Final answer:
The security with the greater EPS adjustment should be used first in the dilution calculation of earnings per share because it indicates the most significant dilutive effect on the EPS.
Step-by-step explanation:
When recalculating earnings per share (EPS) for a company with dilutive convertible securities, the security that should be used first is the one with the greater earnings per share adjustment. This means that for each convertible security, you calculate the dilutive effect it has on EPS, which involves comparing the potential increase in shares (if the securities were converted) with the adjustment to earnings (like interest savings after taxes for convertible debt). The security that causes the greatest decrease in EPS when diluted, i.e., the one with the greater impact on reducing earnings per share, is the most dilutive and should be used first in the EPS calculation.