Chapter XXXV: How to Make a Sundial

BY F. CHASEMORE.

I.--THE HORIZONTAL DIAL.

A very useful and instructive pastime for boys will be found in the construction of a sundial, full directions for making which I give in this chapter.

The first thing to be done is to make what is called the dialing scale (Fig. 1). It is constructed as follows: With a pair of compasses describe the circle A B C D with any radius, say four inches. Draw the two diameters A C and B D, cutting each other at right angles in the point 0. Join D C for the scale of chords and B C for the scale of latitudes. Through the point B draw the straight line 12--6 parallel and equal to the line A C, and let the point B bisect it. Join the points 0--12 and 0--6, cutting the circle in the points E and F. Now divide the arcs E B and B F each into three equal parts, and from the point 0 draw straight lines through these points of division to the line 12--6, marking the points of intersection 12, 1, 2, 3, 4, 5, 6. This line is called the line of hours.

To make the scale of chords, divide the arc D C into nine equal parts, and then with the compasses, with one leg placed on the point C, protract each division on the line C D. Mark the points on this line from C 10, 20, 30, etc.; the point D will mark 90 degrees.

To make the scale of latitudes, draw lines from the points of division in the arc D C parallel to the line D 0, and cutting the line 0 C in points, counting from 0, 10, 20, 30, 40, etc. Now draw straight lines from D through these points, cutting the arc B C in the points 10, 20, 30, etc., and with your compasses, with one leg on B, protract these distances on to the line B C, which will be the scale of latitudes. Now our dialing scale is finished.

To make the dial, which will be a horizontal one, you must get a piece of zinc plate about one foot square. On this mark all round it, and one inch from the edges, lines making a smaller square of ten inches a side. Plate 1/8 inch thick.

Bisect one line of this square, and draw a line from this point to a point bisecting the opposite side. Now draw two other lines, one on each side of, and one-sixteenth of an inch from, this line, and parallel to it. These lines will then be one-eighth of an inch apart. They are made this distance apart as the style, or gnomon, will be that thickness, and has to stand between them. Now divide the other sides into five equal parts, and join the two second points of division, counting from the bottom. This line, which is called the six-o’clock line, will cut the two parallel lines in the points A C (Fig. 2). Mark the other or top ends of these lines B and D.

Now with your compasses take from the scale of latitudes the latitude of the place where you wish to erect your dial. Suppose you are in London, put one leg of the compasses on the point B, and the other leg on the point in the scale of latitudes marking 51-1/2 degrees, which is the latitude of London. Now mark this distance off on the six-o’clock line from C to E and from A to F (Fig. 2). Now take the length of the line of hours from 12--6 in the compasses, and, putting one leg on the point E, intersect the line C D in the point G. Do the same on the other side, putting one leg on point F, and intersecting the line A B in the point H. Draw the lines G E and H E (Fig. 2).

These lines are the same length as in the line of hours; mark them as that line is marked, using your compasses to get the distances, marking the line from G to E and from H to E; now from the point C draw lines through the divisions on G E to the lines of the inner square; do the same from point A through the line H F. The fourth and fifth lines on the right side must be continued back through the point C to opposite side of square, and the seventh and eighth on the left be continued back through A to right side. Now mark the hours. The double line is the twelve-o’clock line, and must be marked twelve. The line to the right is the one-o’clock line, the next two, and so on to eight on the right side. On the left the line next the twelve-o’clock line is eleven, the next ten, and so on back to four. All the lines can be marked on the zinc with a pointed bradawl.

The dial plate is now finished.

The next step is to make the gnomon. For this get a piece of the same zinc plate about six inches by eight. Along one of the shorter sides, about a quarter of an inch from the edge, draw a line A B, making it equal in length to C--60 on the scale of chords. With one leg of the compasses on the point A, and the other opened out to B, draw the arc B C as in Fig. 3. Now from the same scale of chords take the length of the latitude of the place, and mark it along the arc B C from B, join A C, from C draw a line at right angles to A B, cutting it in the point D (Fig. 3). The triangle A D C will be the gnomon, with the line A D for its base. Cut this triangle out carefully, making the edges quite square. Now you must get a tinman to solder this in its place on the dial-plate, the point A of the gnomon to be at the points A C on the plate, and the line A D along the two lines A H and C G. You must be very careful that the gnomon stands at right angles to the dial-plate.

The dial must be fixed in a sunny spot, if possible in the middle of a large lawn. The best way to do this is to fasten the dial-plate on a square board, which is fastened to a post driven into the ground. The post can be ornamented with rustic work. The dial must be quite level, and the gnomon pointing due north.

The line A C of the gnomon being made at the angle from the base equal to the latitude of the place will be parallel to the axis of the earth, and will show the hours correctly both on long and short days, as the sun’s course is at right angles to it. The dial can be made to show quarters or five minutes if you so divide the line of hours on the dial scale. The dial, if placed in an open, sunny spot, will show the hours from sunrise to sunset.

