PALMER: METHOD FOR CONSTRUCTING A CATENARY. 215 
S 
tan a==— 
c 
sin a=— ¢ (10) 
c 
COS a— 
me = ¥ 
From (1) with (10) we have 
Ke 
Bice i cos a——__. 
7. y 
And c=~—*° when the origin was changed, 
Ww 
EE, { (11) 
Lowe. 
This means that the tension at any point in the cord is equal the 
ordinate of that point, multiplied by the weight per unit length of 
the cord. From which we see 
that if a material cord be hung over 
two smooth pins, as represented in 
< Fig. 2, the position for equilibrium 
for the cord is such that its extrem- 
ities are upon the ‘same horizontal 
| line, and that this line is the direc- 
Fig. 2, trix of the particular catenary formed 
From equation (8) and Fig. 1, 
ye (he)? ==s2-h 3: 
h®?=tahce=s". 
ey h2 
Seely 
s?—_h? 
eel ah ) (E2)) 
From (2) (5 aE Sy 
X Cc 
