Part 6

Only one who has himself often seen the morning's sunrise put an end to a night's observation of the stars can hope to appreciate what Galle's feelings must have been when he saw the planet. To his trained eye it was certainly recognizable at once. And then the good news was sent on to Paris. We can imagine Leverrier, the cool calculator, saying to himself: "Of course he found it. It was a mathematical certainty." Nevertheless, his satisfaction must have been of the keenest. No triumphs give a pleasure higher than those of the intellect. Let no one imagine that men who make researches in the domain of pure science are under-paid. They find their reward in pleasure that is beyond any price.

The Leverrier planet was found to be the last of the so-called major planets, so far as we can say in the present state of science. It received the name Neptune. Observers have found no other member of the solar system comparable in size with such bodies as Uranus and Neptune. More than one eager mathematician has tried to repeat Leverrier's achievement, but the supposed planet was not found. It has been said that figures never lie; yet such is the case only when the computations are correctly made. People are prone to give to the work of careless or incompetent mathematicians the same degree of credence that is really due only to masters of the craft. It requires the test of time to affix to any man's work the stamp of true genius.

While, then, we have found no more large planets, quite a group of companions to Piazzi's little one have been discovered. They are all small, probably never exceeding about 400 miles in diameter. All travel around the sun in orbits that lie wholly within that of Jupiter and are exterior to that of Mars. The introduction of astronomical photography has given a tremendous impetus to the discovery of these minor planets, as they are called. It is quite interesting to examine the photographic process by which such discoveries are made possible and even easy. The matter will not be difficult to understand if we remember that all the planets are continually changing their places among the other stars. For the planets travel around the sun at a comparatively small distance. The great majority of the stars, on the contrary, are separated from the sun by an almost immeasurable space. As a result, they do not seem to move at all among themselves, and so we call them fixed stars: they may, indeed, be in motion, but their great distance prevents our detecting it in a short period of time.

Now, stellar photographs are made in much the same way as ordinary portraits. Only, instead of using a simple camera, the astronomer exposes his photographic plate at the eye-end of a telescope. The sensitive surface of the plate is substituted for the human eye. We then find on the picture a little dot corresponding to every star within the photographed region of the sky. But, as everyone knows, the turning of the earth on its axis makes the whole heavens, including the sun, moon, and stars, rise and set every day. So the stars, when we photograph them, are sure to be either climbing up in the eastern sky or else slowly creeping down in the western. And that makes astronomical photography very different from ordinary portrait work.

The stars correspond to the sitter, but they don't sit still. For this reason it is necessary to connect the telescope with a mechanical contrivance which makes it turn round like the hour-hand of an ordinary clock. The arrangement is so adjusted that the telescope, once aimed at the proper object in the sky, will move so as to remain pointed exactly the same during the whole time of the photographic exposure. Thus, while the light of any star is acting on the plate, such action will be continuous at a single point. Consequently, the finished picture will show the star as a little dot; while without this arrangement, the star would trail out into a line instead of a dot. Now we have seen that the planets are all moving slowly among the fixed stars. So if we make a star photograph in a part of the sky where a planet happens to be, the planet will make a short line on the plate; whereas, if the planet remained quite unmoved relatively to the stars it would give a dot like the star dots. The presence of a line, therefore, at once indicates a planet.

This method of planet-hunting has proved most useful. More than 400 small planets similar to Piazzi's have been found, though never another one like Uranus and Neptune. As we have said, all these little bodies lie between Mars and Jupiter. They evidently belong to a group or family, and many astronomers have been led to believe that they are but fragments of a former large planet.

In August, 1898, however, one was found by Witt, of Berlin, which will probably occupy a very prominent place in the annals of astronomy. For this planet goes well within the orbit of Mars, and this will bring it at times very close to the earth. In fact, when the motions of the new planet and the earth combine to bring them to their positions of greatest proximity, the new planet will approach us closer than any other celestial body except our own moon. Witt named his new planet Eros. Its size, though small, may prove to be sufficient to bring it within the possibilities of naked-eye observation at the time of closest approach to the earth.

To astronomers the great importance of this new planet is due to the following circumstance: For certain reasons too technical to be stated here in detail, the distance from the earth to any planet can be determined with a degree of precision which is greatest for planets that are near us. Thus in time we shall learn the distance of Eros more accurately than we know any other celestial distance. From this, by a process of calculation, the solar distance from the earth is determinable. But the distance from earth to sun is the fundamental astronomical unit of measure; so that Witt's discovery, through its effect on the unit of measure, will doubtless influence every part of the science of astronomy. Here we have once more a striking instance of the reward sure to overtake the diligent worker in science--a whole generation of men will doubtless pass away before we shall have exhausted the scientific advantages to be drawn from Witt's remarkable observation of 1898.

