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ON the following Saturday afternoon Elder Witham came, but so blinding a snow-storm had set in that there were no Sunday services next day.

But to us young folks a far more interesting personage was expected that day, none other than our greatly desired, long-expected schoolmaster, Joel Pierson, from Bates College.

The storm was so severe that we feared he would not be able to reach us, but at about three in the afternoon a horse and pung, piled with luggage, was seen plodding up the lane.

"There's old Joel, trunks, maps and all!" shouted Addison and rushed out to welcome him. We all followed.

Horse, pung, driver and Joel himself were so covered with snow as to be scarcely distinguishable. In the pung was stowed not only a huge trunk, but two great rolls, carefully bound up, containing the much-valued school maps. In a large box, too, was Joel's own school melodeon, which he always took with him to every schoolhouse where he taught, although in point of fact we had a melodeon.

Joel could not sing a note himself. "I have no more voice than a guinea-hen," he often remarked; but he enjoyed music in the schoolroom. "It is a good thing to sing together," he was accustomed to say, it makes us all feel more kindly to each other." Unless we were very late with lessons he never dismissed school, either at noon or night, without singing.

He brought two dozen school song-books.

I would give ten times the price for one of those old song-books now, but they have long since ceased to be printed and sold, and I cannot even hear of a copy. Trite old songs they were, but they went well.

"John Brown had a little Indian."


"Oh, there's nothing but shame to the tardy name." And,

"Pure, cold water! That's the drink for me." And,

"Of all the mighty nations in the East or in the West."

All these are imperishably associated with recollections of Joel Pierson and his school melodeon.

On this Sabbath afternoon of his arrival, Joel came stamping his feet into the wood-house, shaking the snow off his old somewhat worn overcoat, for he was a very saving young man. Grasping Gram by the hand, he sang out in his odd, cheery, falsetto voice,

"Well, now, 'Mother,' it does a fellow good to see you again. Seems just like getting home. And Squire, how are you? Didn't expect to get back here this winter, but here I am, same old sixpence! And Theodora, you look just as good as ever. Your face is as big as a family Bible, and it's such a downright good face that there ought to be a lot more of it. Addison, how you've grown! grown handsome, too! My stars, Addison, you will take the shine all off me among the girls this winter! And Halstead, you limb of the Old Boy, how do you do these days? You've been growing, too. Got to be almost as tall as I am. All the same I'll take the kinks out of you, if you don't behave better than you did some days, last winter!" shaking him heartily by the hand. "And Ellen and Wealthy, you nice little things, how are both of you?" getting one by each hand at once and swinging them clean around him.

"And who's this round-headed chap that seems to have stepped in here since I stepped out?" he demanded suddenly looking me over very critically. Addison made haste to introduce me to Joel, and I stepped forward to shake hands, since shaking hands seemed to be a specialty of his. He grabbed me promptly, gave me a jerk and a tremendous grip. "Then you are another one! All the way from Philadelphia! Right from under the shadow of Girard College. Think you can give me points on education, hey? You look pretty muscley for a youngster. But don't you once think you can handle me, for you couldn't do it "Whereupon he illustrated how easily he could trip me up and set me in a chair; and although this seemed a somewhat informal and hasty sort of greeting, I conceived a great liking for Joel, at once.

There was a vein of semi-extravagant drollery in the man; he was odd, offhand and grotesque in many of his movements; yet he somehow gained one's confidence from the moment he spoke. The fact was that Joel was a young man of sterling principles and a good heart. The Old Squire often said of him, that he was "always on the right side." I am sorry the old photograph which I have of him is so poor a one, yet it looks quite a good deal like him.

By this time we had all drifted into the sitting-room and Joel was greeting the Elder. In short, he fell into his old place in the family quite as if he had been away on a visit only. Addison, Theodora, Ellen and all the others were delighted to have him back again; and from that time onward till the close of school there was always something pleasant and amusing coming off, either in progress or being planned.

Joel enjoyed play the best of any one of his age (twenty-two) whom I have ever met. The sitting-room, evening and morning, was the scene of uproarious fun and laughter as well as of hard earnest study. By the time we had been studying closely for half or three-quarters of an hour for Joel was himself a student as well as teacher he would start up, exclaiming, "It's time to have a fracas!" and perhaps launch a cushion at Addison's head, as a preliminary. Then for five or ten minutes there would be lively times there, when all would subside into study again.

