A single sextant angle furnishes a means of avoiding a known danger by using what is known as the horizontal "danger angle." (Fig. 45.) Note two well-defined objects on the coast either side of the danger to be avoided and describe a circle through them and passing sufficiently outside of the reef to give it a safe berth. With a protractor on the chart note the angle between the objects at any point on the outer part of this circle. If in passing, the angle at the ship between the two objects is not allowed to become greater than this "danger angle" the danger will be given a sufficient berth. This method as well as any use of sextant angles or bearings depends of course on the accuracy of the chart, and caution must be used where it is not certain that the chart depends upon an accurate survey. [Illustration: POSITION BY SEXTANT ANGLES THREE POINT PROBLEM FIG. 44.] [Illustration: HORIZONTAL DANGER ANGLE FIG. 45.] [Illustration: DISTANCE BY VERTICAL ANGLE] [Illustration: VERTICAL DANGER ANGLE FIG. 46.] #Soundings.# Even if objects cannot be seen, due to distance or thick weather, the chart furnishes a valuable aid when a vessel has approached within the limits where it is practicable to obtain soundings. Modern navigational sounding machines permit of obtaining soundings to depths of nearly one hundred fathoms without stopping the vessel. A rough check is at once obtained by comparing such soundings with those given on the chart for the position carried forward by dead reckoning. If a number of soundings are taken and plotted on a piece of tracing paper, spaced by the log readings to the scale of the chart, and this tracing paper is laid over the chart and shifted in the vicinity of the probable position until the soundings best agree with those on the chart, a valuable verification of position may be obtained. This is particularly the case if the area has been well surveyed, and the soundings taken on the vessel are accurate, and the configuration of the bottom has marked characteristics. For instance, in approaching New York the crossing of the 30, 20, and 10 fathom curves will give a fair warning of the distance off the Long Island and New Jersey coasts, and soundings across such a feature as the submerged Hudson gorge extending to the southeastward of Sandy Hook will give a valuable indication of position. The taking of soundings should be resorted to even in favorable conditions, in approaching shoal water, as a check on other means of locating the vessel. Many marine disasters are attributed to failure to make sufficient use of the lead, the simplest of navigational aids.