CHAPTER IV

THE CONSTRUCTION OF SUN-DIALS
" Here have wee then the Art of Numbring TIME by SHADOWES after the most Methodical! Compendious and Perspicuous Manner compleatly and demonstratively delivered for all Planes both by Lines and Numbers. The WORTH of this Work will be best valued by those who after sad wanderings have at length sate down wearied, with the obscure and toylsome Labyrinths of others."
— Sciographia, or The Art of Sbadoives, JOHN WELLS, ESJJUIRE, 1635.
UOTING from a mathematical treatise, we define dialling or gnomonics as treating of the construction of any instru- ment, portable or fixed, which determines the divisions of the day by the motion of a shadow of some object on which the sun's rays fall.
A short definition of differ- ent mechanical forms of sun-dials, and of a few of the terms used in dialling, will be necessary for the full understanding of this chapter, and of any rules for the construction of dials. Dials are portable and fixed. The former are described in another chapter. The term fixed dial is applied to any dial fastened in a permanent position.
87
88 Sun-dials and Roses of Yesterday
The dial may be horizontal or vertical, or inclining, which latter means fixed in any sloping position, fixed on any place that is not .horizontal or verti- cal. A declining dial is one which does not face exactly either north, south, east, or west. A proclining dial is one whose plane is not vertical, but leans forward at the top ; a reclining dial is the opposite, where its plane slopes backward. A refrac- tive dial uses refracted light ; such are the window- dials described in another chapter. A reflective dial is one in which the time is indicated by a spot of light thrown by a bit of mirror ; such are spot-dials. A cylindrical dial is one drawn on a cylindrical sur- face, usually a half-cylinder; these are found on lectern-shaped dials. A globe-dial, star-dial, and a cross-dial are in the forms indicated by their names.
A quadrantal dial is in the shape of a quadrant, usually in portable form. An equinoctial dial is one whose plane is perpendicular to the earth's axis. The expression to rectify a sun-dial means simply to prepare a dial for an observation ; to orient a dial is to place it properly in -regard to the points of the compass.
A nocturnal dial shows the time by the moon's shadow, or by some mechanical device. A very quaint nocturnal dial from Leybourne's Dialling is here reproduced.
For the Centennial Exposition in Philadelphia, in 1876, there was made and set up an interesting sun- dial, having in all sixteen dial-faces. Among them were many of the unusual dials just named. This dial is an instrument of great scientific value, and
Nocturnal Dial. From Ley bourne's Dialling.
The Construction of Sun-dials 89
has been preserved through the thought and care of the late Commander Joseph Philip Mickley, who had it placed upon the lawn of his home near Allen- town, Pennsylvania, and carefully adjusted and re- stored. Mrs. Mickley has given me two photographs of this interesting dial ; they are shown on pages 90 and 92. The dial gives the time at many of the principal cities of this globe.
The elementary astronomical facts upon which dialling is founded are the two motions of the earth, diurnal and annual. The correct way of expressing the two motions is, of course, that the earth turns on its axis uniformly from west to east in twenty- four hours, and is carried around the sun in one year at a nearly uniform rate ; but in dialling the explanations are easier if the idea of the ancients is adopted, — the apparent motion, which is that the sun and stars revolve around the earth's axis once a day, the sun lagging a little behind the stars until its day is four minutes longer, and then back again. This retardation of the sun makes the time as measured by a sun-dial somewhat irregular, and a dial or clock which marks uniform time agrees exactly with a sun-dial but four days a year. These are April 15, June 15, September i, and December 24.
Clock time is called mean time; sun-dial time is apparent time ; and the difference between them is equation of time. This will explain the term used in calendars and almanacs, " clock-fast," " clock- slow."
Atmospheric refraction brings in another error in dialling, since it alters the apparent position of the
90 Sun-dials and Roses of Yesterday
sun, but this effect is very small and need not be considered in a sun-dial, which is, after all, so sel- dom accurate throughout the year.
