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XXIY.— EEMARKS ON THE UNUSUAL SUNRISES AND SUN- 

 SETS WHICH CHARACTERISED THE CLOSE OF THE 

 YEAR 1883. Br REY. SAMUEL HAUGHTON, S.F.T.C.D., 

 M.D., F.R.S. 



[Read, January 21, 1884 ]! 



The older writers on Astronomy, such as Brinkley and Maddy ? 

 state that, on the average, twilight lasts nntil the sun is 18" below 

 the horizon. From this it has been computed that the height of 

 the twilight- producing atmosphere is 



40 miles on hypothesis of one reflexion, 

 12 „ „ „ „ two „ 



5 „ „ „ „ three „ 



o ,, ,, . ,, ,, lour ,, 



Herschel and Newcomb make no statement whatever as to the 

 duration of twilight ; Chambers (in his compilation) says that the 

 average depression of the sun is 18°, which is reduced to 16° or 17° 

 in the tropics, but in England a depression ranging from 17° to 21° 

 is required to put an end to the twilight phenomena. 



Dr. Ball informs me that Professor Schmidt, of Athens, gives 

 (for that place) 15° 5V ; and also that Liais (Paris) fixes the first 

 twilight arc to set at 10° 41', and the second arc at 18° 18'. 



In the following conclusions, drawn from the phenomenal twi- 

 lights of the autumn of 1883, I calculate the zenith distance of the 

 sun, at the close of the phenomena, by the well-known formula 



where 



cos s = a + j3 cos h, 



z = sun's zenith distance. 



h = sun's hour angle. 



a = sin X sin S. 



/3 = cos X cos S. 



A = latitude of place of observation. 



d = declination of sun. 



