384 FERGUSON'S LECTURES. 



LECT. As, if it was required, what is the greatest length of dan 



^-^ tn latitude 51 30'? 



To the log. tangent of 51 30' 0.0993948 

 Add the log. tangent of 23* 2S' 1.6379563 



Their sum 1.737351] is the log. 



sine of the hour-distance 33 7' ; in the time 2 h. 12^ m. 

 The longest day therefore is 12 h. + 4 h. 25 m. = 16 h. 

 25 m. And the shortest day is 12 h. 4 h. 25 m.=:7 h. 

 35 m. 



And if the longest day is given, the latitude of the 



TT 



place is found ; -^ being equal to T L. Thus, if the 



longest day is 13^ hours = 2x 6 h. + 45 m. and 45 mi- 

 nutes in time being equal to 114 degrees. 



From the log. sine of 11 15' 1.2202357 

 Take the log. tang of 23 29' 1.6379562 



Remains 1.9522795 



=the logarithmic tangent of lat. 24 11'. 



And the same way, the latitudes, where the several 

 geographical climates and parallels begin, maybe found ; 

 and the latitudes of places, that are assigned in authors 

 from the length of their days, may be examined and cor- 

 rected. 



NOTE 3. The same rule for finding the longest day in 

 a given latitude, distinguishes the hour-lines that are 

 necessary to be drawn on any dial from those which 

 would be superfluous. 



In lat. 52 10' the longest day is 16 h. 32 m. and the 

 hour-lines are to be marked from 44 m. after 111 in the 

 morning, to 16 m. after VIII in the evening. 



In the same latitude, let the dial of Art. 7. fig. 4. b e 

 proposed ; and the elevation of its stile (or the latitude 

 of the place d, (see engraving, page 376,) whose horizon 

 is parallel to the plane of the dial) being 15 9' ; the 

 longest day at d, that is, the longest time that the sun 



