After adopting a suitable gray as, a "low-visibility" paint for ships, perhaps the next refinement was counter shading; that is, shadows were painted a lighter color, or even white. The superstructure was painted in some cases a light blue, with the hope that it would fade into the distant horizon. However, the effectiveness of the submarine demanded new expedients because within its range of effectiveness no ingenuity could render its intended prey invisible. The effective gun-fire from submarines is several miles and torpedoes can be effective at these distances. However, the submarine prefers to discharge the torpedo at ranges within a mile. It is obvious that, in average weather, low visibility ceases to be very effective against the submarine. The movement of a target is of much less importance in the case of gun-fire than in the case of the torpedo with its relatively low velocity. The submarine gunner must have the range, speed, and course of the target in order to fire a torpedo with any hope of a hit. Therefore, any uncertainties that could be introduced pertaining to these factors would be to the advantage of the submarine's prey. For example, low visibility gave way to confusibility in the discussions of defence against the submarine and the slogan, "A miss is as good as a mile" was adopted. The foregoing factors cannot be determined ordinarily with high accuracy, so that it appeared possible to add somewhat to the difficulties of the submarine commander. Many optical illusions have been devised and studied by scientists. In fact, some of these tricks are well known to the general reader. Straight lines may appear broken, convergent, or divergent by providing certain patterns or lines intermingled with them. Many of these were applied to models in laboratory experiments and it has been shown that confusion results as to the course of the vessel. The application of these on vessels has resulted in the grotesque patterns to be seen on ships during the latter stage of the war. It is well known that these illusions are most effective when the greatest contrasts are used, hence black and white patterns are common. Color has not been utilized as definitely as pattern in confusibility, although there is a secondary aim of obtaining low visibility at a great distance by properly balancing the black, white, and other colors so that a blue-gray results at distances too great for the individual patterns to be resolved by the eye. Color could be used for the purpose of increasing the conclusion by apparently altering the perspective. For example, blue and red patterns on the same surface do not usually appear at the same distance, the red appearing closer than the blue. [Illustration: Fig. 92.--A primary stage in the evolution of the use of geometrical-optical illusions on ships.]