The teaching of mathematics in everyday schools, after centuries of surprisingly little change, in the' latter half of the nineteenth century became greatly
Dial-head of Centennial Dial.
altered. Ordinary school-books and very common- place pupils show that in the early part of that century navigation, land-surveying, and dialling were universally taught. Now, few of the young who go down upon the sea in ships know much of the mathematical side of their calling. When every boy wanted to go to sea, and many did go and be-
The Construction of Sun-dials 91
came ship's captains as soon as they came of age, the study of navigation meant something. The pub- lication of ordnance maps, with many other in- fluences, has set aside the practical and theoretical study of land-surveying. The study of dialling vanished still earlier, with the multiplication of church clocks and watches.
We find Thomas Jefferson amusing himself dur- ing an illness in calculating dials, as told in a letter to Mr. Clay.
" POPLAR FOREST, August 23, 1811.
"DEAR SIR: — While here, and much confined to the house by my rheumatism, I have amused myself with cal- culating the hour lines of an horizontal dial for the latitude of this place, which I find to be 37° 22' 26". The calcu- lations are for every five minutes of time, and are always exact to within less than half a second of a degree. As I do not know that anybody here has taken this trouble be- fore, I have supposed a copy would be acceptable to you. It may be good exercise for Master Cyrus to make you a dial by them. He will need nothing but a protractor, or a line of chords and dividers. A dial of size, say of from twelve inches to two feet square, is the cheapest and most accurate measure of time for general use, and would I sup- pose be more common if every one possessed the proper horary lines for his own latitude. Williamsburg being very nearly in the parallel of the Poplar Forest, the calculations now sent would serve for all the counties in the line be- tween that place and this, for your own place, New Lon- don, and Lynchburg in this neighborhood. Slate, as being less affected by the sun, is preferable to wood or metal, and needs but a saw and plane to prepare it, and a knife point to mark the lines and figures. If worth the trouble, you
9:2 Sun-dials and Roses of Yesterday
will, of course, use the paper enclosed ; if not, some of your neighbors may wish to do it, and the effect to be of some use to you will strengthen the assurances of my great esteem and respect."
Centennial Sun-dial.
The Construction of Sun-dials 93
Many boys even in that century studied dialling at school — not so many in America, for we had our cheap Connecticut clocks so early in our his- tory, and used them so widely ; but in Great Britain dialling was taught, especially in Scotland. Burns says in an autobiographical letter, that he was sent to a noted school "to learn mensuration, surveying, dialling, etc." Hugh Wilson at the same time not only learned dialling, but practised it, and one of his dials still may be seen at Fenwick, near Fal- kirk. The art of dial-making seems to have been the mode at certain times in various localities. Perhaps some man of note or influence awakened a special interest in the vicinity of his residence. Sometimes a gravestone cutter with a pretty taste for novelties turned his tools to dial-making on dull winter days.
The student was not haled on by old mathemati- cal treatises with any thought of its being an easy task to make a sun-dial. He was warned that he must have " skill in spheriques, together with the laws of Motion of the great Luminaries; he must be absolute in all Circular Affections, as Declina- tions, Right and Oblique Ascentions, Altitudes, Amplitudes, Azimuths, Culminations, Arches Diur- nal, Ascendent, Descendent, etc." All these are not simple of speech nor simple of knowledge to beginners, even if they were entitled, Easy Rules for Dialling ; Young Men s Aid in Gnomonics. Still, somehow, men of ordinary education, such as stone- masons and men with scant mathematical knowledge, used to be able to make precisely perfect sun -dials from these common rules. I must confess frankly
94 Sun-dials and Roses of Yesterday
I find it difficult to understand many of the rules which I have seen, and I have had as good an edu- cation in mathematics as have women in general, and as have many men, having studied thoroughly and with great interest algebra and geometry, and hav- ing proved myself one of so capable a class in trigo- nometry that our enthusiastic teacher led his class of girls well on into the knowledge of land-survey- ing. It does not lessen the value of the education received when I state that this teacher of these girl- mathematicians was a good-looking young man who had been graduated but a year or two from Harvard. In spite of the antiquated diction, I like the rules in Leybourne's Dialling better than more' modern rules, but Leybourne's book is rare ; and even the fine rules for dial-making given in the Encyclopaedia Britannica, which seem to me perfectly clear and easy of comprehension, have been stigmatized to me within a week as " blind, confused things."
