We study a power-series expansion for a conserved quantity K in the case of the two-dimensional Henon-Heiles potential. An alternative technique to that of Gustavson [Astron. J. 71, 670 (1966)] is applied to find the coefficients in the expansion for K. The technique is used to determine twelve orders for the conserved quantity K, more than twice as many as that calculated by Gustavson. We investigate the degree of constancy of our truncated K in regions where the motion is known to be chaotic and also where it is nonchaotic