HOW TO MAKE A SUN-DIAL

Long before clocks and watches had been invented, people began to measure time with sun-dials. Nowadays, when almost everyone has a watch in his pocket, and can have a clock, too, on the mantel-piece of every room in the house, the sun-dial has ceased to be needed in ordinary life. But it is still just as interesting as ever to anyone who would like to have the means of getting time direct from the sun, the great hour-hand or timekeeper of the sky. Any person who is handy with tools can make a sun-dial quite easily, by following the directions given below.

In the first place, you must know that the sun-dial gives the time by means of the sun's shadow. If you stick a walking-cane up in the sand on a bright, sunshiny day, the cane has a long shadow that looks like a dark line on the ground. Now if you watch this shadow carefully, you will see that it does not stay in the same place all day. Slowly but surely, as the sun climbs up in the sky, the shadow creeps around the cane. You can see quite easily that if the cane were fastened in a board floor, and if we could mark on the floor the places where the shadow was at different hours of the day, we could make the shadow tell us the time just like the hour-hand of a clock. A sun-dial is just such an arrangement as this, and I will show you how to mark the shadow places exactly, so as to tell the right time without any trouble whenever the sun shines.

If you were to watch very carefully such an arrangement as a cane standing in a board floor, you would not find the creeping shadow in just the same place at the same time every day. If you marked the place of the shadow at exactly ten o'clock by your watch some morning, and then went back another day at ten, you would not find the shadow on the old mark. It would not get very far from it in a day or two, but in a month or so it would be quite a distance away. Now, of course, a sun-dial would be of no use if it did not tell the time correctly every day; and in fact, it is not easy to make a dial when the shadow is cast by a stick standing straight up. But we can get over this difficulty very well by letting the shadow be cast by a stick that leans over toward the floor just the right amount, as I will explain in a moment. Of course, we should not really use the floor for our sun-dial. It is much better to mark out the hour-lines, as they are called, on a smooth piece of ordinary white board, and then, after the dial is finished, it can be screwed down to a piazza floor or railing, or it can be fastened on a window-sill. It ought to be put in a place where the sun can get at it most of the time, because, of course, you cannot use the sun-dial when the sun is not shining on it. If the dial is set on a window-sill (of a city house, for instance) you must choose a south window if you can, so as to get the sun nearly all day. If you have to take an east window, you can use the dial in the morning only, and in a west window only in the afternoon. Sometimes it is best not to try to fasten the dial to its support with screws, but just to mark its place, and then set it out whenever you want to use it. For if the dial is made of wood, and not painted, it might be injured by rain or snow in bad weather if left out on a window-sill or piazza.

It is not quite easy to fasten a little stick to a board so that it will lean over just right. So it is better not to use a stick or a cane in the way I have described, but instead to use a piece of board cut to just the right shape.

Fig. 1 shows what a sun-dial should look like. The lines to show the shadow's place at the different hours of the day will be marked on the board ABCD, and this will be put flat on the window-sill or piazza floor. The three-cornered piece of board abc is fastened to the bottom-board ABCD by screws going through ABCD from underneath. The edge ab of the three-cornered board abc then takes the place of the leaning stick or cane, and the time is marked by the shadow cast by the edge ab. Of course, it is important that this edge should be straight and perfectly flat and even. If you are handy with tools, you can make it quite easily, but if not, you can mark the right shape on a piece of paper very carefully, and take it to a carpenter, who can cut the board according to the pattern you have marked on the paper.

Now I must tell you how to draw the shape of the three-cornered board abc. Fig. 2 shows how it is done. The side ac should always be just five inches long. The side bc is drawn at right angles to ac, which you can do with an ordinary carpenter's square. The length of bc depends on the place for which the dial is made. The following table gives the length of bc for various places in the United States, and, after you have marked out the length of bc, it is only necessary to complete the three-cornered piece by drawing the side ab from a to b.

TABLE SHOWING THE LENGTH OF THE SIDE bc.

