D I A 



Vertical East Dial 



Here the plane of the Dial is in the meri- 

 dian, and the gnomon a parallelogram per- 

 pendicular to it (as represented in the Fig.) 

 and the shadows upon the plane will evi- 

 dently be all parallel to the gnomon, and to 

 one another. Moreover, at 6 o'clock, the 

 sun, being due east, will be in the plane of 

 the gnomon, and .*. cast the shadow per- 

 pendicularly upon the Dial or on Pp. To 

 find the 7 o'clock mark, let S be the sun at 

 that hour, and S F a ray proceeding from it cutting the Dial in 7j then 

 in the plane right /d. A C F7, C 7, = C F X tan. ^ C F7 height of 

 style X tan. 15 . C 8 = height of style X tan. 2 X 15. &c. Similarly 

 may be constructed a vertical West Dial. The East Dial will not shew 

 the hour after 12 o'clock at noon, nor the West Dial before. 



General Problem*. 



1. Given the latitude of the place, and 

 the position of the plane of the Dial, 

 both with respect to the meridian and 

 horizon ; it is required to find the ele- 

 vation of the style, the distance of the j_jf 

 sub-style from the meridian, and the 



arc intercepted between the meridian 

 and any other given hour line. 



Let B O A be the plane of the dial, 

 given in position both with respect to 

 the horizon H R, and the meridian P E A C ; then in the right angled A 

 B N R, the /s. B N R, N B R are given, .'. B R may be found ; but P R 

 == latitude, .". P B is known. Now let a plane pass through O P, and 

 let it be turned about till it becomes perpendicular to BOA, and let it 

 cut the circumference of B A in M, then P M is that meridian which is 

 perpendicular to B O A, .'. in the right angled A PMB, PB and / 

 PBM are known, .'. PM = elevation of the style, and MB, the dis- 

 tance of the substyle from the meridian, may be found. Draw P T, 

 making an ^ of 15<> with P B ; then will T be the 1 o'clock mark, and to 

 find it we have PB, and BPT 15, and / PBT supplement of 

 N B R, .*. B T may be found, and so on for the other hours. 



2. To determine the curve, traced out by the extremity of the shadow 

 #f a vertical gnomon on a horizontal plane. (Noddy.) 



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