One of Joel's least amiable traits, perhaps, was his penchant for playing practical jokes, never of a dangerous kind, yet tricks none the less, which sometimes occasioned a considerable commotion in the house. He had been the youngest of a family of boys at home, and his older brothers had enured him to rough sport while very young. In person Joel was rather above medium height, not of symmetrical form, but quite muscular; in complexion he was sallow, with black hair, gray eyes and a nose far from Grecian. Both in voice and gestures he was noticeably peculiar.

I mention all these memories of Joel Pierson, chiefly because they are so interesting to me, personally; for he was the first teacher who aroused the desire in me to study, for learning's sake, to acquire knowledge for the benefit which he made plain would come to me from it.

What a contrast the old schoolhouse presented by noon, Monday, from the aspect of gloom and discontent which it had worn under the regime of Master Sam Lurvey! Every vacant place on the walls was filled with Joel's large, colored maps; he had even brought and hung up a red curtain at the window behind his desk to give warmth of color to the gray old interior. This was a hint which Theodora and Catherine acted on to add two more colored curtains for the back side of the room. In winter a dash of such strong color cheers a room wonderfully.

The melodeon with its stack of song-books was set up in front of the desk; a small globe, too, made its appearance from the capacious melodeon box; and a large, unabridged Webster's dictionary was laid open on the desk, with an invitation to every one to come and consult it frequently.

Even the worser boys in the school felt the influence of these improved preparations for study. They knew, too, from past experience that Joel could govern, as well as instruct, if necessary. He was one of those teachers, however, who have very little personal dignity to sustain. As long as pupils were of the right spirit and desirous of study, Joel cared very little for any joke or minor irregularity which they might perpetrate, even if it set the whole school laughing. He would laugh, too, as heartily as any one. If he thought we were getting a little dull from prolonged study and quiet, he would even get up a laugh in school himself; he was a believer in laughter.

On the other hand, however, let a pupil grow indolent with a tendency to mischief and disorder, and Joel would immediately find means to make him grieve profoundly. The use of the rod was not then prohibited in the schoolroom. If a boy really meant to be bad and unruly, Joel would keep an eye to him for about three days, without saying much, then send out for a big birch stick and without more ado proceed to give the evil-doer such castigation as he would vividly remember all the remainder of his life. It was currently said that when once Joel had. fallen to birching a boy, he would never desist till the stick was worn out!

There were no such punishments administered that winter, however; for the most part good feeling prevailed throughout the term. Joel wished to hear nothing of Master Lurvey from any one; and he set the classes at work much as if there had been no attempt at a winter school before he came. Our arithmetic class first made a rapid review, then settled to do some diligent cyphering on advance work. It was while reviewing Decimal Fractions that an incident occurred which was remembered for years afterwards.

"Why do you place the sign + after this decimal?" Joel asked me in class.

"Because it will not come out without a remainder and I wish to show that the answer I have here isn't the whole of it," I replied rather hazily.

"What did you attempt to divide?"

"150,000,000 by 7," said I.

"And you got?"

"21.428571.428571.428571+ "

"Do you see anything peculiar about it?"

"Yes; the same set of figures, 428571, occur in the quotient, over and over, and I never come out without a remainder."

"The next, Catherine, what sort of a decimal do you call this?"

"A repetend, or circulating decimal."


"Because we keep coming around to the same set of figures in the quotient, I suppose, and would always have a remainder at the end, even if we continued dividing all day."

"But if you were to divide all day steadily, adding cyphers, you must get the decimal down very small," said the master, quizzically. "There couldn't be much left of the remainder, could there? Seems to me you might get it down pretty near nothing. What do you think, Thomas Edwards?"

Thomas pondered the question for some moments. The problem appeared to have occurred to him in this light very forcibly, for the first time. "Why, I should really think that anybody would get it down to nothing by dividing long enough," replied he, thoughtfully.

This was just such an answer as Joel liked to get. "It does look that way, doesn't it, Thomas?" said he, argumentatively. "It would seem that we might tire that remainder out if we kept annexing cyphers and chased it long enough. According to the atomic theory of matter, you come at last to atoms which are indivisible. Now if that theory is correct, I see no reason why, in numbers, we would not in time come to a point where further division would be impossible. Isn't that the way it looks to you, Thomas?"

"Why, yes, it kind of seems to me so," replied Thomas, still very thoughtfully.

"What is a repetend, Theodora?"

