26 RAVLKKiil, TJic MccJianical Prvicipks of FligJit. 

 If wc eliminate /3 between (46), (47), we get 



/f/y=^.U-.3 (^^V + ^^^)(^^o^ + ^^^^i"^^) . (48), 



9l'''C0S"-'e 



from which we sec that if fli be given (as well as S^ JV, u), 

 U \s least when 6 = 0, viz., when the phase of maximum 

 \-ertical velocity coincides with the phase of greatest 

 inclination. In this case by use of (44) we have 





If we regard JF, S, u as given, the smallest value of U 

 corresponds to 9i being large in comparison with ^o which is 

 given by (44).* 



The smallest value is 



^=-|^, (50). 



The work required to be clone is here the same function 

 of S, IV, and the iiorizontal velocity as was found in (14), 

 where V has the meaning here assigned to «. 



We see from (46) that, under the circumstances sup- 

 l)osed, O1 + /J is numerically small in comparison with Oo, 

 and a fortiori in comjjarison with fij. Accordingly the 

 forward edge of the plane is inclined downwards when the 

 motion of the plane is downwards. 



As regards the pressure, it is by (43) proportional to 



':'o + (Oi + /5) cos//, 



in which the second term is relatively small. The pressure 

 acts always upon the under side of the plane, and the 

 weight is approximately supported in all phases. 



■ It must not be forgotten that 6^ itself has been assumed to be small. 



