From the above data we are able to determine the probability of being discovered. We take the case of the largest and fastest ocean liners, such as the _Lusitania_ as one illustration. We will assume that the _Lusitania_ is making her maximum speed of about twenty-five knots, which is about the maximum of speed yet attained in a large surface freight-and passenger-carrying ship, and from our scale of vision as applied to upper diagram No. 5 we see that her top works will become visible above the horizon at a distance of eighteen and three-eighths miles from the periscope of the submarine. The commander in the submarine, by using his range and direction finder with which all military submarines are fitted, finds the ship to be pursuing a course and speed that will cause her to pass probably within ten miles of the submarine station in about thirty-five minutes, which is too far off to attack by torpedo. Now, while submarines have a submerged speed of only about ten knots, the commander is quickly able to ascertain that he can intercept the twenty-five-knot boat by laying his own course at right angles to the approaching ship, and that, if the ship keeps her course and speed, in thirty-five minutes he can be within torpedo range, as will be seen by reference to this sketch (see diagram, position No. 5). [Illustration: DIAGRAM TO ILLUSTRATE THE COMPARATIVE VISIBILITY AND CONSEQUENTLY THE COMPARATIVE SAFETY OF SURFACE SHIPS AND CARGO-CARRYING SUBMARINES] Now take for another comparison a slow-speed merchantman of the tramp type making ten knots, which is about the economical speed for this class of ship. Her smoke might be the first thing to betray her approach, but for purposes of comparison take her smoke-stack also, which is the first solid portion of the ship to appear. The smoke-stacks of this class of vessel would probably not be over forty feet in height above water level, therefore, if she were making the same course as the high-speed ship, it will be observed by referring to diagram, position No. 4, and the distance and speeds mentioned thereon, that the submarine at a speed of ten knots has more time to get nearer the course of the approaching ship and can have more time to calculate the enemy's speed of approach and direct course, and thus launch his torpedo with more certainty of making a hit. But assume that this approaching slow-speed ship had no solid opaque portion extending over fifteen feet above the surface of the water, as is the case in a cargo submarine as shown in position No. 3 on the diagram of the earth's surface. One now sees that she would pass the waiting submarine below the horizon, and the intervening round of the sea's surface would prevent the submarine from seeing her; thus she would pass by unseen and in safety.