We consider extremely type-II uniaxial superconductors in the context
of anisotropic London theory and study the high vortex density limit w
hen the magnetic induction is tilted with respect to the axis of symme
try. We obtain some further properties of the vortex-flux arrangement
recently considered by Preosti and Muzikar - two sets of orthogonal li
nes, along and perpendicular to the c-axis. We obtain the critical lin
e in the diagram of anisotropy, gamma, versus the Ginzburg-Landau cons
tant, kappa, below which such decomposition may occur. In the reversib
le region of the H-T diagram we propose a method, based on torque and
magnetization experiments, to check the existence of this orthogonal s
tate.