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the like clifs lying betweene Calis and Bullin." 6. These clifs on either side the sea, lying iust opposite the one ynto the other; both of one substance; that is, of chalke and flint; the sides of both towards the sea, plainely appearing to bee broken off from some more of the same stuffe or matter, that it hath sometime by nature been fastned vnto; the length of the said clifs along the sea shore being one side answerable in Effect, to the length of the verie like on the other side, and the distance between both, as some skilfull say. lers report, not exceeding 24 English miles; are all great arguments to prooue a coniunction in time long past, to haue beene betweene these two countries; whereby men did passe on drie land from the one vnto the other, as it were ouer a bridge or Isthmus of land, being altogether of chalke and flint, and containing in length about the number of miles before specified, and in bredth some sixe English miles or there abouts, whereby our countrie was then no Iland but Peninsula being thus fixed vnto the maine continent of the world." "It is further to be noted, that in our ancient language the cut off or broken mountaines on the sea sides, are more rightly and properly called clifs, then by the name of rocks or hills; that appellation being more fitting vnto the inland mountaines; but the name of cleft coming from our verbe to cleaue, is onto these more aptly giuen, for that they seem vnto our vieu as cleft or clouen from the part that sometime belonged vnto them."

The writer then proves that the Netherlands from their low, level and sandy soils must have formerly been under water and that for a longer period than during the flood, because of the innu. merable shells there found. The way in which they became dry land was by the breaking through of the Isthmus between Eng. land and France, and the flow of water into the most huge Westerne Ocean.”

“ That the Sea on the West side of the said Isthmos was lower then the sea on the East side thereof, is besides this great worke thereby wrought, to be iudged by the sundry flats and shallowes on the East side, as well on the coast of England as of Flanders. And contrariwise on the West side, no such flats at all to bee found, whereby may well be gathered that as the Land vnder the Sea remaineth on the one side lower than on the other, so accordingly did the Sea also. It is moreover to bee iudged by the very present course of the Sea: for it is obserued that the currant of the water is more swift downe the channell towards the West, then from the West unto the East; old shippers of the Netherlands affirming, that they haue often noted the Voyage from Holland to Spaine to be shorter by day and a halfe sayling, then the voyage from Spaine to Holland. That the seas are different in height one from the other, euen in places where they haue but narrow separations of Land betweene them, is very manifest, for heretofore at such time as some of the Kings of Egypt went about by cutting the separation of land which is betweene the Red-Sea and Mare Mediterranean or the Midland sea, to bring them both into one, it was found by the water-leuel, that the Red-sea was much higher than the Mediterraneum sea, and beeing but shallow in diuers places, it was feared it would in those places not haue bin nauigable, but rather that people might haue passed through it on foot, and for this and other inconueniences which might haue ensued, it was left vndone. Moreover it hath also bin found that the sea on the West side of America, is higher then the Atlanticke sea which lieth on the East side, so as if it had so bin that the Isthmos of land might haue bin cut through, that passage there might haue been made into the Pacifike sea, without sailing so farre about as by the straights of Magellan yet would some other great inconueniences haue grown through the inequalitie of the heighths of these two seas."

“ Another reason there is that this separation hath bin made since the floud, which is also very considerable, & that is, that the Patriarch Noe hauing had with him in the Arke all sortes of beasts (all else besides throughout the whole world beeing destroyed) these then after the floud beeing put foorth of the Arke to encrease and multiply, did afterward in time disperse themselues ouer all partes of the continent or maine land, but long after it could not bee before the rauenous wolfe had made his kind nature knownevnto man, and therefore no man unlesse hee were mad, would euer transporte of that race for the goodnes of the breed, out of the continent into any Iles. But our Ile as is aforesayd, continuing since the floud fastned by Nature ynto the great continent these wicked beasts did of themselues pass ouer."

