o4S Desaipticn of an Instrument for the Measurement 



jccts, a distance taken with this sextant will be cleared by oi)- 

 servation. 



Fig. 2, represents the addition to a common sextant; A the in- 

 dex mirror ; B the horizon glass ; NO the telescope ; GLM is a 

 circle having B for its centre ; QPG is a quadrantal arc attaclicd 

 to the tube FG, whose axis is the axis of motion of this arc. Tiiis 

 tube is fixed to another, D, placed before the horizon glass by a 

 brass frame CEF ; at D within the tube is fixed a prism, its re- 

 fraction taking place in the plane of the arc QPG: the prism Iwis 

 siich a shape that only the reflected rays can pass throiigli it. 

 At G is another prism for the star, whose refraction is in the 

 same plane, but in the opposite direction. HK is another arc 

 capable of being carried round the circle by an index below, and 

 moving upon a joint K, the direction of the axis being a line 

 joining K and B. 



In taking an observation with this instrument, take the alti- 

 tudes of the otjjects; at the expiration of about five minutes, take 

 them again; from the change of altitude their real altitudes will 

 be known at the end of the next five minutes, which will allow 

 sufficient time to make every preparation. Knowing the longi- 

 tude by account, we can ascertain the true distance hetween the 

 moon and star within a few minutes, which is sufficiently near 

 tor our purpose. Move the index bearing HK, till the arc KG equal 

 true distance known nearly. Elevate the two quadrantal arcs, 

 till from the point of intersection R the arc RK, and from the 

 fame point RG, shall equal the true altitudes of the moon and 

 star res])ectivelv, at the expiration of the second five minutes. 

 Then at the end of this time measure the distance, which will be 

 the real one ; for since KG=MS the true distance nearly, RK = 

 ZM= moon's true altitude, and RG=:ZS= the star's true al- 

 titude; the spherical triangle KRG = ZMS = s;Pp, .: aline joining 

 R and B if produced would pass through the zenith when the two 

 objects are brought into contact, .: RG and RK will be two ver- 

 tical circles, and the prisms will elevate and depress vertically. 



In order to adapt the instrument to all possible values of the 

 ouantity of refraction and parallax, it may be accompanied with 

 a number of prisms having different angles, and which will bring 

 the object nearest to its true place ; and finding the difference 

 between the ap])arcnt distance and the distance thus cor- 

 rected by direct :: ascertain the true distance. Thus let SM 

 (fig. 4) be the true distances ; sm the apparent ; let the prism 

 bring the objects into the position S'M', when 'Mm and iS are 

 very small ; MM' : M'/ : : M'w : mt'. This will, however, only 

 be an approximation to the truth, which will seldom deviate so 

 tar as to introduce an error of unportuuce. 



A more 



