1904.] The Longitudinal Stability of Aerial Gliders. 107 

 also 



u * V sin a = 0'17V, v = 0'98V. 



Substituting these values in the above expressions for X u . . ., we 

 have 



mX u = 1-66KSV, mG u = 0-l7KSVa, 



mX v = 0-32KSV, mG v = - 0'03KSVa, 



mXi = 0-73KSVa, mGg = 0'09KSVa 2 . 



Substituting these values in the expressions for A, B, C, D, E, given 

 in § (2), and remembering that by the conditions for steady motion 

 mg = KSV 2 /(a), we obtain 



A = \a 2 , B = 92 a 2 /Y, C = 18a- 1340 a 2 /Y 2 , 



D = 295 alY, E = 36400 a/Y 2 , 



and therefore 



H = BCD - AD 2 - EB 2 = 4-8 . 10 5 ,- 3-6 . 10 7 f~ 



V 2 V 4 



-4-3. 10 4 ^- 3-08. 10 8 ^. 



This expression will be positive if V 2 > 774a, and this condition will 

 also make C positive. The glider will therefore be stable if its 

 velocity is greater than ^(7 74a), the units being feet and seconds. 



Ex. 2. — Let us now take the angle of gliding to be 35°, and assume as 

 before k 2 = -J a 2 . At this angle we have 



/(a) = 0-84, /'(a) =0-6, 



<f>(cc) = 0-26 r <f>'(a) = 0-5. 



With these values, we have 



mXu = 1-34KSV, mG u = 0-35KSVa, 



mX v = 1-1KSV, mG v = 0-21KSVa, 



mXe = -O'lKSVa, mGe = 0'08KSVa. 



Substituting in the expressions for A, B, etc., we have 



A = -|-a 2 , B = 27 a 2 /Y, 



C = 15-2a + 50 a 2 /Y 2 , D = 380 a/Y + 240 a/Y = 620 a/Y, 



E = 25600 a 2 /V 2 , H = 5600 a 3 /V 2 - 17400000 a 5 /V 4 . 



The latter is positive when V 2 > 3100a, which is therefore the con- 

 dition of stability. 



Ex. 3. — Let us now take an oblong plane lamina ; the values of / (a) 



