The Laws of successful scouting and of the use of "search curves" have been worked out mathematically, and they are used to find an enemy of which one has certain information; but they are also used by the enemy to avoid being found, and they aid the enemy that is sought almost as much as they aid the seeker. And the sought has the advantage that the use of force, if force can be employed, breaks up the application of the mathematics of the seeker. It is true that two main bodies of two fleets may stumble against each other in the night-time, or in a fog or heavy mist. To prevent this possible occurrence, or to prevent a night attack by destroyers, no sure means has yet been found except examination before dark of a very large area around the fleet that is sought; but the area is too great for a search rigid enough to give complete security, and will probably be so until swift aircraft can scout over long distances at sea. Accepting for the minute the convention that the main body of each side goes at the cruising speed of 10 knots, and that darkness lasts 12 hours, each side will go 120 miles in darkness; and if the two main bodies happen to be going directly toward each other they will approach 240 miles in the darkness of one night. Therefore, a coming fleet, in order to feel entirely safe, would in daylight have to inspect by its scouts a circle of 120 miles radius. To insure safety against destroyer attack, the area would have to be much greater on account of the greater speed of destroyers. [Illustration]