greater bases than might be shown in such a table, the computation 

 is quickly made by applying in the formula last given in the com- 

 putation above. 



The bearing of a horizontal base constructed on the ground 

 must be ascertained in order that the angle between it and the line 

 of sight from the instrument may be known and used in the com- 

 putation of a corrected base. If the work is being executed by 

 means of a plane-table, with the table in orientation, the direction 

 of the base may be drawn on the sheet. If a transit is being used 

 for the work, the bearings of the base and the line of sight may be 

 determined, either directly by means of the compass, or by the angle 

 between them and a line of known direction. 



When occupying a point at which it is desired to use this base 

 for ascertaining the distance between it and the point occupied, the 

 correct length of the observed base may be obtained in the follow- 

 ing manner: 



Fig. 32 



Suppose a b represents the base established and a d and b d the 

 lines of sight, from the station occupied, to the base. Since the angle 

 d' y at the instrument, is so very small, if a perpendicular were 

 erected from a to the line connecting the instrument at d, with the 

 center of the base, the angle which it w r ould make with b daiV^ 

 so closely approaches 90 that it may be considered as such. Orient 

 the plane-table as closely as possible, either with the magnetic 

 needle or by inspection; then, by placing the alidade upon the point 

 a on the paper, sighting to the signal a on the ground and drawing 

 the line d a upon the paper, we have the angle, x, between the base 

 and the line of sight. Plot upon the paper the line a b as long as 

 possible. For instance, if it is 10 ft. on the ground, if possible, 

 plot it 10 in. on the paper. Then from a erect a perpendicular to 

 d b. Then a b', measured by the same scale as that by which a b 

 was plotted, wMlbe the length of the corrected base, or B, to be 

 used in the fore-going formula. If a table of sines is available, and 

 also a protractor, the angle y may be measured and the length of a b' 

 found by multiplying the sine of y by the length of a b. The 

 same principle applies to a signal erected vertically, which is above 

 or below the station occupied. 



52 



