Determining North-South Line Via Watch Method: Theory & Reason
When the Sun is on the meridian and is due South (local noon in Northern Hemisphere) your hour hand will point to (or close to 12) - assuming your local noon and civil noon are similar! (Daylight saving means 1pm fills this role).

The Sun crosses the sky in 24 hours, the hour hand travels round the watch in 12 hours. Hence the watch hour hand is twice as fast, so when the hour hand has reached 2pm, the Sun has only gone half as far (ie "to 1pm"), so if you point the hour hand towards the Sun in this case, the meridian is an hour further behind rather than 2 hours.

By the time we get to 4pm the Sun will have travelled "two watch hours" away from the meridian and so on.