"It is the figure, or set of figures, in the circulating decimal, which is constantly repeated, and is indicated by a dot over that figure, or over the first and the last of the set of figures."

"In the example above, what figures constitute the repetend and how would you indicate them on the board, Thomas?"

Whereupon Tom wrote 428571 428571 428571.

"Every time you annex a cypher and divide by 7, you decrease the actual remainder tenfold, and it does seem, doesn't it, Thomas, that in time, by dividing long enough, you might get that remainder very near down to nothing at all," continued Joel, as if still arguing the question. "How many in the class think that it might be divided out to nothing, by working long enough?"

Not a hand went up, at first.

But after a while Thomas boldly thrust up his hand. The others laughed. Joel laughed, too.

"It could never be done," said Addison.

"How do you know?" exclaimed Thomas whom the laughter irritated a little. "Did you ever try it? Did any of you ever try it?"

"No; I never tried it," replied Addison dryly.

"Then you don't know; and you had better not state what you don't know," retorted Thomas.

"And you had better try it?" advised Addison, ironically.

"Yes, Thomas, suppose you try it," said Joel. "I do not think any one ever has tried it, so you will be on new ground and there's no saying exactly what the result may be."

Thomas was a very resolute boy; he never declined a challenge from any one. What he thought he knew he would always stick to, through thick and thin.

"All right!" he exclaimed. "I will try it. At any rate I will not say I know a thing till I do know it," he added with an aggressive glance at Addison who sat with a provoking grin on his countenance.

At noon we bantered Thomas a good deal. "Laugh, if you want to!" he rejoined stoutly. "I'm not so sure. I said I would try reducing it down, and I will."

This was on Saturday, for at that time it was customary to have Saturday holiday but once a fortnight. School was no sooner dismissed at night, than Thomas carefully cleaned the blackboard and placed his dividend, for proving the circulating decimal a hoax, along the top margin of the board in small figures, to wit, 7/15.000000000000, and began dividing. "I can divide half an hour before dark," said he. "Then I will go home, get my supper and get a lamp and come back."

Catherine privately tried to dissuade him, but he was resolute to keep his word and see how long-winded a circulating decimal really is.

"You will soon get the blackboard full of figures," remarked Joel who enjoyed a thing of this sort immensely. "But here is a lead pencil and a tab of blank white paper. You can carry the operation from the board to a sheet of paper and then from one sheet to another; and as fast as you cover the sheets you can pin them up in a row from the end of the board around the room to the right."

We went home and left Thomas there hard at work. About seven in the evening Catherine called at the Old Squire's.

"I thought I would come down and study with Theodora awhile; it is sort of lonesome at home this evening," she said, laughing.

"Is Tom at the schoolhouse?" I asked.

"Yes; he came home to get his supper and a paper of pins, but took a lamp and went back; and he filled his pocket with doughnuts before starting."

Joel laughed heartily.

"Suppose he will stay there all night?" queried Addison.

"I'm sure I don't know," replied Catherine. "Mother is inclined to think that you kept him after school, Mr. Pierson."

This amused us boys.

"He picked up all the white and brown paper that he could find in the house," continued Catherine. "He said he should want it."

The thought of Thomas down there at the schoolhouse alone, chasing that circulating decimal, diverted us so much that it was difficult to study. At length Joel exclaimed, "It's good walking; let's all go down and see what he is about!"

This proposal was hailed with a shout; and immediately we set off. Even Wealthy went along. On coming in sight of the schoolhouse, the light of a lamp could plainly be seen through a window.

"Let's scare him," said Halstead.

"You couldn't do it," Catherine said.

"No, no," remarked Joel. "We will not disturb him, nor interfere with him in any way. Let him work. We will merely peep in on the sly to see how he is getting on and then go away. Thomas is all right. I like his grit."

We approached softly, and first Joel, then Addison and the rest of us peeped in at the window near the doorstep. Thomas sat in the desk figuring away smartly on paper; the lamp was set on the melodeon hard by. Its light illuminated the room faintly; but we could see that the blackboard was closely covered with figures, and that there were as many as fifteen sheets of paper pinned up already.

Some one at length made a misstep and laughed. The sound reached the figurer's ear inside. "Oh, I hear you, out there!" he exclaimed, but without looking up.

We stole away. Afterwards Catherine told the girls that Thomas came home at about one o'clock.

The next day was Sunday, but we saw Thomas go past at about eleven o'clock in the forenoon, in the direction of the schoolhouse; and it was dusk when he returned.

