In the Beginning

 In 1578, William Bourne created the plans for a submarine in his book "Inventions and Devises, very necessary for all Generalles and Captaines , or Leaders of men as well as sea as by land". John Napier also had plans in his book “Secret Inventions", but Cornelius Drebblel was the only one to successfully create the vessel and make it seaworthy for the English Navy.

​​​​​​​“In a diving-boat made in the form of a diving-bell, the pressure, and therefore also the volume, of the air depends on the depth of the boat under water. Let us suppose that the boat is floating underwater; if it is then propelled downwards, the pressure on the enclosed air will increase and the volume diminish, with the result that the upward pressure grows less — by Archimedes' Principle — and the boat goes deeper and deeper. But if, on the other hand, the boat while floating under water is 

given an upwards impulse, the air pressure will decrease and so the volume, and with​​​​​​​ it the upwards pressure, will increase, the boat being thereby made to rise, until it floats above the water.” - Cornelis Drebbel, Gerrit Tierie. 

This method worked up to a certain depth, which was measured by Cornelius Drebbel using a quicksilver barometer. For the submarine to work, it had to be elongated and divided into compartments with ballast tanks so it could dive and surface.

"These inventions besides devises of sayling under water with divers, other devises and strategems for harming of the enemyes by the Grace of God and worke of expert Craftsmen I hope to perform." - John Napier

"He made a ship, with which one could row under water and sail from Westminster to Greenwich — a distance of two Dutch miles. Yes, even five or six miles, as far as one wished; and in the ship it is possible to see without a candle and to read the Bible or any other book; which ship was to be seen lying in the Thames — London's river — until a few years ago."  - Cornelius Van der Woude of Alkmaar, 1645.

"The impenetrability of air is shown by the Diving-Bell, ... shaped somewhat line an inverted tumbler... As the vessel descends, the air in it is condensed by the upward pressure of the liquid, and water enters. The lower it gets, the more the air is compressed, and the greater the amount of water admitted. The impenetrability of the air, however, keeps the greater part of the bell clear of water, so that several persons may descend in it to the bottom of the sea." From G. P. Quackenbos, A Natural Philosophy (D. Appleton and Company, New York, 1866), pp 166-167​​​​​​​​​​​​​​

In 1689, the first improvement to the diving bell was when Denis Papin figured a way to pump fresh air into flexible hoses which were attached from the bellows to the diving bell, providing fresh air.