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



practice would be a rather tedious operation. I£ also the 

 tape were standardized in catenary, the third term would be 

 replaced by 



io 2 l 3 n _ . 2 y \_ w ^ 3 cos2 ? 

 12EAT/ 1 sm y- 12EAT 2 ' 



a very small quantity indeed, as pointed out and exemplified 

 in a different form in the paper just quoted. 



Effect on the Sag Correction of using Tapes of 

 diferent Density. 



In the standard traverse work of the Malay States 

 Survey Department, the tape used is of steel or invar wire of 

 rectangular section about T ] g inch wide and -^ inch thick, 

 weighing about 5*1 oz. Av. per chain of 66 feet. This wire 

 can be obtained from Messrs. J. Chesterman & Co., Sheffield, 

 in continuous lengths of 1000 feet or more. It was customary 

 to obtain it in lengths of about 10 chains or 660 feet, and to 

 mark it off locally at every chain standard when flat at about 

 90° F. (the mean temperature of working) with 20 lb. tension. 

 In order to obtain the odd linkage of his traverse lines the 

 surveyor was also supplied with a steel box tape 66 or 100 feet 

 long, with divisions etched on it to hundredths of links 

 standard, also at about 90° F. under 20 lb. tension. This 

 box tape could be attached to a loop at the end of the ^ tape 

 by a split hook; and it was arranged in marking off the latter 

 that the divisions on the box tape should read correctly. 

 Obviously it was desirable that the box tape should have the 

 same density as the -^ tape ; but it was not possible to show 

 the etching on the former clearly with a less width than ^ inch. 

 The thickness was reduced somewhat to counteract this, but 

 could not be reduced with safety to give a less density than 

 7*3 oz. per chain. The question having arisen as to whether 

 this extra density at the end of the series could appreciably 

 affect the sag correction of the ^ tape for which tables had 

 been calculated, the writer was led to investigate the question 

 mathematically; and as he has not seen the result published 

 anywhere, he appends it to this paper in case it may be of 

 use or interest to other surveyors. 



In the case in point the denser tape is at one end of the 

 series, and this is the case the writer first solved; but he 

 afterwards worked out the more general case where the 

 denser tape may be anywhere in the series ; and as this 

 includes the other the working out of it onlv will be given. 



