4511 



HYDROGRAPHIC MANUAL 



Page 362 



Figure 76. — Optical principles of a sextant. 



4511. Principles oj the Sextant 



The construction of the sextant is based on two simple principles: First, the optical principle that 

 the angle of incidence equals the angle of reflection in a plane which contains the normal to the re- 

 flecting surface at the point of reflection. In a sextant (fig. 76) the image of an object at G is reflected 

 by the index mirror A so that the angle GAH is equal to the angle HAS, the line HA being the normal 

 to the surface of the mirror A. Likewise, the angle ABK is equal to the angle KBC. Second, the 

 geometric principle that when a ray of light undergoes two successive reflections in the same plane, 

 the angle between its first and last direction is equal to twice the angle between the reflecting surfaces. 

 From this principle the angle JCG is equal to 2BKH. The angle ABC is a constant for any sextant. 



In the sextant the index mirror A is carried on the index arm AE. It follows, then, that if the 

 mirrors are so arranged as to measure an angle of 0° when the index arm is at D, any angle such as 

 BKH resulting from a movement of the index arm must equal the angle DAE. 



But according to the second principle the angle BKH, and consequently the angle DAE, is equal 

 to one-half of the measured angle JCG. The limb or arc of the sextant is therefore graduated so that 

 any angle such as DAE may be read at double its value or the equivalent of the angle JCG. 



4512. Navigating Sextant 



As the name implies, a true sextant is limited to one-sixth of a circle, so that the 

 maximum angle that can be measured with it is 120°. The instruments, almost uni- 

 versally known as sextants, are actually quintants, constructed for the measurement of 

 angles up to 144° or slightly larger. 



Two types of sextants are used by the Coast and Geodetic Survey. The larger 

 and more precise is a navigating sextant, sometimes called an astronomic sextant. The 

 arc of this sextant has a radius of approximately 7^ inches, or 19 centimeters. It is 

 constructed so that angles up to approximately 144° can be measured with it. The 

 arc is graduated by divisions 10 minutes apart, but by means of a vernier it can be 

 read to the nearest 10 seconds. The average navigating sextant weighs approximately 

 3K pounds. 



