522 Self-Calculating Sextant. 



They appear to be new in practice, certain to demonstra- 

 tion, and promise to become useful. 



1st. Reflex vision, which diminishes the scale on the cir- 

 cular arc to half its natural dimensions, enlarges the scale on 

 the line of cotangents to double its natural dimensions ; thus 

 creating a difference of four to one in favour of the accuracy 

 of the latter. 



2d. Besides the advantage of reading from a larger scale, 

 a farther benefit we think of importance, is obtained by the 

 introduction of a line of cotangents. Our knowledge is thus 

 advanced a step without trouble or thought, being told di- 

 rectly, or by inspection, the relative proportions of two sides 

 of a right-angled triangle, which otherwise could only be 

 made by indirect means, or calculations founded on a mea- 

 surement of the arc. 



The instrument proposed, besides other advantages, pos- 

 sesses all the properties of a good Sextant. 



Its form is convenient for ascertaining angles, whether 

 vertical or horizontal. Thence it is adequate to every pur- 

 pose for which a Sextant is wanted. 



Its chief peculiarity consists in the introduction of a lineal 

 scale, by the inspection of which, many important and fre- 

 quently recurring problems may be solved on the spot, with- 

 out a reference to books, or any calculation beyond the most 

 simple ; thus saving much time, while we are made inde- 

 pendent of foreign aid, and obtain results we think more 

 satisfactory and accurate than can be had by instruments 

 in common use. 



In a right-angled plain triangle, if one side be made radi- 

 us, the other side becomes the tangent of the angle opposite 

 to it, and the hypothenuse the secant of the same angle. 

 The scale in question is a line of cotangents, the several di- 

 visions of which are noted by the index converted into a 

 hypothenuse or secant. 



Every movement of the index announces two things ; — on 



