Axis of Symmetry 



Figure 199 — Some streamlines due to a dipole, for equally spaced values of ip. 



— \_l{x- x^ + m(y-y^) + n(z- z^)] 



[119s] 



Since mn(y- y^)/r^ and nn(z- z^)/r^ obviously represent potentials due to dipoles with axes 

 directed toward y or toward z, respectively, the potential can be regarded as the sum of the 

 potentials due to three component dipoles having moments Zfi, m^, ti/x; these moments represent 

 the vector components of the moment n regarded as a vector. 



Streamlines selected for equally spaced values of i>, including the a;-axis, are shown 

 in Figure 199, which may refer to any plane through the dipole axis. Only half of the symmetric 

 diagram in this plane is shown. 



Reversing the sign of n reverses the direction of the axis of the dipole and reverses 

 all velocities. As an alternative, n may be kept positive and the axis for 6 may be drawn in 

 the opposite direction. (See Reference 1, Article 95; Reference 2, Section 15.20, 15.22, 15.26.) 



120. VARIABLE POINT SOURCE, 0!1 FLOV/ NEAR A SPHERICAL CAVITY 



In the flow from a point source, the potential and the velocity q^, taken positive when 

 directed outward from the source, are 



A A 



[120a, b] 



303 



