206 



THE APPLICATIONS OF PHYSICAL FORCES. [BOOK in. 



II. THE SEXTANT. 



The instrument we are about to describe was formerly called an 

 octant or reflecting quadrant. It is used by sailors to take the 

 heights of stars or the angular distances of the moon from the stars 

 called " lunar distances." 



The invention is due to Hadley (1731) ; but several scientific men 

 including Newton, Hooke, Thomas Godfrey of Philadelphia, and 

 Harris, had thought of a similar instrument, 

 based on the same principle. Hadley was the 

 first who made it, and who proved its great 

 practical utility. 



The sextant is an application of a very 

 simple geometrical principle, which is itself an 

 immediate consequence of the laws of reflection. 

 It is as follows : 



When a ray of light, before it reaches the 

 eye, has undergone two successive reflections 

 on two plane mirrors, the angle of deviation of 

 this ray is exactly double the angle of the two 

 mirrors. 



Suppose SI (Fig. 144) a ray coming from a 

 light source, a star for instance ; it falls at I 

 on the mirror M, is Deflected towards F and falls 

 on the second mirror N; there it is reflected a 



second time, takes a new direction I'O and reaches the eye. The angle 

 SOI' formed by the incidental ray and the second reflected ray is 

 double the angle a formed by the two mirrors. 1 



The following is a description of the sextant as it is now made. 

 It is composed of a circular sector, with a graduated arc measuring 

 about 60 (hence its name sextant ; formerly an arc of only 45, or 

 the eighth of the circumference, was used and the instrument was 



1 The demonstration of this proposition is very simple : the angle at is equal 

 to the difference of the angles Sir and II'O, that is to say to 2(90 i) 2(90 i") 

 = 2(i' i}. On the other hand, the angle a is equal to the difference of the angles 

 li'B and 1'IA, that is = i' i. The angle of the two mirrors is therefore half the 

 angle of deviation. 



FIG. 144. Theoretical prin 

 ciple of the sextant. 



