ASTRONOMY. 



Ixxix 



c. By the zenith telescope. 



The zenith telescope furnishes the most precise means known for the deter- 

 mination of the latitude of a place. For the theory of the instrument and method 

 when applied to refined work the reader must be referred to special treatises* 

 It will suffice here to state the principle of the method, which may sometimes be 

 advantageously applied by the geographer. Let z, be the meridian zenith distance 

 of a star south of the zenith, and z„ the meridian zenith distance of another star 

 north of the zenith. Let 8, and 8„ denote the declinations of these stars respec- 



tively. Then 

 •whence 



^ = I (S^ _}_ 8„) + h (2. - ^„). 



It appears, therefore, that this method requires only that the difference (s^ — z„) 

 be measured. Herein lies the advantage of the method, since that difference 

 may be made small by a suitable selection of pairs of stars. With the zenith 

 telescope the stars are so chosen that the difference (z, — 0,,) may be measured by 

 means of a micrometer in the telescope. 



The essential principles and advantages of this method may be realized also 

 with a theodolite, or other telescope, to which a vertical circle is attached, the 

 difference (2, — 5„) being measured on the circle ; and a determination of latitude 

 within 5" or less is thus easy with small theodolites of the best class (/. <?., with 

 those whose circles read to 10" or less by opposite verniers or microscopes). 



6. Determination of Azimuth. 



a. By observation of a star at a known time. 



T^ = sidereal time of observation, 

 a, 8 = right ascension and declination of star observed, 

 / = hour angle of star, 



= ^s — a, 

 <^ =z latitude of place, 



A = azimuth of the star at the time T, counted from the south around by the 

 west through 360°. 



The azimuth A may be computed by the formulas 



a = sec <^ cot 8, d = tan <}> cot 8, 



a sin / (i) 



tan A = — - 



I — ^ cos / 



The angle A will fall in the same semicircle as /, and A is thus determined by its 

 tangent without ambiguity. The quantities a and ^ will be sensibly constant for 



* Among which Chauvenet's Manual 0/ Spherical and Practical Astronomy is the best. 