As some will read this book who will care for sun- dials, and perhaps will like to construct one, but can- not understand the application of any rules such as those of Leadbeater or Ferguson, I will give plain rules for making a horizontal dial, worded by H. R. Mitchell, Esq., of Philadelphia, though he disclaims all originality in their construction and phrasing. They seem to me perfect in their simplicity and exactness of information, and with the attached Fig- ures i, 2, and 3, must be readily understood ; and when these are grasped, I am sure the rules for ver- tical dials, given in the Encyclopaedia Britannica, will at once seem clear and applicable.
The Construction of Sun-dials
95
RULES FOR MAKING A HORIZONTAL DlAL
To lay out the lines for a Horizontal Sun-dial in its simplest form, we will first make the Stile or Gnomon.
Figure I. Lay off the horizontal base line, then with a Protractor ascer- tain the angle which must be the same as the Latitude of the place, say for New York it is about 40° 44'. Start- ing from the point B,
mark the angle with a Figure 1
line BC, -and draw also
the perpendicular line AC at right angles to the base AB. This gives you the triangular Gnomon in its simplest form ; they are generally cut away at the back in a fanciful out- line, as indicated by the dotted lines, always leaving the line BC untouched, for its line is the shadow line.
Then the angle ABC will be correct for this Latitude.
For the Face of the Dial draw the line AB, and then the line CD, at right angles to AB. The points C and D will be your six o'clock points.
At the intersection of these lines, £, draw a circle, the radius of which will be equal to the length of the line BC in Figure I.
Then another circle inside, the radius of which will be equal to the length of the line AB in Figure I. Now the outside circle, A to D and A to C, divide in two equal parts, and then subdivide each of these parts into three, so as to make twelve equal parts, indicated by ooooo ; and do the same with the inner circle, indicated by zzzzz.
Now with a rule draw lines parallel to CD, from each
96 Sun-dials and Roses of Yesterday
of the points of division, o, in the two upper quarter circles, then draw lines parallel to AE from each point, z, on the inner circle.
Marking the points of intersection, then from the central point, £, draw lines through these various intersections, and where these lines cross, the circles will be your hour points.
In drawing the figures for the hours, they should have the same inclination as the lines radiating from E. The half and quarter hours should be made in the same way, by dividing the distances between the points on the outer and inner circle, and where the lines from E intersect, will give you the marks for the halves and quarters. The minutes, if you choose to put them, can be spaced off with the eye ;
The Construction of Sun-dials
97
the lower circles can be figured in just the same way as the upper, extending the hour marks to, say, 4 A.M. and 8 P.M., but for any ordinary practical use 6 o'clock in the morning and 6 o'clock in the evening covers all that is needed.
Figure 3.
In laying out a Dial in this way, no allowance has been made for the width or thickness of the Stile or Gnomon ; it a thin Gnomon, say, Jg- of an inch, is used, it is hardly nec- essary to make any allowance ; but if you want to use a heavy Gnomon, say, -fy or 1 inch thick, then instead of one line AB, there must be two parallel lines the same distance apart as the width of the Gnomon, and instead of striking
H
98 Sun-dials and Roses of Yesterday
the circle from the central point £, two semicircles must be made with the centres where the line CD intersects the two parallel lines, or what is probably an easier method would be to cut the draft into two equal parts along the line AB, and place between them a strip of paper just the width of the proposed Gnomon.
As the hour lines about the middle of the day are closer together than those earlier in the morning or later in the afternoon, it makes a much better Dial to shift the centre toward the 1 2 o'clock mark, and draw a new circle from this point, and the lines radiating from E can be extended to this new circle, and the Stile or Gnomon will have to be increased in proportion ; but the point must not be moved, it must always be on the line between the two 6 o'clocks, as shown in Figure 3.
In setting the Dial, care should be taken that it is always perfectly level, that the Gnomon does not incline to either right or left, and should point to the true north (not the magnetic).
If this Dial is properly made and set, and its time cor- rected by the time equation (which you will find in the United States Nautical Almanac), it can be depended upon as an accurate timekeeper.
I have been asked for still simpler rules for use by folk of very slight education ; among others, the negroes of the South, - - not the negroes of the better schools, but those who know simply a little arith- metic and a little geography ; the geography need be only enough to tell the dial-maker the latitude of his home, which I assume to be the spot where he is to place the dial.
