﻿112 Mr. A. E. Young on the Form of a Suspended 



for both free and constrained ends. By continuing the 

 expansion of (1 + b 2 s 2 )* it appears that the integral by A can 

 be written 



A r-i as cosh as /b 2 ^ &V b 6 s 6 Y] 



A |_smha S + - -j [-Y-zg +^y ~ • • • )], 



which shows that further terms rapidly decrease. The rest 

 of the factors in (21) appear to be all of a smaller order than 

 those of the first approximation. 



This is as far as the writer has been able to carry the 

 investigation, and though it has not been found possible to 

 obtain a general solution of either equation (19) or (20) he 

 ventures to think that, so far as the surveyor's tape is con- 

 cerned, he has shown that the approximate solution first 

 derived is sufficient, and proves that if only an adequate 

 tension is used and the lengths of the bays in sag are not 

 extreme, the effect of stiffness on the sag correction is quite 

 negligible. 



Tlie General Catenary Formula. 



The ordinary catenary formula as applied to surveyors' 

 tapes has been worked out fairly completely both when the 

 tape is considered inextensible and when the elastic extension 

 due to the tension is taken into account. An able and useful 

 paper on u A System of Accurate Measurement by means of 

 long Steel Ribands " was read before the Royal Society of 

 New South Wales in 1885 by Mr. G. H. Knibbs, C.M.G., 

 formerly Professor of Surveying at Sydney University, and 

 now Commonwealth Statistician, in which formulae are given 

 for the cases of chord both horizontal and inclined, but 

 applying more particularly to the method by which the sag 

 correction is eliminated by altering the tension, a method of 

 chaining which has, however, not been found very convenient 

 in practice, the more usual process being to preserve a 

 constant end tension and calculate corrections. Another 

 paper, on " The Measurement of Distances with Long Steel 

 Tapes,''' was read by Mr. C. W. Adams, Chief Surveyor, 

 Blenheim, New Zealand, before the Victorian Institute of 

 Surveyors in 1888. In this the series for the sag correction 

 in terms of the end tension is rigorously developed for a 

 number of terms, and tables are supplied for use with various 



ratios of -^- and for various slopes. These papers contain 



practically all that is required by the surveyor engaged on 

 all except the most refined traverse work. The theory as 

 applied to Base-Line measurement and the effect of the 

 elastic extension are dealt with in more detail in Appendix 