-------------------------- Place. b c Inches. -------------------------- Albany 4-11/16 Baltimore 4-1/16 Boston 4-1/2 Buffalo 4-11/16 Charleston 3-1/4 Chicago 4-1/2 Cincinnati 4-1/16 Cleveland 4-1/2 Denver 4-3/16 Detroit 4-1/2 Indianapolis 4-1/16 Kansas City 3-15/16 Louisville 3-15/16 Milwaukee 3-11/16 New Orleans 2-7/8 New York 4-3/8 Omaha 4-3/8 Philadelphia 4-3/16 Pittsburg 4-3/8 Portland, Me 4-13/16 Richmond 3-15/16 Rochester 4-11/16 San Diego 3-1/4 San Francisco 3-15/16 Savannah 3-1/8 St. Louis 3-15/16 St. Paul 5 Seattle 5-9/16 Washington, D. C. 4-1/16 --------------------------

If you wish to make a dial for a place not given in the table, it will be near enough to use the distance bc as given for the place nearest to you. But in selecting the nearest place from the table, please remember to take that one of the cities mentioned which is nearest to you in a north-and-south direction. It does not matter how far away the place is in an east-and-west direction. So, instead of taking the place that is nearest to you on the map in a straight line, take the place to which you could travel by going principally east or west, and very little north or south. The figure drawn is about the right shape for New York. The board used for the three-cornered piece should be about one-half inch thick. But if you are making a window-sill dial, you may prefer to have it smaller than I have described. You can easily have it half as big by making all the sizes and lines in half-inches where the table calls for inches.

After you have marked out the dimensions for the three-cornered piece that is to throw the shadow, you can prepare the dial itself, with the lines that mark the place of the shadow for every hour of the day. This you can do in the manner shown in Fig. 3. Just as in the case of the three-cornered piece, you can draw the dial with a pencil directly on a smooth piece of white board, about three-quarters of an inch thick, or you can mark it out on a paper pattern and transfer it afterward to the board. Perhaps it will be as well to begin by drawing on paper, as any mistakes can then be corrected before you commence to mark your wood.

In the first place you must draw a couple of lines MN and M′N′, eight inches long, and just far enough apart to fit the edge of your three-cornered shadow-piece. You will remember I told you to make that one-half inch thick, so your two lines will also be one-half inch apart. Now draw the two lines NO and N′O′ square with MN and M′N′, and make the distances NO and N′O′ just five inches each. The lines OK, O′K′, and the other lines forming the outer border of the dial, are then drawn just as shown, OK and O′K′ being just eight inches long, the same as MN and M′N′. The lower lines in the figure, which are not very important, are to complete the squares. You must mark the lines NO and N′O′ with the figures VI, these being the lines reached by the shadow at six o'clock in the morning and evening. The points where the VII, VIII, and other hour-lines cut the lines OK, O′K′, MK, and M′K′ can be found from the table on page 78.

In using the table you will notice that the line IX falls sometimes on one side of the corner K, and sometimes on the other. Thus for Albany the line passes seven and seven-sixteenth inches from O, while for Charleston it passes four and three-eighth inches from M. For Baltimore it passes exactly through the corner K.

TABLE SHOWING HOW TO MARK THE HOUR-LINES.

