"Your father let me have the book," said he; "and see my chalk marks for the sun's shadow."
Rollo looked, and found that Jonas had put down quite a number of chalk marks along in a line, where they had first began to mark the place where the shadow of the door reached into. Rollo and Lucy had forgotten all about their plan of making such a series of observations; but Jonas had gone on regularly, making a mark every Monday, at noon, precisely. As the sun, at that season of the year, was going round farther and farther to the south every week, it shone in farther and farther upon the floor, so that each chalk mark was farther in than the one made the week before.
In order to make his marks at the right time, Jonas wanted to know, every Monday, when it was precisely twelve o'clock, and this led him to make his noon mark, having seen the account of it in the book which Rollo's father had lent him. He learned there that the shadows of all upright objects are cast exactly north at twelve o'clock, or rather very nearly north; near enough for his purposes. Now, as the post of the barn door was upright, he knew that the shadow of it would be in the north and south line at noon. Of course, if he had a north and south line, or a meridian line, as it was called in the book, drawn upon the floor, he knew that he could tell when it was noon, by the shadow of the post coming then exactly upon that line. He explained this all to Rollo, and Rollo was very much pleased with it indeed. He determined to have a noon line somewhere in the house.
Rollo asked Jonas what was the way to draw a noon line. Jonas told him that there were several ways. One way, he said, was to observe some day, by the clock, when it was exactly noon, and then to mark, upon the barn floor, the line where the shadow of the edge of the post fell precisely at that moment. Another way was to get a compass needle, and put it down upon the floor, and then draw a north and south line precisely in the direction that the needle indicated. That would, of course, be a north and south line, because the compass needle always pointed north and south. He said that he adopted both these methods to make his noon line. First, he got a compass needle, which Rollo's father had lent him, and put that down upon the barn floor just at the foot of the door post, and observed the direction; and he also noticed when it was twelve, by the clock in the house, and he found that, when it was twelve by the clock, the shadow of the post came exactly to the line indicated by the direction of the compass needle; and so he knew that that was a correct meridian line.
JONAS'S DIAL.
That evening, Rollo told his father about his hour-glass, and also about Jonas's noon line. His father said it was very difficult to draw a meridian line.
"O no, father," said Rollo; "Jonas has drawn one, and he told me how, and it was a very easy way."
"Yes," said his father, "it is easy to draw something which you can call a noon mark; but it is a very difficult and delicate operation to do it with any considerable degree of exactness."
"I think that Jonas's is exact," said Rollo.
"It probably may be as exact as he could make it with his means and instruments; but there are a great many sources of error which he could not possibly have avoided."
"What?" asked Rollo.
"Why, in the first place, the clock is not exact. It is near enough to answer all the purposes of a family; but it may often be a minute or more out of the way. Then besides, while Jonas is going from the clock out to the barn, the shadow is slowly moving on, all the time; so that he cannot tell exactly where the shadow was, when it was precisely twelve by the clock.
"Then again, it is not always exactly noon when the shadow comes to the north and south line. It varies a little at different seasons of the year, though it is so near that we say, in general terms, that at noon all shadows of upright objects point to the north. Still, it is not precisely true, except on a very few days in the year. Then, again, the post of the barn door is not exactly upright."
"I thought they always made door posts exactly upright," said Rollo.
"They do make them as nearly upright as they can, with the common carpenters' instruments; but they are not exact. To set a post of any kind, with great precision, perpendicular to the horizon, would require very expensive mathematical instruments, and very laborious and nice observations. Then, again, if the clock had been exact, and the post perfectly upright, Jonas could not have marked the place of the shadow exactly. The shadow has not an exact and well-defined edge; and then, even while he was marking at one end, the shadow would be moving along at the other end, and so his noon mark would not be exactly straight."
"Why, father, he could make the mark right along quick."
"No matter how quick he might make it. It would take some time, wouldn't it?"
"Only a very little," said Rollo.
"And do you suppose the sun would stand still, even during that little time, so as to let the shadow remain stationary?
"However," continued his father, "I don't say this to disparage Jonas's noon mark. I dare say, it is accurate enough for his purposes. He only wants to know from it when it is time for him to come in to dinner, or something like that. I only want you to understand what exactness is, and to see, a little, how difficult it is to attain to any considerable degree of it, in such cases. So thus, it seems, that Jonas has got a sort of a dial?"
"Why, it only tells him what o'clock it is at one hour in the day," said Rollo. "But I think he might make it do for all the afternoon and forenoon."
"How?" inquired his father.
"Why, all he has got to do is to watch some day when it is nine o'clock, and ten o'clock, and so on, every hour; and then make a line where the shadow comes every hour, just as he did for twelve o'clock. Then he will have marks for every hour in the day, and when the shadow comes along to these marks, one after another, he will know what time it is."
"O, but the difficulty is," said his father, "that the shadow will not come to the same places, at the same hours, on different days. It will come to the meridian line, at twelve, always,-that is, nearly to it; but it will not come to any other lines regularly,-that is, if the object, which casts the shadow, is upright."
"Will any other kind of object carry the shadow regularly?" asked Rollo.
"Yes," said his father, "an object that leans over to the north, so as to point to the North Star. If you and Jonas could put a post into the ground so as to have it point to the North Star, then you could mark, all around it, the places to which the shadow would come for every hour in the day, and afterwards it would come to the same places regularly, or nearly so. It would be near enough for your purposes; and I don't know but that it would be quite a respectable dial for you."
Rollo then asked his father why it was that a post, which pointed to the North Star, would bring a shadow any more regularly to the hour marks, than an upright one would; but he said that Rollo did not know enough, yet, to understand the explanation, even if he were to try to explain it. "Therefore," said he, "you must wait until you study astronomy before you can expect to understand it; but you can now, in the mean time, make such a dial, if you wish to do it."
Rollo did wish to do it very much. He accordingly told Jonas all that his father had said. It seemed very strange to Jonas, that a post, pointing to the North Star, should have its shadows move round any more regularly than a post in any other position. He could not imagine what the North Star could have to do with the shadows. Still, he determined to try the experiment.
A few days after this, Jonas did try the experiment. He got two narrow boards, which were once pickets belonging to a picket fence, one end of each was sharp, so that it could be driven down into the ground. Then he selected a certain part of the yard, in a corner, where the dial would be out of the way, and yet the path to the barn led along pretty near it. The reason why Jonas got two boards was this: he knew that, if he drove only one stake into the ground, and inclined it towards the North Star, it would be very likely to get started out of its proper position; but if he had two, he could drive the second one down perpendicularly from the end of the first, and then nail the two ends together; and that would keep all steady.