with the internal angle at 135 degrees, exactly bisected by the direction of the wind. This was a flexible formation which meant when close-hauled the leading division of ships would already be in line ahead. 4th Order: the fleet would divide into three double columns with the centre column slightly ahead. This was the most flexible formation and allowed the fleet to react to any course before the wind. 5th Order: the fleet would divide into three parallel lines, close hauled with the Admiral's column in the centre. To clarify terminology, 'before the wind' means the ship is sailing in the same direction as the wind; 'close hauled' means the ship is sailing into the wind at an angle. Hoste detailed the navigational methods required to allow each ship in the fleet to reach these formations effectively. He also summarised the advantages of fighting from either windward or leeward positions. The Windward position allowed a fleet to control the battle, blew smoke from their guns onto the enemy fleet and allowed them to use fireships against the enemy. However it has the disadvantage that in heavy seas it may not be able to open its lower gun ports without risking flooding. The Leeward position allowed ships to easily drop out of the line when damaged and allowed ships full use of their gun decks. See also Naval tactics in the Age of Sail. Advanced tactics Hoste also analysed where and how to double the enemy line and demonstrated five methods to avoid being doubled. This section of the book focuses strongly on defense rather than attack which reflects the strategic position of the French Navy in the late 1690s. Naval signalling was briefly considered and he suggested a simple system of thirty-six signal flags of three colours. Particular types of signals were restricted to certain positions or groups of ships. British signalling at the time was very confusing and lacked standardisation. Influence Hoste's rigorous mathematical treatment of naval tactics dominated French naval strategy throughout the 18th century. It was only when the French Revolution removed experienced officers and sailors from the French navy, destroying its fighting ability, that British ships were able to take tactical risks and gained decisive victories. References External links 1652 births 1700 deaths French Navy officers from Brest, France 17th-century French mathematicians 17th-century French Jesuits