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DECLINATION LINES OF SUNDIALS - Page 4

For example, the arc STU represents the path of the shadow cast by the nodus on June 21. This arc cuts the horizontal line at U. The point U lies between the hours of 4 and 5 in the morning. Estimate the distance from the point where the hour line of 4 crosses the horizontal line, to the point at U. This will be found to be about io minutes. Therefore, the sun will rise at 4:10 a.m. (Apparent Time) on June 21, in latitude 45'N. An almanac computed for 450 north latitude shows the time of sunrise to be 4:12 a.m., (Apparent Time) which compares favorably with the sundial reading.The construction of the lines of declination on the south vertical sundial is typical of those sundials whose planes lie oblique to the axis of the earth. The Construction The example shows the construction of the lines of declination for a south vertical sundial in 5o°N latitude. Figure 1 shows the completed sundial; the line C'12 is the substyle line. The foot of the perpendicular style is marked at F'. The horizontal line, on this sundial, passes through the foot of the perpendicular style, at right angles to the substyle line. On any sundial whose plane lies oblique to the axis of the earth, the equinoctial line is a straight line, and perpendicular to the substyle line. To find the position of the equinoctial line and other lines of declination, another diagram is used, draw PE perpendicular to PC. This line represents the equinoctial. Draw PN and PS for the greatest northern and southern declination of the sun. Angles NPE and EPS are equal to 23°27'. Produce CF, cutting PS at b, PE at a, and PN at o. C' corresponds to the point C. Lay off the distance Ca, from C' to a', on the substyle line C'12. The equinoctial line will pass through the point a', perpendicular to the substyle. With C as a center, describe arcs cutting the line PE, whose radii are equal to the distances from C' to the points where the equinoctial line cuts the various hour lines. Through the points thus found on PE, draw lines from C cutting PS and terminating in PN at o, d, e, etc. These lines represent the hour lines on the sundial plate (Co = 12; Cd = I and II; Ce = 2 and Io; etc.).

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