30 A SYSTEM OF ACCURATE MEASUREMENT 
int above the distant end equal in height to the height of the 
axis of the ae a above the near end, which should 
be underneath it. en, on the other hand, it is undulating 
or precipitous, necessitating sth suspension of the riband, it is 
obviously more convenient to hold one end to the axis of the 
telescope. The effect on the length of the Aone arising from 
this suspension is eliminated by an increase of te 
The ribands are of steel, of uniform area in thet transverse 
sections, and are to be had, I believe, in sizes from ‘045 inch wide 
and ‘015 thick occas and weighing from about ‘2 tb per chain, 
to about 1:5 Ib per chain. Riband weighing -3 ib per chain, about 
075 inch wide, in a 5-chain length, marked at every tenth 
link, has been found very convenient Sand satisfactory. 
These ribands are elastic, and if stretched by the application of 
any moderate tension, return upon its removal to their origina 
lengths. tension sufficient to cause a permanent change in 
length i is never required in practice, hence eniaiat comparisons 
with a standard are unnecessary. 
y experiment it has been found that, through a very great 
range of tension, the change in length varies as the product of the 
tension and the length of the riband. The change in different 
ribands, of the same length and material, varies inversely as the 
areas of their transverse sections, or what is equivalent, as their 
weights. 
This change in a soft steel riband, one chain of which weighs 
e pound avoirdupois, is ‘00000779 chain for each pound o 
pent a and for each chain in its length. (Vide Appendix I.) 
The weight of the riband should form the basis of computations, 
in preference to the area of the transverse section ; it being im- 
possible to measure the latter with any degree of precision. 
The variations in length arising from the ef ae mee of any 
tension may be found by means of the following form 
l, L = Original and stretched lengths (unit 1 eee 
D == Weight of unit of riband (unit 1 lb.) 
# = tension applie 
k = 00000779 shake 
7. =1(1+4), or Z-1=1(4). 
The elasticity of steel riband is constant or nearly so, at 
ordinary temperatures. Its value has been given for 60° Fahren- 
heit, and may be accepted for all temperatures occurring in_ the 
practice of surveying, without involving appreciable error. It is 
probable, however, that the elasticity increases with the tempera- 
ture. It varies also in different kinds of steel, but only slightly. 
Ata dull red heat a sited will be je permanently lengthened by 
the — of even a moderate 
