We report the first observations of the first harmonic (directed flow, v_1),
and the fourth harmonic (v_4), in the azimuthal distribution of particles with
respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion
Collider (RHIC). Both measurements were done taking advantage of the large
elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it
is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is
about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8)
harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data
tables are at
http://www.star.bnl.gov/central/publications/pubDetail.php?id=3