II.--THE EQUATORIAL DIAL.

The horizontal sundial would be suitable for all places north and south of the equator. But in southern latitudes the style must point due south instead of north, and the numbering must be done from right to left instead of from left to right. The method, however, already described would not do for any place situated _exactly_ on the equator. The reason for this is--the style, or gnomon, being parallel to the axis of the earth, it would be horizontal at the equator, and perpendicular at the poles, and the shadow would be parallel to the style at the equator and perpendicular to it at the poles. The style must be regulated in height by the size of the dial-plate, and the length of the line of hours, in the scale, must be regulated by the height of the upper edge of the style from the dial-plate.

I will now explain the construction of the equatorial dial. The dial-plate is to be cut about eighteen inches long by twelve inches wide. The inner lines are to be drawn all round, about one inch from the edges, as in the dial already described. Divide the dial-plate into two equal parts by a line drawn from points bisecting the long sides, as in Fig. 1 in the accompanying illustrations. This line is the twelve-o’clock line. The two lines A B and C D are to be drawn parallel to this line, one on each side of and a sixteenth of an inch from it. Before the hour lines can be drawn the style must be made. This must be rectangular in shape, with the long sides equal in length to the twelve-o’clock lines between the inner lines of the plate, and must not, for this size of dial-plate, be more than two inches wide or high. The dialing scale must now be made. It consists only of the line of hours. Draw the two lines O A and O B at right angles to each other, and make each equal in length to the height of the gnomon, or style--viz., two inches. Draw B C parallel to O A, and make it about ten or twelve inches long. Describe the arc A B, with O for the centre, and O A and O B for radii, as in Fig. 2. Divide this arc into six equal parts, and draw lines from the point O through the points of division to cut the line B C in the points 1, 2, 3, 4, 5. The six-o’clock point will not be required. This is the line of hours. With your compasses mark on the side lines of the dial-plate, from the points A B and C D, the divisions of the line of hours. Join the corresponding points on each side of the twelve-o’clock line by lines drawn parallel to it. These lines will represent the hours, and are numbered 1 to 5 to the right and 11 to 7 to the left. Fig. 3 shows this dial.

This dial does not show the time before seven o’clock in the morning or after five o’clock in the evening. The reason of this is, the days and nights at the equator being equal--viz., twelve hours each--the sun rises and sets at six o’clock. At six o’clock, the sun being exactly on the horizon, any object placed in the middle of a perfectly horizontal plane would cast an indefinite or unlimited shadow, as the shadow of the upper part would be parallel to the plane, and of course could not meet it. The dial can be made to show any time after six in the morning or before six in the evening by lengthening the dial-plate. Fig. 4 will show how inconvenient it would be to have a plate to show the time before seven or after five o’clock. In Fig. 4 the hour from five to six is divided into quarters, and shows that for 5.30 the plate must be about double, and for 5.45 about four times, the length required to show the time between seven and five o’clock. So that a plate about six feet long would be required for a dial having a style two inches high.

The style is to be soldered to the dial-plate between the two lines A B and C D, and must be equal in thickness to the distance between them. The dial must be set up in a horizontal position with the gnomon directed due north and south.

Both these dials are horizontal. I will now explain the construction of vertical dials, or dials that are fixed in an upright position against a wall or house. The dialing scale, as already described, will be required for the construction of a vertical dial to be fixed on a wall facing the south.

Cut the zinc plate twelve inches square, and mark it with the inner square, the twelve-o’clock lines, and the six-o’clock line, as in the horizontal dial. From the line of latitudes, in the scale, take the length equal to the difference between 90 deg. and the latitude of the place (that is, not as in the horizontal dial, the latitude, but the complement of it).

Taking London as the place, take from the scale 38-1/2 deg., which is the difference between 90 and 51-1/2 deg. This distance must be marked off on the six-o’clock line from the points A and C. The rest of the construction is the same as for the horizontal dial, with the exception that the hours are limited to fourteen, viz. from five to seven o’clock, and are numbered backwards, or from left to right as in Fig. 5. The style is made as for the horizontal dial, but the angle C A B is to equal 38-1/2 deg. in the case of London, or the complement of the latitude. The base A D is to equal the length of the twelve-o’clock lines, measuring from the six-o’clock line to the inside line at the lower edge, or the lines A B and C D. In fixing this dial care must be taken to let it face due south.

