PALMER: METHOD FOR CONSTRUCTING THE CATENARY. 221 
DM——. (20) 
OO’=a, for when xo, y-=a. If instead of the perfectly general 
form of the equation we have the form 
x 
Cc 
egy eae 
which we should have when employing this curve in a construction 
for the common catenary, then 
c 
OO/=—— 
2 
and the constant sub-tangent DM=c. 
It would seem now that this fact of a constant sub-tangent should 
afford the means for the kind of construction desired for this curve. 
And it is found that the curve may be drawn in a most satisfactory 
way by its use, as follows: 
In Fig. 6 let OY and OX be the axis. Lay off OO’ equal to the 
I 4 
constant a and make PD rer Or if the form 
(oe x 
inane c 
is to be drawn, make 
OO, 
2 
and OD—c: 
2 
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