Final answer:
According to the notice, the primary condition to ensure safety for travelers on an Atlantic voyage during wartime is flying the flag of one of Great Britain's allies.
Step-by-step explanation:
The main condition for travelers to be safe during an Atlantic voyage according to the notice is flying the flag of one of Great Britain's allies. The notice explicitly states that vessels flying the flag of Great Britain or any of her allies are liable to destruction in the war zone, implying that flying the flag of a non-allied nation could offer some safety. This notice reflects the perilous conditions of the Atlantic during a time of war, particularly during World War I. It dismisses the security offered by the presence of women and children or the content of the cargo, focusing solely on the flag that the ship bears.
Additionally, the historical context provided describes the Battle of the Atlantic during World War II, highlighting the ongoing threat German U-boats posed to Allied shipping and the strategies employed to protect these vessels, such as the use of sonar and the convoy system. The sinking of the Lusitania is noted as a particularly egregious example of the dangers of Atlantic travel during wartime, especially on ships associated with the Allies.