18 OUTLINES OF NATURAL PHILOSOPHY. 



The perpendicular is to be let fall, as in the last case, 

 from the star on the meridian ; and there being 

 two sides of the spherical triangle given, and the 

 angle opposite to one of them, the calculation is 

 as before. 



This problem is useful for finding the latitude, when 

 two equal altitudes of a star are observed, and the 

 interval of time between the observations. The 

 half of the interval gives the horary angle, and so 

 the latitude may be found as above. 



27. In the above formulas it may happen, that 

 a = 0, or that the star is in the horizon, or 90 

 from the zenith. The horary angle is then 

 found, if the latitude and declination are given, 

 from a right angled triangle, of which one of 

 the sides, containing the right angle, is the ele- 

 vation of the pole, the other, the arch between 

 the star, when rising or setting, and the meri- 

 dian ; and the hypothenuse is the distance of 

 the star from the pole. 



In this case, the horary angle, (converted into time), 

 is the time of half the stay of the star above the 

 horizon, (or under it),, and if it be called H, 



cos H = tan / X tan d. 



The other side of the triangle, or the azimuth of the 

 rising or setting star, is also called the Amplitude, 



and 



