108 Dr. G. H. Bryan and Mr. W. E. Williams. [Jan. 7, 



are given by Langley for a lamina of 30" by 4 - 8" the shorter side 

 being in the plane of motion. In the absence of any information as to 

 4> (a), we shall assume (whether correctly or incorrectly) the same 

 values as for square planes. 



Let the moment of inertia be given, as before, by k 2 = \a 2 . 



For an angle of 10° we have 



/(*) = 0-44, f{a) = 1-5, 



<£(a) = 0-49, <j>'(a) = 0-59. 



Substituting these values in the expressions for the coefficients, we 

 have 



mX u = 1-6KSV, mG u = 0-26KSV«, 



mX v = 0-6KSV, mG v = - 0'4KSV«, 



mXo = 0-56KSVa, mGe = 0'13KSVa 2 . 



Substituting again in the expressions for A, B, C, D, and E, we 

 have, assuming k 2 = ^a 2 , 



A = W = h« 2 , 



B = Jc 2 X u + Ge = -( l-6- + 0-13«AKSV = Q0a 2 /V, 

 m\ 2 J 



C = vG u -uG v -X- e G u = 19*4a - 760a 2 /V 2 , 



D = u(X v G u -X u G v )-gG v = 280a/V, 



E = g(X v G u -X u G v ) = 35000a/V 2 . 



Therefore 



H = 3-2. 10 5 ^-1-2.10 7 ^, -3-9. 10*^-1-2. 10*?* 



\2 y4 y2 y4 



This is positive if V 2 > 470a, which is therefore the condition of 

 stability. 



5. Gliders Formed of two Planes. 



Proceeding now to consider the stability of systems made up of 

 several planes rigidly connected together, we shall first consider the 

 stability of a gliding system supported on two slats Si S-2, which are 

 so narrow that displacements of their centre of pressures due to varia- 

 tions of the angles of incidence of the wind may be neglected. 



We shall first suppose that the two slats are in the same plane, and 

 that the centre of gravity is also in this plane. 