Take a piece of pine board a half-inch thick and four- teen inches square. This will do to make a twelve-inch
The Construction of Sun-dials
99
D
dial. Paint it with several coats of good oil-paint. Make
the gnomon from another piece of board half an inch thick
and six inches square. To shape the gnomon
draw lines on Figure 4,
from corner to corner,
like AE and CD which
make E the centre.
Then draw the line GF
passing through £, mak- ing this line parallel to
lines AC and BD, Of
course the angle CAP
is a right angle of 90
degrees, and the line
AE, being half of it,
makes EAF an angle of
45 degrees.
It should be easy to find other angles by dividing these
spaces equally. A very easy way is to divide it into divi-
sions of 100 and these subdivide into 50, and so on as shown in Fig- ure 5.
Let us make a gno- mon for Tuskegee, Ala- bama. The latitude of Tuskegee is about 32.1 degrees. The dotted line
HI is drawn on the an- Figure 5. i r i j j
gle or 32.1 degrees, and
the figure HIJ forms the proper shape for a gnomon for a sun-dial to be used at Tuskegee.
Now turn to Figure 6.
On the large square of board find as nearly as possible the
ioo Sun-dials and Roses of Yesterday
centre and draw from it three semicircles marked E, F^ and G. The outer circle, £, is to have a radius of 6 inches, the next circle, F, a radius of 5| inches, and the circle G a radius of 5 inches. Then draw three similar semicircles
Figure 6.
having D for a centre. C and D must be il inches apart. Between the circles E and F you can draw in small marks the lines for the hours, half-hours, quarters, and minutes, while between FG you will draw the large hour figures which can be plainly seen.
The Construction of Sun-dials 101
The outside circle E will be about 12^ inches in diameter. The middle circle /"will be about 1 1-|- inches in diameter. The inside circle G will be about 10 inches in diameter.
We now must set the triangular gnomon HIJ of Figure 5 in its proper place. Place it on the dial-face so the point H is at xx. J will then reach the circle G, and that point G should be numbered XII, the noon hour.
Draw a straight line yyzz, across the dial-face run- ning through xx (where the point of the gnomon meets the face). This line yyz and zzx are the 6 o'clock morn- ing and evening hours.
Fasten the gnomon firmly in place by screws from under- neath, or in any way you prefer. And then place your dial-face in absolutely horizontal position, and with the gnomon pointing exactly north. Put in the other hour lines by using a good watch keeping correct time, and making the line of the gnomon at precisely i, 2, 3 o'clock, etc.
Of course these hours can be carefully calculated, but this set of rules is not given for persons capable of such precise calculations. And certainly no excuse is necessary for availing oneself of the easier method obtained through consulting a watch when the En- cyclopedia Britannica, in its elaborate rules for dial- making, advises the same thing in certain cases. There should also be allowance made for equation of time, if the dial-maker knows how to do so. But without these perfecting details this sun-dial will be found an excellent timekeeper.
While every detail of a sun-dial must be exact, I wish to draw special attention to the importance of the precise shaping and setting of the gnomon ;
IO2 Sun-dials and Roses of Yesterday
for great ignorance about the gnomon is dis- played even by architects. Upon a house which stands in a neighborhood filled with mathematical interest, near the home of Godfrey, the inventor of the seaman's quadrant, not far from the influence of Franklin, lover of dials, and under the magic spell of the sun-dial of Ahaz, and, moreover, in the only locality in the United States where sun-dials can be found in any number — upon this house is erected a fine dial-face, which even at first glance looks unnatural to you ; then you note quickly that the gnomon is a brass or iron bar standing at right angles to the dial-face, upon which are marked correctly lines and numerals for a ver- tical dial for that latitude. Though this dial with its absurd stick of a gnomon had been erected for some years, I persisted in inquiring until I learned that the dial had been made in London, and on its way hither the gnomon was lost ; so the house archi- tect "made a new one," and the man added: "It doesn't matter, anyway ; it doesn't keep any time, it's only an ornament. I am told that a sun-dial is never right within sixteen minutes."