R E F 



Time =r _ 



15o v(cos. (I + 3). cos. (I $)) 



4. Twilight is occasioned by the refraction and reflexion of the sun'a 

 rays passing through the atmosphere, and continues till the sun descends 

 about 18 degrees below the horizon. 



To find the duration of twilight. 



Let h and h' be the hour angles corresponding to the beginning and 

 end of twilight, I the latitude, and the sun's declination j then 



cos. li tan. 1. tan. 



cos. h> sin. 18. sec. 1. sec. 8 tan. I. tan. 3 

 hence li' h may be deduced. 



Cor. Twilightwillcontinue all night, if I + S be greatarthan 72^_ 

 To find the time of year when twilight is shortest. 



sin. =. tan. 9. sin. I 

 and sin. h = sin. 9. sec. I 



The first equation gives the sun's declination, or the time when the twi- 

 light is shortest; and the second gives the duration of it. 



Ex. In latitude 52, the time of shortest twilight will fall about March 

 2, and October 11 j and the duration will be about 1A. 58m. 



5. The refraction varies with the state of the barometer and thermo- 

 meter. 



Dr Maskelyne's Formula. 



Let a =- height of barometer in inches, h height of Fahrenheit's 

 thermometer, x = zenith distance, r = 57" tan. z j then 



Refraction = ^-^ X tan. (* 3 r) X 57" X 



Dr Young's Formula. 



.0002825 .= v. y + (2.47 + .5 v 2 ) -}- 3600 v -~ 4- 3600 (1.235 -J- 

 .25 c s ) g- r being the refraction, v the sine of altitude, and s the 



From this last formula, the following Table, taken from the Nautical 

 Almanack for 1827, is computed, 



243 