“But now whether the breach of this our Isthmos, were caused by some great Earthquake, whereby the sea first breaking through, might afterward by little and little enlarge her passage, or whether it were cut by the labour of man in regard of commoditie of passage, or whether the inhabitants of the one side or the other by occasion of war did cut it: must needs remain altogether uncertain: but that our Ile hath bin continent with France and that since the deluge hath here bin shewed by euident reasons and markeable demonstrations."


[Extract from the Nineteenth Semi-Annual Report of John D. PHILBRICK, Superintendent of Public Schools of the City of Boston.]

In the first stages of instruction, much pains should be taken to enable the pupils to obtain clear and distinct ideas of numbers by associating their names with visible objects. Teachers often commence with the names of numbers, without reference to sensible objects, and then proceed at once to the tables in addition, subtraction, multiplication, and division, which the pupils are required to repeat by rote. This method is eminently preposterous. It is a good illustration of “how not to do it.” It is much better to teach the pupils first to count real objects, and then make computations upon them, before perplexing them with abstract conceptions. When children have been made familiar with the perception of numbers, as presented in the various objects around them, the next step is to make them acquainted with the increase of numbers by unity; and then follows the comparison of numbers with respect to their value or magnitude. In developing the first ideas of numbers, the skilful teacher would proceed somewhat in the following manner:

I hold up onc pencil.
Say, one pencil.
You see in my hand one book.
Hold up one hand, one finger.
I will make one mark on the board.

How many

Say, one mark.
Make one mark on your slates.
You see in this hand one pencil, and in this one pencil.
One pencil and one pencil are two pencils.
Say, one pencil and one pencil are two pencils.
Hold up two hands; two fingers.
Say, one hand and one hand are two hands.
How many books do I hold up?
Two books.

I make on the board one mark and one mark. marks have I made ?

Two marks.
I erase one of the marks. How many remain ?
One mark.
Make two marks on your slates.
Here are two pencils and one pencil.
Two pencils and one pencil are three pencils.
Say, two pencils and one pencil are three pencils.
Hold up three fingers, two fingers, one finger.
See how many marks make on the board.
Three marks.
Jane may come, and make three marks.
Make three marks on your slates.

The above is not presented as a pattern to be followed literally, but as an imperfect illustration of what is meant by developing elementary ideas of numbers.

If the children have been taught the first lessons in drawing they may be directed to make straight lines in different directions, instead of being merely requested to make marks without regard to their character. Thus, in every lesson so far as possible bring into use what has been previously learned. Having pursued this mode of teaching till the pupils are acquainted with the application of numbers to objects as far as ten, the Numeral Frame may be brought into use, and from this point it should be constantly used during the whole primary course of arithmetical instruction. No teacher who has once learned its great value as a piece of apparatus will cease to use it.

There are different descriptions of this piece of apparatus. For instruction in the lowest classes, it is desirable that it should contain ten wires, and that each wire should have ten balls; black and white should alternate.

When the pupils have acquired distinct ideas of numbers as far as a hundred, a knowledge of their names, and the ability to count readily, they are prepared to learn the signs of numbers or figures.

As before, the names of numbers have been all along associated with sensible objects; now the signs should in like manner be taught in connection with real things, only one sign or figure being presented at a time.

I imagine that a model teacher would proceed to teach her pupils [if she has the fourth class] to write numbers in a way not very different from the following:

You see in my hand one pencil.
I will make the figure that stands for one.
Make the figure on your slates.
When I point to it [on the board], say figure one.
How many balls ?
Two balls.
Yes. You see this figure; it stands for two.
Make it on your slates.

[Pointing to the tablet of numbers.] You see the figures on this tablet. Who will come and point out figure one ? two ?

How many straight lines on the board ?
Three straight lines.
Make the same on your slates.
Now we make the figure that stands for three.
You may make it on your slates.
Thus proceed to nine.

It would be found best, probably, to extend the training indicated above over three or four lessons, multiplying the illustrations.

Arrange marks and figures on the board as follows:

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