ne VL. S28 Jp" dear 
tees - a + : 
L. On the Equilibrium of the Funicular Curve when the String 
is extensible. By H. Mosetey, Esg. B.A.* 
qEt the forces acting on the point (2, y) of the curve in the 
directions of the axes be X Y. 
Let the length of the corresponding branch of the curve be 
(s) and the tension at its extremity T. 
Then since by a property of the funicular polygon all the 
forces acting on the branch (s) if applied at its extremity 
would be in equilibrum with the tension (T) at that point, we 
have, calling » the mass of an unit of (s), and S its length 
before distension, the mass of each linear unit being in this 
case considered unity, 
fRpeds+ TH 0 oh (1) 
[Ypds+ TA s0 oon... (2) 
T 
ds—(1+y)dS=0........ (3) 
(E being the modulus of extension) 
CF as 0e ee Ss ~ (4) 
From the two first equations, we get 
yf[Xuds—xrfYuds 
q.yguse? aedy =0 
ds 
—yd ¢ 
sty = = the perpendicular on the tangent = p 
Now, 
(suppose), .*. differentiating S we obtain (observing that dy 
SXpds—dzxfYpds=0) 
(Xy—Ya)pds—d(Tp)=0..... (a) 
Again, differentiating the equations (1) and (2) multiplying the 
former by dz and the latter by dy and adding, we get 
dT + (Xdz+Ydyjp=0....... (B) 
And by equations (3) and (4), 
1 
oy 
1+ = 
Xy— Yoa)ds 
abi 
ieee Sesh +dadT=0 
SS at a 
* Communicated by the Author. 
from: 
