1904.] The Longitudinal Stability of Aerial Gliders. 109 



Putting <f> (a) = and ft = ft = in the expressions of § (3), we 

 have all the Y's equal to zero and 



mX K = K(S 1 + So)(2«/(a) + i/'( a )), (9) 



mX v = K(Si + S 2 ) (2vf (a) + uf (cc)), 

 mXo = - K (Si^x + (%ufa, + «/'a), 

 fflO« = - Ki>/' (a) (Si?/! + S 2 ?? 2 ), 

 wG- v = Kuf (a) (Si^/i + S 2 ?y 2 ), 

 mG-j = Ki;/ / ( a )(S 1 7 ?1 2+ v S 2 ^ 2 2 ). 

 Now for equilibrium we must have 



Si?/i + S 2 ^ 2 = 0. 



In this case, G«, and X<j vanish, and therefore, from (6), we see 

 that the coefficients C, D, E, will be zero, and the equilibrum is critical 

 or neutral. 



[This result, which is also evident from first principles, holds good 

 equally when the centre of gravity is not in the plane of the laminae. 

 In order to make the system really stable, the laminae must be inclined 

 at small angles to the line joining their centres. 



Calling these angles ft and ft, neglecting <f> (a), and writing 

 a' = a - ft, a" = a - ft, we get in the equations (8), 



ntXu = K^Si (2w/(a') + vf(oO) cos ft, 

 mX v = K2Si (2vf(oc') - uf (a,')) cos ft, 

 mXo = -K2Si7 ?1 (2?//(a') + y/ , (a / ))cosft, 

 »iY„ = K2Si(2V(a') + ^/ / (a'))sinft, 

 mY, = K2Si (2*/ (a*) - <(<*')) sin ft, 

 mY<j = - K2Sm (2ft/ (a') + r/' (a')) sin ft, 

 wG M = -Kvl^pif'ia), 

 mCx v = Kw2Si^]/'(a'), 

 mGe = K^S^i/'O*')- 

 The conditions for steady motion give 



- &Si/(a') sin ft + &S 2 /(a") sin ft, 

 mr//V 2 = ^^/(a') cos ft + &S 2 /(a") cos ft, 



= /jSi/(a') r/i COS /J + &S 2 /(a") ^ 2 COS ft. 



With these substitutions, those of the nine coefficients X M . . . Gq which 

 vanish in the limiting case of coplanar laminae are given by 



