore 
Pw sin gee Pu? sin *Z 
247 24 (ee 2S 
zontal value, it must evidently be multiplied by the sine of the 
zenith distance or angle. Thus the sin *£ is simply converted into 
sin *Z. 
To reduce this quantity to its hori- 
VI.—Correction for Temperature in steel tapes. 
It has been suggested that the correction for agg ates may: 
e compensated by varying the tension of t and, when 
supported throughout its entire length. Pe 1-00115. as 
the coefficient of expansion for 180° Fahr., and -00000779 as the 
extension for 1 Ib. tension, the following expression for the com- 
pensation may be deduced :—If A¢ and A/f= differences of tension 
temperature At = ‘8203w Af From this equation it is 
evident that a riband machi 1-2191 tb. per chain would require 
a difference of 1%b. in tension for every change in temperature of 
* Fahr., and therefore the compensation is practicable with only 
the very ‘lightest ribands. 
VII.— Table of Tensions to be applied toa Wire Riband weighing 
1 1b. per chain, and standard length at a tension of 334 lb. 
Length | Angle of chord of Riband from horizontal line. 
sus- | 
pended. ‘+0-| +10— | +20- | +30— | +40 | +50 
ao 
Semsomasine 
SRS2eS_ 
“8883 
Nore.—The standard tension and the tensions for the different 
lengths suspended for riband of any other weight may be found by 
proportion, or by multiplying the quantities in the table by the 
weight of 1 chain of the riband, expressed as a fraction of a fe 
