"This would be a 40 percent to 53 percent reduction.A history based on the German archives written for the British Admiralty after the war by a former U-boat commander and son-in-law of Dönitz reports that several detailed investigations to discover whether their operations were compromised by broken code were negative and that their defeat ".. was due firstly to outstanding developments in enemy radar ..." The graphs of the data are colour coded to divide the battle into three epochs before the breaking of the Enigma code, after it was broken, and after the introduction of centimetric radar, which could reveal submarine conning towers above the surface of the water and even detect periscopes.