158 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
Consider now two panels 2 and n + 1, the lower girders of which are called » and 
n-+ 1. Let W be the angle, which the radius from the center, O, of a frame to a girder 
forms with the horizon, and + the angle which the sides of the panels subtend at the center 
(see Fig. 11). 
We have: 
Pas: = Fa41+ Tn cos (30) 
where Fn,, and Tn are given by (30) and (29"). 
Let: 
T,, = K sin 6,, 
F,,.,=—-KX sin 6, ,, cos ¢. 
Where K = _cosec 2 Q is independent of variations in y and 6. 
2 sin’ 6 
Further: 
6, =60,41.+% and Vay. + 7 = 
7 x 
6, = — - ry ak y=) = Ho 
(ha 2) 
P,,,c0[ sin 6,—sin 6,,, | «| cos (W,,,-~ 
al +1] & [cos (bess - ©) 
35 e . C 
= GOS (Ce th =) || oc sin y,,,) sin e271 
2 
and since # is constant we have: 
Eee Oo STIG ene A (31) 
that is, the P-force is proportional to sin p and hence to the distance of the girder from 
the neutral axis, but it must be borne in mind that if the longitudinals were Spare irregularly 
or if aand a, varied, Pn,, would not follow this law. 
The result here obtained is important, because it follows that a shearing force acting 
at any frame produces in the next frame a system of P-forces which in the ideal structure 
here under consideration is in full accord with the theory of bending. 
