At large distances, using Equations [137y, z], 



2 All , , ,„ 2^ 30; 2 , , 3a; 



4>^ (1 - H^)^'^^sin CO ^ =--Ae^a^ 



5 ^^3 5^2^5 5 ^5 



approximately, since kC,^ r and k = ea. Thus the disturbance of the fluid extends effectively 

 to only a short distance. 



The velocity components are 



A\L / \-p.^ \ 1/2 



C 3 „ 4-+1 



64- — --(2C2-l)Zn-- 



^2_i 2 C-1 



sin w, [137f' 



^ =-(1-2^2) ^ 3+ --<:^n^ sino;, [J37g"] 



/l/x / 1 3 4+1 , , , 



tf, =— ^ 3+ </7i^ cos w. [137h" 



" ' ' ^2_i 2^ <-l' 



The pressure in this case can be found from Equation [lie] or Equation [lid]. The kinetic 

 energy is given in Reference 1 and in the table following Section 147, Case 29(3). 



In the last three cases there is no axis of symmetry, hence no stream function exists. 



An extensive comparison of the theoretical formulas for the pressure with observation, 

 resulting in general good agreement except in the wake, was reported by Jones. ^^'^ (See 

 Reference 1, Article 105, 106; Reference 2, Section 15.57; Zahm.^°2, 174^ 



138. PLANETARY ELLIPSOIDS (OR OBLATE SPHEROIDS) AND CIRCULAR DISKS 



For an ellipsoid of planetary form, or an oblate spheroid, the treatment of the last 

 section requires only minor modifications. 



For this case, oblate-spheroidal coordinates ^, /i, w are defined thus: 



X = A;/i4, y = oTcos w, s = oTsin «, ,- [138a, b, c] 



Sr=/;;(C2^1)i/2(i_^2)i/2_ [138d] 



356 



