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



of the second to the numerator of the third term, we have 



[_ —9/ wlcosE\ 



^rin'f / 3 5co S *g \ "I 



_ / «^cos|V \040 1152/ •"•J w; 



- V 1- t 2 ; 



If the component at the lower end is used we shall have 

 T 1 = T 2 — wl cos f, and the sign of the terms in the deno- 

 minators by cos f must be changed. 



Also if the tape has several bays in sag it will be seen 

 that the value of T decreases by wl cos f from bay to bay; 

 so that in calculating the sag correction of them all (supposed 

 equal in length) we have, using the first term of the sag 

 correction from equation (33), a series of the form 

 ic 2 P sin 2 5 I" 1 



24T 2 



/ lo/cosfy 

 V " 2T„ / 



...], (35) 



+ r g ,___«.xo + 



/ 3wl cos f \ 2 / , _ 5wl cos £ \ 



where T. n is the observed tension at the upmost support. 

 By expanding these factors and bringing them to the nume- 

 rator this expression can he put into the form 



w 2 Z 3 sin 2 fr n'tflZcos? , /•, *\ w 2 Z 2 cos 2 f 1 



kip'/ 3 sin' f r ™[cos| /rodeos^" | j (3g) 



If in the example already considered the tape had been 

 used on a slope of 30°, or f =60°, supported at every 2 chains 

 with a tension of 14 lb. applied to the upper end, we should 

 have total sag correction 



5 x O000564 2 x 1584 3 x 0'866 2 



24xl4 2 

 f ox OC00564 x 1584 /5 x 0*000564 x 158 A^ 2 

 X \ 1+ " 14x2 " ' V 14x2 



= 1-078 (1 + 0-160 + 0-025) =1'194 inches, 



which shows that the third term can usually be neglected. 



)■} 



