PALMER: METHOD FOR CONSTRUCTING THE CATENARY. 229 
For which 
I=V v(w-E2c). si) 
(6) The level to which the curve shall fall being given, required the 
length of cord which will just reach that level, and also the plotting of 
the curve. 
For this case it appears to be wholly impossible to derive an 
equation similar to (21) which will serve as a method, as in Case 
II (a). 
But the problem may be solved in a manner entirely satisfactory 
from the standpoint of the draftsman by resorting to what has not 
thus far been found necessary—the drawing of a few tentative lines 
on the ‘‘simple catenary” diagram. 
Ry a K 
: Z| 
B Sj le 
yy Yy Yip ' 
yy z 
Y y; : 
GY = 
ey 
eZ ’ : 
poe 7 
RET erase Near este Cha Gee nN aa 
Fig. to, 
Fig. 10,B, and B, are the given abutments and MN the horizontal 
line to which the curve is to be tangent. 
Lay out this figure on the plotting of the simple catenary already 
prepared, MFR being the curve. Then transfer a sufficient num- 
ber of points across by means of horizontal lines and the dividers, 
