Chapter 23, Problem 18P

$\alpha$ -Phellandrene and $\beta$ -phellandrene are isomeric compounds that are minor constituents of spearmint oil; they have the molecular formula $C_{10}{H}_{16}$. Each compound has a UV absorption maximum in the 230–270 nm range. On catalytic hydrogenation, each compound yields 1-isopropyl-4-methylcyclohexane. On vigorous oxidation with potassium permanganate, $\alpha$ -phellandrene yields

Propose structures for $\alpha$ -and $\beta$ -phellandrene.