#Vertical angles.# The vertical angle of elevation of an object whose height is known will give the distance, and combined with a bearing or other information this permits of locating a vessel where better means cannot be used. Distance tables are published for this method. (Fig. 46.) The vertical angle is measured with a sextant and must be the angle at the ship between the top of the object and the sea level vertically beneath it; for a hill or mountain, therefore, the eye of the observer should be near the water. The object should not be so distant that curvature becomes appreciable. The "vertical danger angle" is a means of avoiding a known danger, on a principle similar to that of the horizontal danger angle; that is, the angle of elevation of a known object is not permitted to become greater than a fixed amount depending on the distance from the object to the danger to be avoided. #Positions by sound.# In thick weather sound affords a valuable aid to the navigator. In narrow passages noting the echo of the whistle from a cliff is a method resorted to, as for instance in Puget Sound and along the Alaska coast. Fog whistles and bell buoys are maintained at many places. Submarine bells have recently been introduced at a number of points along the Atlantic coast, and vessels may be equipped to receive these submarine signals transmitted through the water, which indicate also the general direction from which the sound comes. #Need of vigilance.# Too great importance cannot be attached to frequent verification of positions by the best available means, particularly when approaching the land. Neglect of this or overconfidence has caused many disasters. A notable instance was the loss of one of the largest Pacific steamers on the coast of Japan in March, 1907. In the afternoon of a clear day this vessel ran on to a well-known reef about a mile from a lighthouse, resulting in the total loss of vessel and cargo valued at three and a half million dollars. The captain was so confident of his position and that he was giving the reef a sufficient berth that he laid down no bearings on the chart and took no soundings. [Illustration: FIG. 47. FIELD'S PROTRACTOR AND PARALLEL RULER IN USE ON A CHART, PLOTTING BEARING OF A LIGHTHOUSE.] #Instruments.# The principal instruments needed for use with charts are; dividers for taking off distances and latitudes and longitudes, parallel ruler for transferring directions to or from a compass rose and for taking off or plotting the latitude on a mercator chart, protractor of 180 degrees for reading the angle with the meridian of any direction or for laying off on the chart any given angle with the meridian, and three-arm or other full-circle protractor for plotting a position by the three-point problem.