48 



HYDROGRAPHIC MANUAL 



they can be seen fairly well when looking 

 directly at them (see 5-40). In such cases 

 the sextant should be set to the expected 

 angle at the next position so that the re- 

 flected image of the right-hand object will 

 be in the field of view of the telescope. There 

 are several methods of finding approximate 

 angles : 



(a) The angle may be scaled from the 

 boat sheet with a protractor at the approxi- 

 mate location of the next position to be fixed. 



(b) If the angle is not changing too 

 rapidly, the rate of change between the two 

 preceding angles may be applied to deter- 

 mine the approximate angle at the next fix. 



(c) The relation between the faint signal 

 and a conspicuous object near the signal may 

 be noted and that object reflected first. A 

 slight movement of the sextant will bring 

 the signal within the field of view. 



(d) If the observer first determines the 

 angle subtended between the ends of thumb 

 and little finger with the arm outstretched, 

 he can. roughly approximate an angle by 

 sighting over his hand and stepping off the 

 angle along the horizon. 



If the center object is difficult to reflect, 

 the observers may measure the right angle 

 and the sum angle between the right and left 

 objects, subtracting the former from the lat- 

 ter to obtain the left angle. If the right-hand 

 object is difficult to reflect and left one very 

 distinct, the sextant may be held upside down 

 to look directly at the right-hand object and 

 reflect the left-hand one. This is an awkward 

 procedure but may be necessary occasionally. 



3-15 Inclined angles. — Sextant angles for 

 control of hydrography should be measured 

 between objects in approximately the same 

 horizontal plane as the observer. If it is 

 necessary to measure an angle between two 

 objects having considerable difference in ele- 

 vation, the angle must be corrected before it 

 is used for plotting. When one of the ob- 

 jects is at or near sea level and the other 

 at a sufficient elevation to cause an appre- 

 ciable error, the inclined angle may be cor- 

 rected by use of the graph in Figure 8. This 

 graph is based on the formula : 



CosC = 



CosO 



Cos h 



in which C is the horizontal or computed 

 angle, is the observed inclined angle, and 

 h is the angular elevation of the elevated 

 object from the point of observation. 



To find the correction to an observed angle, 

 enter the graph at the left-hand margin 

 with the altitude angle as an ordinate and 

 from this point extend a line horizontally 

 until it intersects the curve representing the 

 observed inclined angle, interpolating be- 

 tween the curves if necessary. The abscissa 

 of the point of intersection read on the 

 horizontal scale at the bottom of the graph 

 will give the correction to be applied. The 

 correction is subtractive for angles less than 

 90 degrees, and additive for angles greater 

 than 90 degrees. 



3-16 Protractors. — Three-point sextant 

 fixes are plotted graphically with three-arm 

 protractors. There are two types of protrac- 

 tors in general use: (1) the metal three-arm 

 protractor and (2) three-arm plastic pro- 

 tractors constructed of transparent material 

 in two sizes. 



3-17 Metal three-arm protractor. — The 



metal three-arm protractor (Fig. 9) consists 

 essentially of a graduated circle about 6 

 inches in diameter with one fixed and two 

 movable arms pivoted at its center so that 

 the extension of each fiducial edge always 

 passes through the precise center of the 

 graduated circle. The arms are about 18 

 inches long, and each arm is fitted with a 

 removable extension about 15 inches long. 

 The circle is graduated to half-degrees and 

 has a vernier and tangent screw on each 

 movable arm which permits a setting to the 

 nearest minute. The graduations of the cir- 

 cle should be accurate to within one-half 

 minute, and the arms should be truly radial 

 also within one-half minute. 



The center arm of the protractor is fixed 

 at the zero of the scale. The graduations of 

 the circle are marked with two sets of num- 

 bers so that angles may be read to the right 

 or left of the zero of the scale. The con- 



