[satterly] 



STUDY OF A CATENARY 

 Table I 



41 



The tensions at A and B must now be found. A piece of the same 

 chain, exactly half the length of the hanging chain, was taken and hung 

 up between spring balances so as to exactly cover the main hanging 

 chain (Fig. 5). The balances read up to 250 gms. in multiples of 10 

 gms. and were of the cylindrical design. The spring balance at A was 

 placed horizontally to take the horizontal tension at that point, and 

 the balance at B was placed at the right slope, as shewn in the figure, 

 to read the tension there. The balances read 70 and 149 gms. respect- 

 ively, and it might be thought that these are the values of To and Ti, 

 but it was quickly discovered that such spring balances do not read 

 correctly unless they hang vertically, and so they had to be calibrated. 

 A was calibrated as shewn in the lower figure of Figure 5, and B as 

 shewn in the right hand figure. When A read 70 gms. the total load 

 was 87 gms. Therefore, To = 87 gms. Similarly, when B read 1493^ 

 gms. the total load was 153 gms., therefore, Ti=153 gms. 



We have now To = wc = 87 gms. 

 Ti = wY= 153 gms. 

 therefore, since w = 0-778 gm. per cm. c=112 cms. 

 66 



and Y 



778 



= 84-8 cms. 



whereas the difference between the measured ordinates= 105 -3 — 21 

 = 84-3 cms.; a fair agreement. 



Sec. III. Sig. 4 



