212 KANSAS UNIVERSITY QUARTERLY. 
tion is not such as to, suggest at once a graphical method for plot- 
ting even the simplest case of the curve. 
But a closer study of the equation makes possible a method not 
only suitable for drawing the simple cases of the curve, but like- 
wise for plotting a catenary to conform to any set of conditions 
which may have a physical realization, with exactness, and with no 
computing whatever. 
To make clear the meaning of all features of this equation, and 
to lead logically to the demonstration of the rules which are to be 
presented for the various cases, the equation of the catenary will 
be deduced and some of its most notable properties considered 
with their graphical illustrations. 
EQUATION OF THE CATENARY. 
Sh EE TRE x N 
Fig. 1. 
Fig. 1 shows the cord. of uniform weight suspended ' from a sup- 
port, A, falling to a lowest point, O, called the vertex, and rising ~ 
to another support omitted from the figure: 
Take for the origin of coérdinates the lowest point, O. Now 
consider a portion of the cord, as it hangs in equilibrium, between 
the lowest point O and any point P, the codrdinates of which, with 
reference to O, are x and y. ; 
Let T be the tension in the cord at this point P, and 7), the ten-, 
sion at the lowest point O, 