While at breakfast the following morning, at about seven o'clock, Ellen chanced to glance out and espied Thomas hurrying along the road toward the schoolhouse.

"He is going to tackle that circulating decimal again," cried Addison.

Joel was so amused that he sat laughing throughout breakfast; and it was with great difficulty and sedulously staring at the floor, or ceiling, that we kept sober faces during family prayers.

When we arrived at the schoolhouse at a few moments before nine that morning, Thomas was in the act of completing a sheetful of 428571s, which he hastily added to the row of similar sheets which now extended clean around the walls! The interior of the room presented a truly odd appearance, and there was a great deal of merriment even after the bell rang! The usual morning exercises were held, however, and then according to custom the first class in arithmetic was called. Such a vast assemblage of figures as the blackboard and all those sheets of paper presented we had none of us ever contemplated before! There were a hundred and twenty-two sheets of paper pinned in rows around the house. It was quite enough to make one's head swim, as Ellen remarked, to then attempt to enumerate them.

Thomas took his place in the class quite as a matter of course; he looked as confident as ever; and the fact that we were all regarding him with broad smiles on our faces did not appear to embarrass him in the least.

"At our last recitation, on Saturday, we had the subject of circulating decimals," Joel now observed. "The question whether a circulating decimal, consisting of a repetend, could ever be reduced and brought out without a remainder, was then raised. One of our number thought this might possibly be done by dividing long enough; and we have before us, as I conclude, the result of his efforts in that direction. Am I right, Thomas?"

"Yes, sir," replied Thomas promptly.

"What results, if any, have you obtained from your calculations?"

"Well, sir," replied Thomas, getting up slowly and facing half around so as to have all his work in full view, "I have proved and settled a number of points in my own mind at least. One of these points is that this is really and truly a circulating decimal, for as you can all see it has brought me clean around the room to the point where I started from," indicating the long circuitous row of figured sheets of paper, with a wide gesture of his hand.

"So we see," said Joel, laughing. "But what result has come from the constant division, after annexing cyphers? Have you come out without a remainder, at last?"

"Oh, no, sir, not yet!" cried Thomas, quite as a matter of course and as if surprised at such a question. We all laughed heartily at his tone.

"You still think then that by dividing long enough you might come out without a remainder?" questioned Joel.

"I am sure of it," said Thomas, with enthusiasm. Addison burst forth laughing, but Catherine and Theodora looked at Tom in perplexity.

"Have you any idea how long it would require?" continued Joel.

"Yes, sir," said Thomas at once. "I think I see exactly how long it would require."

"Well, how long?" exclaimed Joel.

"Forever," replied Thomas, emphatically. "No more, no less."

"Forever's a long while," said Joel.

"Well, yes," said Thomas, "and that is a long example. It will take just forever to do it in. It can be done in that time, but in nothing less."

"Isn't forever the same thing as eternity?" asked Theodora.

"Yes; eternity, or infinity," replied Joel. "Thomas has got as near the truth of the matter as any one can get, I think; and I am glad he made this trial and came to this conclusion from his own reasoning, without aid. It is worth more to him and more to you all than anything I could have said about it. Thomas will never forget what a circulating, or infinite, decimal is, I will warrant."

"No, I shall not," said Thomas. "I've been thinking of a great many other things, too, while I sat making those figures. One thing I've thought of is what you said about matter and atoms, atoms that are supposed to be indivisible. I don't believe anybody would ever come to an 'atom' so small but that it could be divided again. Or at any rate it would take just as long to divide down to an indivisible atom, as it would to get that decimal down. And that is forever. That is what nobody ever could come to. So nobody can ever find an atom which can't be divided. When folks talk about atoms, they are talking of something no one ever found, or ever can find. So really there is no such thing as an atom which cannot be divided."

"Thomas, you are getting us into very deep water," said Joel. "We had better return to finite decimals, I think."

The blackboard was cleared of the figures; and Tom's many sheets of paper were used to kindle the fires that week, but the points brought out that morning lingered a great while in my mind. I have pondered them often in later years, and have heard them discussed by learned authorities who considered themselves philosophers. But I have never really heard anything clearer on the subject than Thomas gave us in about thirty words that morning; and Tom never thought of such a thing as being a philosopher. It was the fresh, spontaneous effort of a school-boy's mind, and it had its effect on his whole after life.

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