18 GENERAL NAVIGATION. 



it, the so-called " bow and beam bearing," the distance from the object 

 at the latter position being the distance run between the times of tak- 

 ing the two bearings, gives the maximum of accuracy, and is an 

 excellent fix for a departure, but does not insure safety, as the object 

 observed and any dangers off it are abeam before the position is 

 obtained. 



By taking the bearings at two ]3oints and four points on the bow, a 

 fair position is obtained before the object is passed, the distance of 

 the latter at the second position being, as before, equal to the distance 

 run in the interval, allowing for current. Taking afterAvards the 

 beam bearing gives, with slight additional trouble, the distance of 

 the object Avhen abeam: such beam bearings and distances, with the 

 times, should be continuously recorded as fresh departures, the im- 

 portance of Avhich will be appreciated in cases of being suddenly shut 

 in by fog. 



A table of multipliers of the distance run in the interval between 

 any two bearings of an object, the product being its distance at the 

 time of the second bearing, is given in the light list and in Bowditch. 



Danger ang-le. — The utility of the danger angle in passing outly- 

 ing rocks or dangers should not be forgotten. In employing the 

 horizontal danger angle, however, caution is necessary, as, should 

 the chart be inaccurate, i. e., should the objects selected be not quite 

 correctly placed, the angle taken off from it may not serve the pur- 

 l^ose. It should not, therefore, be employed when the survey is old 

 or manifestly imperfect. 



The vertical danger angle may be conveniently used when passing 

 elevated points of known heights, such as lighthouses, cliffs, etc. 

 The computation of the distance corresponding to the height of the 

 object and its angular elevation requires for small distances merely 

 the solution of a plane right triangle; the natural cotangent of the 

 angle multiplied by the height in feet gives the distance in feet. The 

 convenient use of this method, however, requires tables such as those 

 published by Captain Lecky in his little book entitled " The Danger 

 Angle and Offshore Distance Tables." 



This book very usefully extends the vertical angle method to find- 

 ing a ship's position at sea by observing the angular altitude of a 

 peak of known height and its bearing. The tables give heights up to 

 18,000 feet and distances up to 110 miles. When the angles are not 

 too large they should be observed " on and off the limb " and the 

 index error of the sextant thus eliminated, in preference to correct- 

 ing the single altitude for it. It must be remembered that in high 

 latitudes the bearing of a distant object needs correction for the 

 convergence of the meridians before being laid down on a mercator 

 chart. The correction may be found by the following formula, 