The east and west vertical dials are made something like the equatorial horizontal dial, with a rectangular style. The same scale is required for making the line of hours, the lines of which are regulated in length by the height of the style. Make the plate about eighteen inches long and twelve inches wide, and draw the double lines which in these dials represent the six-o’clock line, as in Figs. 7 and 8. These double lines are drawn, making an angle with the lower edge of dial-plate equal to the latitude of the place. The style is cut rectangular, with the long sides equal to the double six o’clock lines, and the short sides two inches long. Draw the scale making O A and O B two inches long, and mark the hour line. Before the points on the hour line can be marked in on the dial-plate, a plan (Fig. 9) must be made. Draw on a large piece of paper a plan of either dial-plate, and mark in the double lines. Through these draw the line A B perpendicular to them as in Fig. 9. On this line, on each side of the double lines, mark the points on the hour line, and through these points draw lines parallel to the double lines, and letting them cut the sides of the plan of the dial-plate. The points where the lines cut it can be transferred to the dial-plate with a pair of compasses, and the hour lines drawn in parallel to the six-o’clock line. The style must be fixed in its place, and will be parallel to the axis of the earth when the dial is fixed up with the long sides quite horizontal. The east dial is marked as in Fig. 7, and the west as in Fig. 8, if for the northern hemisphere. For the southern, the west dial would take the place of the east, and the east, the place of the west with the numbering reversed.

There are several other kinds of sundials, which may be used for any degree of latitude, a few of which I will describe.

The first of these is the globular (Fig. 10). This is a white globe (any size), supported on an axis which is fixed in a position parallel to the axis of the earth (or making an angle with the horizon equal to the latitude of the place, and pointing due north or south), in which position the globe is acted on by the sun exactly as the earth is. The globe is divided into twenty-four equal parts by lines running from pole to pole, and has an equator drawn around it, on which the hours are marked from 1 to 12 twice over. The axis is fixed in a stand so that one of the six-o’clock lines is in the zenith. The time is indicated by the edge of the shaded part (caused by the sun illuminating one-half of the globe, leaving the other in shade) passing over the hour lines. An ordinary globe answers very well for this dial, if it is rectified for the latitude, and placed so that the brass meridian is directed north and south.

Fig. 11 is another pattern; it is basin-shaped, and is made of a hollow hemisphere of metal, whitened inside, and has the inside divided into twelve equal parts by lines running from pole to pole, which are numbered on the equator from 6 to 6. A wire is stretched from pole to serve as the style, which casts a shadow on the line corresponding to the hour. The position of this dial is the same, as regards the axis of the earth, as Fig. 10.

Fig. 12 represents what I call the trough-shaped dial. It is made of metal-plate bent into the shape of a half-tube; the ends are closed with semicircular metal plates. The interior is divided into twelve equal parts by lines running parallel to the edges, and are numbered from 6 to 6. A wire is stretched from the centres of the semicircular end plates to serve for the style.

This dial must be fixed, with regard to the position and direction of the style, as the other dials are. This is the one constant condition of all dials, that the edge of the style that is to cast the shadow must be parallel to the axis of the earth.

Fig. 13 is a very simple dial, and is the last I shall describe. It consists of a circular dial-plate divided into twenty-four equal parts, numbered from 1 to 12 twice over. The style is a perpendicular wire fixed in the centre of the plate. The plate is hinged to a stand, so that one of the twelve-o’clock lines runs directly from the top to the bottom.

From the construction of the dials 10, 11, 12, 13, they can be used in any latitude, as well as on the equator, but of course the numbering would have to be reversed for the southern hemisphere. They all have an arrangement by which the style can be fixed at the required angle to suit the latitude of the place.

TABLE OF MINUTES.

_To be Added to or Subtracted from the Sundial for each Day in the Year._

The sun does not always point out the true time, as on some days it is behind time and sometimes before it. The table below gives the minutes to be added to or subtracted from the time pointed out by the sun for each day in the year:--

_January._
Day. Min.
1 + 4
4 + 5
6 + 6
8 + 7
11 + 8
13 + 9
16 + 10
19 + 11
23 + 12
27 + 13
31 + 14

_February._
3 + 14
19 + 14
26 + 13

_March._
3 + 12
4 + 11
12 + 10
15 + 9
19 + 8
22 + 7
25 + 6
28 + 5

_April._
1 + 4
4 + 3
8 + 2
12 + 1
19 - 1
25 - 2
30 - 3

_May._
1 - 3
17 - 4
28 - 3

_June._
4 - 2
10 - 1
19 + 1
24 + 2
29 + 3

_July._
4 + 4
10 + 5
19 + 6

_August._
1 + 6
11 + 5
16 + 4
21 + 3
25 + 2
29 + 1

_September._
4 - 1
7 - 2
10 - 3
13 - 4
16 - 5
18 - 6
21 - 7
24 - 8
27 - 9
30 - 10

_October._
3 - 11
7 - 12
10 - 13
14 - 14
19 - 15
27 - 16

_November._
10 - 16
17 - 15
21 - 14
25 - 13
28 - 12

_December._
1 - 11
2 - 10
6 - 9
8 - 8
10 - 7
12 - 6
14 - 5
16 - 4
18 - 3
21 - 2
23 - 1
27 + 1
29 + 2
31 + 3