Self-Calculating Sextant. 



bl'S 



the limb (as in other instruments), the measure of an angle ; 

 — on the line of cotangents, the relative proportion of two 

 sides of a right-angled triangle. This last is a piece of in- 

 formation which no other instrument gives direct. 



This additional information gives a command over the 

 quantities concerned much greater than otherwise could be 

 had. 



Availing ourselves of the lineal scale^ our first aim will be 

 to reduce the problem to a case of right-angled triangles. 

 In all that respects heights and distances on the vertical or 

 horizontal planes, this may, in general, be done with the ut- 

 most ease. 



On the vertical plane, every altitude may be viewed as a 

 perpendicular to the horizontal line passing through the eye 

 of the observer, and since the instrument affords the means 

 of ascertaining that line, and also the proportion which the 

 height bears to the distance, it is evident that we are put 

 in possession of considerable information on the subject. 

 If we wish farther to know the actual measurement of parts, 

 set the instrument a division backward or forward on the line 

 of cotangents, and advance or retreat. By measuring the 

 intervening space you may then proceed with facility and cer- 

 tainty. 



Let BC be a mountain whose height and distance are un- 

 known; occupying the station A, apply the instrument ver- 

 tically to your eye, and having ascertained the horizontal line 

 AB, look steadily along it by direct vision, and move the index 

 Ac until you see the top of the object C by reflex vision 



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