-----------------+-----------------------------+------------------------ | Distance from O to the line | Distance from M to the | marked | line marked PLACE. +---------+---------+---------+-------+--------+------- | VII. | VIII. | IX. | IX. | X. | XI. -----------------+---------+---------+---------+-------+--------+------- | Inches. | Inches. | Inches. |Inches.|Inches. |Inches. Albany | 1-15/16 | 4-3/16 | 7-7/16 | | 3-1/16 | 1-7/16 Baltimore | 2-1/8 | 4-11/16 | 8 | | 2-7/8 | 1-7/16 Boston | 2 | 4-5/16 | 7-7/16 | | 3-1/16 | 1-7/16 Buffalo | 1-15/16 | 4-3/16 | 7-7/16 | | 3-1/16 | 1-7/16 Charleston | 2-7/16 | 5-3/8 | | 4-3/8 | 2-1/2 | 1-1/8 Chicago | 2 | 4-5/16 | 7-7/16 | | 3-1/16 | 1-7/16 Cincinnati | 2-1/8 | 4-11/16 | 8 | | 2-7/8 | 1-7/16 Cleveland | 2 | 4-5/16 | 7-7/16 | -- | 3-1/16 | 1-7/16 Denver | 2-1/8 | 4-1/2 | 7-11/16 | | 2-7/8 | 1-7/16 Detroit | 2 | 4-5/16 | 7-7/16 | | 3-1/16 | 1-7/16 Indianapolis | 2-1/8 | 4-11/16 | 8 | | 2-7/8 | 1-7/16 Kansas City | 2-1/4 | 4-11/16 | 8 | | 2-7/8 | 1-5/16 Louisville | 2-1/4 | 4-11/16 | 8 | | 2-7/8 | 1-5/16 Milwaukee | 1-15/16 | 4-3/16 | 7-7/16 | | 3-1/16 | 1-7/16 New Orleans | 2-11/16 | 5-3/4 | | 4-1/16| 2-5/16 | 1-1/8 New York | 2 | 4-5/16 | 7-11/16 | | 3-1/16 | 1-7/16 Omaha | 2 | 4-5/16 | 7-11/16 | | 3-1/16 | 1-7/16 Philadelphia | 2-1/8 | 4-1/2 | 7-11/16 | | 2-7/8 | 1-7/16 Pittsburg | 2 | 4-5/16 | 7-11/16 | | 3-1/16 | 1-7/16 Portland, Me | 1-15/16 | 4-3/16 | 7-1/8 | | 3-3/16 | 1-1/2 Richmond | 2-1/4 | 4-11/16 | 8 | | 2-7/8 | 1-5/16 Rochester | 1-15/16 | 4-3/16 | 7-7/16 | | 3-1/16 | 1-7/16 San Diego | 2-7/16 | 5-3/8 | | 4-3/8 | 2-1/2 | 1-1/8 San Francisco | 2-1/4 | 4-11/16 | 8 | | 2-7/8 | 1-5/16 Savannah | 2-9/16 | 5-9/16 | | 4-1/4 | 2-1/2 | 1-1/8 St. Louis | 2-1/4 | 4-11/16 | 8 | | 2-7/8 | 1-5/16 St. Paul | 1-15/16 | 4-1/16 | 7-1/8 | | 3-3/16 | 1-1/2 Seattle | 1-13/16 | 3-15/16 | 6-5/8 | | 3-3/8 | 1-1/2 Washington, D. C.| 2-1/8 | 4-11/16 | 8 | | 2-7/8 | 1-7/16 -----------------+---------+---------+---------+-------+--------+-------

The distance for the line marked V from O′ is just the same as the distance from O to VII. Similarly, IV corresponds to VIII, III to IX, II to X, and I to XI. The number XII is marked at MM′ as shown. If you desire to add lines (not shown in Fig. 3 to avoid confusion) for hours earlier than six in the morning, it is merely necessary to mark off a distance on the line KO, below the point O, and equal to the distance from O to VII. This will give the point where the 5 A.M. shadow line drawn from N cuts the line KO. A corresponding line for 7 P.M. can be drawn from N′ on the other side of the figure.

After you have marked out the dial very carefully, you must fasten the three-cornered shadow-piece to it in such a way that the whole instrument will look like Fig. 1. The edge ac (Fig. 2) goes on NM (Fig. 3). The point a (Fig. 2) must come exactly on N (Fig. 3); and as the lines NM (Fig. 3) and N′M′ (Fig. 3) have been made just the right distance apart to fit the thickness of the three-cornered piece abc (Fig. 2), everything will go together just right. The point c (Fig. 2) will not quite reach to M (Fig. 3), but will be on the line NM (Fig. 3) at a distance of three inches from M. The two pieces of wood will be fastened together with three screws going through the bottom-board ABCD (Figs. 1 and 3) and into the edge ac (Fig. 2) of the three-cornered piece. The whole instrument will then look something like Fig. 1.

After you have got your sun-dial put together, you need only set it in the sun in a level place, on a piazza or window-sill, and turn it round until it tells the right time by the shadow. You can get your local time from a watch near enough for setting up the dial. Once the dial is set right you can screw it down or mark its position, and it will continue to give correct solar time every day in the year.

If you wish to adjust the dial very closely, you must go out some fine day and note the error of the dial by a watch at about ten in the morning, and at noon, and again at about two in the afternoon. If the error is the same each time, the dial is rightly set. If not, you must try, by turning the dial slightly, to get it so placed that your three errors will be nearly the same. When you have got them as nearly alike as you can, the dial will be sufficiently near right. The solar or dial time may, however, differ somewhat from ordinary watch time, but the difference will never be great enough to matter, when we remember that sun-dials are only rough timekeepers after all, and useful principally for amusement.

FOOTNOTE: