38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



demanded at one time a neutral aeroplane with no stability whatever 

 against pitching, on the ground that " stable " aeroplanes were too 

 violent in their motion in gusty air. Another disadvantage of ex- 

 cessive statical stability lies in the tendency of the machine to " take 

 charge " and take a preferred attitude relative to the wind at a time 

 when such a maneuver may embarrass the pilot, as when approaching 

 a landing. However, it appears possible that a machine with the 

 minimum of " statical " stability may be given the maximum of damp- 

 ing and so have a very slow period of pitching. The motion will be 

 nearly dead beat. 



This digression with regard to damping z's. " statical " stability 

 applies wnth equal force to the rolling" and yawing motions of the 

 aeroplane to be considered under " lateral stability." 



For low speed, 36.9 miles, similar calculations give for the longi- 

 tudinal motion 



2i.6D* + Ss.iD^ + i49.8D~ + 22.iD + S4 = o. 



Routh's discriminant 



B,C,D^-A^D^'-B^^E^=-i2Xio\ Unstable. 



Short oscillation : 



D'-+(BJAJD + C,/A, = D^ + 3.90 + 6.94 = 0, 

 £>=- 1.95 ± 1. 77i 



p= — — =3.58 seconds, 



t= —^ = .36 second to damp 50 per cent. Stable. 



Long oscillation : 



D^-+ {DJC^-B^EJC^'')D + EJC^ = D'~ - .os6D + .36 = 0, 

 D= +.028±.594J, 



p= ^^ = 10. s6 seconds, 

 •594 



t= — -^ = —24.7 seconds, 

 — .028 



or + 24.7 seconds will double the initial amplitude. Unstable. 



At this speed Routh's discriminant is negative, indicating that the 

 motion is unstable. The instability is seen to appear when the real 

 parts of the roots corresponding to the long oscillation become posi- 

 tive. The motion is rapid : only 1 1 seconds' period compared with 

 35 seconds at high speed, and any initial displacement will double 

 itself in two periods. The damping of the motion has vanished and 

 although the increase of amplitude is not so rapid that there is danger 



