SOLUTION OF A MECHANICAL PROBLEM. 
[From the Quarterly Mathematical Journal, vol. i. (1857), pp. 405—406.] 
A heavy plane is supported by parallel elastic strings of small extensibility; 
and the strings are of the same length and extensibility : required the position of 
equilibrium. 
Imagine the plane horizontal, and let n be the number of strings, (a, h), (a', b'), 
&c. the coordinates of the points of attachment; £, y the coordinates of the centre 
of gravity of the plane; W the weight; let the equation of the horizontal line about 
which the plane turns be 
x cos a. + y sin a — p = 0 ; 
and let 86 be the inclination of the plane in its position of equilibrium to the hori 
zontal plane, and w8l the force generated by an increase 81 in the length of one of 
the strings. 
We have for the conditions of equilibrium 
£ (a cos a + b sin a — p) co80 — W =0, 
£ (a cos a. + b sin a — p) aw86 — Wg = 0, 
£ (a cos a + b sin a — p) bco80 — Wy = 0; 
or putting £a = L, £6 = M, £a 2 = A, £a6 = H, £6 2 = B, we have 
W 
L cos a + M sin a — np ^ = 0,