Section III, 1920 



[37] 



Trans. R.S.C. 



The Practical Study of a Catenary 

 By John Satterly, F. R.S.C. 



(Read May Meeting, 1920) 



The catenary furnishes to the student beginning the calculus 

 one of the prettiest examples of applied mathematics. Yet it is rare 

 that the student verifies the equation by practical work on a real 

 hanging chain. The author has for some years encouraged his students 

 to see what they could get out of such an experiment and the following 

 results may be of interest to others. 



Mathematical Treatment 

 The equations of the catenary are obtained as follows: 

 Let BAC (Fig. 1) be the hanging chain. Then considering one 

 half only of the chain we get AB, Fig. 2, 

 Let w = weight of unit length of chain 



s = the length of chain from AB to some point, P 

 To = the tension at A, the lowest point 

 Ti = the tension at P 

 6 = the slope of the chain at P 

 Then applying the triangle of force to the three forces, To, Ti and 

 ws ( = the weight of the chain AP), we get 



Ti cos ^ = To (1) 



Tisin <9 = ws (2) 



ws 

 T"o 



tan d 



F,o / 



