I will suppose that the teacher of a common school, undertakes to show his boys, who, we will suppose, are acquainted with nothing but elementary arithmetic, how longitude is ascertained, by means of the eclipses of Jupiter"s satellites; not a very simple question, (as it would, at first view, strike one,) but still one which, like all others, may be, merely by the power of the subdivision alluded to, easily explained. I will suppose that the subject has come up at a general exercise,--perhaps the question was asked in writing, by one of the older boys. I will present the explanation, chiefly in the form of question and answer, that it may be seen, that the steps are so short, that the boys may take them themselves.
"Which way," asks the teacher, "are the Rocky Mountains from us?"
"West," answer two or three of the boys.
In such cases as this, it is very desirable that the answers should be general, so that throughout the school, there should be a spirited interest in the questions and replies. This will never be the case, if a small number of the boys only take part in the answers; and many teachers complain, that, when they try this experiment, they can seldom induce many of the pupils to take a part.
The reason ordinarily is, that they say that _any_ of the boys may answer, instead of that _all_ of them may. The boys do not get the idea that it is wished that an universal reply should come from all parts of the room in which every one"s voice should be heard. If the answers were feeble, in the instance we are supposing, the teacher would perhaps say;
"I only heard one or two answers: do not more of you know where the Rocky Mountains are? Will you all think, and answer together? Which way are they from us?"
"West," answer a large number of boys.
"You do not answer fully enough yet; I do not think more than forty answered, and there are about sixty here. I should like to have _every one in the room_ answer, and all precisely together."
He then repeats the question, and obtains a full response. A similar effort will always succeed.
"Now, does the sun, in going round the earth, pa.s.s over the Rocky Mountains, or over us, first?"
To this question, the teacher hears a confused answer. Some do not reply; some say, "Over the Rocky Mountains;" others, "Over us;" and others still, "The sun does not move at all."
"It is true that the sun, strictly speaking, does not move; the earth turns round, presenting the various countries, in succession, to the sun, but the effect is precisely the same as it would be, if the sun moved, and accordingly I use that language. Now, how long does it take the sun to pa.s.s round the earth?"
"Twenty four hours."
"Does he go towards the west, or towards the east, from us?"
"Towards the west."
But it is not necessary to give the replies; the questions alone will be sufficient. The reader will observe that they inevitably lead the pupil, by short and simple steps, to a clear understanding of the point to be explained.
"Will the sun go towards, or from, the Rocky Mountains, after leaving us?"
"How long did you say it takes the sun to go round the globe, and come to us again?"
"How long to go half round?" "Quarter round?"
"How long will it take him to go to the Rocky Mountains?"
No answer.
"You cannot tell. It would depend upon the distance. Suppose then the Rocky Mountains were half round the globe, how long would it take the sun to go to them?" "Suppose they were quarter round?"
"The whole distance is divided into portions called degrees; 360 in all.
How many will the sun pa.s.s, in going half round? In going quarter round?"
"Ninety degrees then make one quarter of the circ.u.mference of the globe.
This you have already said will take six hours. In one hour then, how many degrees will the sun pa.s.s over?"
Perhaps no answer. If so, the teacher will subdivide the question, on the principle we are explaining, so as to make the steps such that the pupils _can_ take them.
"How many degrees will the sun pa.s.s over in three hours?"
"Forty-five."
"How large a part of that, then, will he pa.s.s, in one hour?"
"One third of it."
"And what is one third of forty-five?"
The boys would readily answer fifteen, and the teacher would then dwell for a moment, on the general truth, thus deduced, that the sun, in pa.s.sing round the earth, pa.s.ses over fifteen degrees every hour.
"Suppose then it takes the sun one hour to go from us to the river Mississippi, how many degrees west of us, would the river be?"
Having thus familiarized the pupils to the fact, that the motion of the sun is a proper measure of the difference of longitude between two places, the teacher must dismiss the subject, for a day, and when the next opportunity of bringing it forward occurs, he would perhaps take up the subject of the sun"s motion as a measure of _time_.
"Is the sun ever exactly over our heads?"
"Is he ever exactly south of us?"
"When he is exactly south of us, or in other words, exactly opposite to us, in his course round the earth, he is said to be in our meridian. For the word meridian means a line drawn exactly north or south from any place."
There is no limit to the simplicity which may be imparted, even to the most difficult subjects, by subdividing the steps. This point for instance, the meaning of meridian, may be the subject, if it were necessary, of many questions, which would render it simple to the youngest child. The teacher may point to the various articles in the room, or buildings, or other objects without, and ask if they are or are not in his meridian. But to proceed:
"When the sun is exactly opposite to us, in the south, at the highest point to which he rises, what o"clock is it?"
"When the sun is exactly opposite to us, can he be opposite to the Rocky Mountains?"
"Does he get opposite to the Rocky Mountains, before, or after, he is opposite to us?"
"When he is opposite to the Rocky Mountains, what o"clock is it there?"
"Is it twelve o"clock here, then, before, or after it is twelve o"clock there?"
"Suppose the river Mississippi is fifteen degrees from us, how long is it twelve o"clock here, before it is twelve o"clock there?"
"When it is twelve o"clock here then, what time will it be there?"
Some will probably answer "one," and some "eleven." If so, the step is too long, and may be subdivided thus:
"When it is noon here, is the sun going towards the Mississippi, or has he pa.s.sed it?"
"Then has noon gone by, at that river, or has it not yet come?"
"Then will it be one hour before, or one hour after noon?"
"Then will it be eleven, or one?"