﻿I ST I 1 4^ 



Wire or Tape including the Effect of Stiffness. 125 



number of equal concentrated loads each =W spaced at 

 equal distances along the tape in sag. The result is Sag 

 Correction = 



i_r 



241V 



wH 



2 + 2Wio/ ( ^-^+W 2 (m 2 -l)l, . (45) 



where m is the number of spaces = number of loads + 1. 

 If we make m = 2, we obtain 



— ^ 2 [> 2 Z 2 + 3Wt^ + 3W 2 ], 



the same as making n — \ in formula (44). 



In order to test these formulae the writer had some expe- 

 riments made which were carried out by Mr. W. A. Wallace, 

 a Surveyor of the Trigonometrical Survey Department of the 

 Malay States. A -^ tape 7 chains long was stretched in sag- 

 under 20 lb. tension, and the movement of one end was 

 noted when a weight of 1 lb. was placed at successive 

 intervals of 1 chain along the tape, and also when 1 lb. 

 weights were placed at each chain. The tape weighed 

 5'1 oz. per chain of 66 feet. The following are the results 

 giving the differences between observed and calculated 

 -effects : — 



Position of Weight. 



Movement 

 observed. 



Movement 

 calculated. 



Difference, j 

 obs. — calc. 



W at 1 chain 



0-357 link 

 0-521 „ 

 0710 .. 

 0664 „ 

 0-536 „ 

 5-641 „ 



0-346 link 

 0-577 .. 

 0-602 ., 

 0-692 .. 

 0-577 „ 

 5-731 .. 



+0013 link 

 -0056 ,. 

 +0-018 .. 

 -0 028 .. 

 -0041 .. 

 -0-090 .. 



,, 2 chains 



„ 3 ., 



,, 4 ., 



,. 5 , 



,, 1 to 6 chains incl... 



The differences are greater than the writer would have 

 expected, and may be due to differences of elasticity in the 

 tape which has of course been assumed to be homogeneous. 

 Mr. Wallace was not satisfied with the conditions under 

 which the tests were made. Allowance was made for change 

 of temperature, but he notes that there were passing clouds 

 which may have affected the temperature of the tape more 

 than the thermometers. There was also a slight breeze, and 

 it was intended to repeat the experiment under more favourable 



