to the cable we obtain 



T difr/ds = - B sin a <|> (4) 



Eliminating ds from equations (2) and (4), we obtain 



dT _ _ F 

 T d<t» R sin a (Ji 



which may be integrated to give 



(5) 



log T/T - -J- cat ♦ (6) 



Also, eliminating ds between (1) and (2), we obtain 



dy = 4- sin ty dT 



1 f T 

 or y = v sin <J> dT (7) 



J T 



Now introduce the variable t = T/T Q . Then equation (3) may be written as 

 T - £ = Fs 



Ts = l~J (8) 



Also (6) becomes 



log t = -|- dot 4 (9) 



and changing the variable of integration from T to t in (7), it becomes 



y = -j j sin ♦ dt - p£ J sin $ dt = ^-^j- j sin $ dt, by (8) 



Hence y/s = j-~ \ sin $ dt (10) 



Equations (8), (9) and (10) are the mathematical expressions from which T 

 may be calculated in any given case. For a given value of R/F, sin $ in (10) is 

 given as a function of t from (9). The integral in (10) may then be evaluated 

 numerically or graphically, giving y/s as a function of t. But by (8) T/Fs is also 

 given as a function of t. Thus equations (8), (9) and (10) express in parametric 

 form, with t as the parameter, that T/Fs (dimensionless tension) is a function of 

 R/F and y/s; i.e. T/Fs = f(R/F, y/s). 



