

IV. On the Lines that divide each semidiurnal Arc into Six 

 equal Parts. By W. A. Cadell, Esq. F. R. S. Lond. & 

 Edin. 



[Read 2d June 1816.] 



THE divisions of the day which different nations have em- 

 ployed, are denoted by hour-lines of various kinds on the 

 sphere. Of these hour-lines, drawn on a supposition that ne- 

 glects the inequalities of the Earth's motion, there are three 

 kinds. 



The first kind denotes hours counted from the meridian^ equal 

 to each other at all declinations of the sun. These lines are 

 great circles on the sphere, passing through the poles of the 

 equator, and every pair intercepting a similar arc on each of 

 the parallels. Of this kind are the hour-lines of sidereal time, 

 counted from the meridian, and the hour-lines of solar time, 

 counted from the meridian. 



The second kind of hour-line denotes hours counted from the 

 horizon^ equal to each other in duration at all declinations of the 

 sun. These lines are great circles which touch the greatest vi- 

 sible parallel on the one hand, and the greatest invisible paral- 

 lel on the other ; each pair of these great circles cuts off a si- 

 milar arc from each diurnal arc. They are the horizons of 



different 



