PALMER; METHOD FOR CONSTRUCTING THE CATENARY. 219 
Xx 
(cpa 
So if an exponential curve of the form Y= OF ery were obtain- 
able, a catenary could be produced from it as in Fig. 4. 
\ 
rN, 
Y 
2S 
F Y 
ee : 
0" 
B 
i) X 
Fig. 4. 
It is merely necessary to reverse the curve ABC on the drawing, 
which can be done readily by transferring points to symmetrical 
positions by use of the dividers, when the result is the symmetrical 
curve DBF, whose equation is 
Then, with these two curves plottéd in position as shown, a 
catenary can be quickly obtained by adding ordinates. To do this 
draw a series of vertical lines conveniently spaced, and with the 
dividers set off the ordinate of the curve DPF, upward from the 
curve ABC, on each vertical. Join the points thus plotted with a 
smooth curve and the result is the catenary. 
It will be noticed, also, that the value of s, the length of the 
catenary, is at once shown at every point along the curve by this 
figure. For, by equation (7), 
ef x LMP. 
foo 2) 
