96 HYDROGRAPHICAL SURVEYING [chap. iv. 



quite sufficient to begin on. The bearing is only wanted to 

 plant the meridian fairly square on the paper, and the compass 

 bearing will give us this near enough to be able to lay off any 

 bearings which may be taken in the course of mapping the 

 detail. The compass will never be used in any of the important 

 parts of the chart, unless our survey partakes of the nature of 

 a sketch or running survey. 



If, however, regular triangulation is likely to fail, true bear- 

 ings in the course of the work may be necessary to carry it on, 

 and in this case we must begin with a careful true bearing. 

 Prepara- In preparing the triangles for working, they will of course 

 ^on of never be found exactly correct, i.e., the three observed angles 



will be either more or less than 180°. 

 Spherical In dealing with this theoretically, the sum of the three 

 Excess. theodolite angles taken at the corners of any triangle will 

 be greater than 180°, in consequence of each angle observed 

 being in a different plane. This is known as the spherical 

 excess, and in extended triangulations for topographical pur- 

 poses, as the survey of India, etc., must be taken into account. 

 For practical nautical work we need not regard it, as our 

 instruments are not large enough to measure angles so exactly, 

 nor is our w^ork of sufficient extent 

 Correct- In dealing with the amount the triangle is in error, for the 



ingthe three angles of the triangle must be corrected to make the 

 Triauerles. 



precise 180°, before using them for calculation, circumstances 



must guide its distribution among the angles. 



An angle observed with a large theodolite should have more 

 value given to it than others. One station may have been 

 more exposed to the wind than others, which would depreciate 

 the value of the angles observed there. 



Without any indications of this kind to guide, it is as well 

 to divide the error equally among the angles ; but it must be 

 remembered, that an alteration in the small angle will make 

 more difference in the resulting position than in either of the 

 other two, so that if this angle at all approaches the limit 

 which should be used for a receiving angle (30°), it is perhaps 

 well to put the smallest amount of change into it, but it is of 

 course impossible to guess where the error is. If the angles 

 have been repeated often enough, the resulting error any way 

 will be very small. 



