32 A SYSTEM OF ACCURATE MEASUREMENT 
hen the values for 4 have been computed for the various 
inks of the riband used, T’ and T may be found very approxi- 
mately by the equations 
T =t+(h-t) cin ¢ 4 Coe 
oie sin wig eee 
ese equations, though empirical, are very accurate for values 
of 3 between 60° and 90° ; and as these angles most ote es 
occur in practice, will be found as a rule sufficiently ace 
By means of the foregoing formule, surveyors are donde to 
construct for the ribands used by them tables of tensions for use 
in the field. 
When the tension applied to the riband is large compared with 
its weight, the curve in which it hangs has a small ordinate ; and 
consequently a slight error in the amount of the tensions does not 
materially affect ‘the difference in the length between the curve 
and its chord. Owing to the difficulty, however, of holding the 
ends of the riband at any desired points when it is under ‘great 
tension, there is a practical limit to the amount that may be applied. 
This limit is between 20 and 25 Ib. for men of ordinary strength. 
For obvious reasons, there is a limit also to the length of riband 
that may be used. This s may be said to be about 5 chains in rough 
and undulating country, and about 10 chains in level country. 
A 5-¢ riband weighing 1°5 lb., if standard length, at a tension 
of 10 a squines a tension of 19-5 Ib. when the whole length is 
suspended ; ; it is therefore eminently adapted for use in precipitous 
country,—a fact which has been verified by considerable experience. 
If it be preferred a use a constant tension, and to apply 
corrections for the defects in length arising from the suspension of 
ante lengths of riband, these may be ‘found by means of the 
ollowing formule :— 
i= angle eroeing the chord of riband and the zenith 
Pw* 
we when = 90° 
and when os cgi from 90° 
in *¢ 
og 4 ( S mS cos =) 
end of the riband, or 
Pw? sin * Z 
lw cos & 
Hine) 
Ps 
if the tension be applied to the lower 
ym if the tension be applied to the upper 
