It shoiold "be noted that v is in the same phase on all beams , and so is 

 9 , but these phases may differ from those of F and G. 



Consider next the beam- foil relations expressed by Equations [UTa,b], 



which may be written: 



F r 



V = v^ + , — ; 6 = e^ + r— 

 o k^ ^2 



To make F/k and G/k vary the same as v and 6 , respectively, assume 

 k = F, k « XG. Then 



k, = cX ; kp - eX^ ; v = v^ <=^ 1 ; 6 <=^ 6 = 1/X [68h,iJ,k] 

 1 ' ^ ' o o 



Turning now to the foil, assume that the values F' , G' , v' , and 9' 

 for the reference system satisfy Equations [i;6a,b] for a certain set of 

 values of the foil parameters. MaJce these equations valid for all other 

 systems of the group in such a way that all terms of each equation vary 

 in the same ratio; that is, so that they are « F = eX in [i+6a] and 

 « G a eX^ in [USb]. The necessary variation of the foil parameters and 

 of S is found to be: 



m a TeX^ ; h <^ X ; I-, "^ I = teX^ 



B o 



c^ = cX^ /T ; c^ « cX /T ; S « i/ZT" 



p T U 



B = leX ; C <=^ tgX ; E^^ « leX ; L « X 



Or, if B, C, and E have Theodorsen's values as stated following 

 Equations [U5a,b], then 



b = X; e«X; 2.^« teX/^ 



68 



