38 A SYSTEM OF ACCURATE MEASUREMENT 
4 
equation as inappreciable (ye ha 13 pe aes $4 ke. Therefore, 
2 
t—tr- ee O very nearly. 
It may be observed that when ¢=90° this equation becomes 
aw? 
r-t’= ou th agreeing with the equation when the ends are in the 
same horizontal plane. 
With regard to the rejection of the term (r-t#)’ ini it will 
Ww 
prove upon examination to be of very small value, and further, 
the error introduced by omitting it is partly balanced by the 
exclusion of the term ial AB 
360r* 
The equation may also be arrived at by assuming the curve to 
be circular. Radius of curvature p= ¥" at middle of curve, about 
c 
A ——— Therefore p= =6=sin 0 +- ee ae 
w'e. w w w sin € 6 
tn 5 Sant ean 2 
oe + &e. Therefote; vide Appendix IT) L=1+ a . 
<% 
4 a 
et hs ae But L=1+ (r-#) Lf scovabistee ty hea sin 2Z 
6407+ 2 
very approximately. 
IV.—Equations T/T =t+(h—t) sin + — cos ¢. 
formule are inexact, but are sufficiently se for 
all 5 ib., suspended at an angle of 30° from a horizontal line, and 
standard length at a tension of 33} Ib., is only about ‘13 Ib., and 
me a 10-chain riband about ‘88 ib, Atan a ngle of 60° the errors 
re 1:26 and 1°36 ooanea and as these are the extreme 
scien in a very he eavy riband, the As wrap may very safely be 
used i in all ordinary circumstances 
l’w* sin *f 
. Pur 
V.—LZquations r= _— “i 
quations r 242 eee Ge Ty 
L —Tis evidently the correction, and in "ee, ITI this was 
shown. to be ae very approximately, and / and ¢ are equivalent. 
© Ea Appendix TV, it was shown that (-—0) 222 sin very 
