A Graphical Method for Constructing the 
: Catenary. 
BY WALTER K. PALMER. 
INTRODUCTION. 
An inspection of the various works on mathematics, mechanics, 
graphics and drafting will reveal the fact that, while ready drawing- 
board constructions are available for most of the curves encoun- 
tered in engineering drafting, no method has been presented for 
constructing the catenary which is applicable to all the sets of 
conditions that may from physical considerations be imposed. 
Many discussions of the curve are offered; but, with no exception 
thus far noted, they either deal with one or two simple cases of 
construction, neglecting wholly the more general cases, or presume 
some kind of an approximation or involve a series of tedious com- 
putations which, in the end, yield only an approximate result; 
and in most instances these objections are all present. No purely 
graphical construction, such as is desirable from the standpoint of 
the draftsman, has been given, it is believed, even for the mere 
plotting of the curve when it is not required to conform to fixed 
conditions. 
While this curve is, perhaps, not of such general importance or 
wide application in engineering drafting as some others for which 
ready constructions are available, it would still seem that a direct 
and exact drawing-board construction for it, such as the construc- 
tions for the parabola, hyperbola, etc., would be of interest and 
value to draftsmen generally. 
An examination of the equation of the catenary would seem at 
first to show conclusively that the objections mentioned are entirely 
unavoidable. It would appear that no means can be had for de- 
termining the curve in conformity to given conditions, which does 
not involve approximations of some sort, since the parameter of 
the catenary is involved in a transcendental equation, impossible 
to solve by ordinary algebraic methods; and the form of this equa- 
(211) KAN, UNIV, QUAR., VOL. VIT, NO 4, OCT,, 1898, SERIES A 
