TO PARENTS AND TEACHERS.

THE objects of this little book may, perhaps, require explanation, as the idea of teaching children geometrical, or linear drawing without instruments, is rather a novel one.

But all practical teachers will, I think, admit that in these days of progress, any book which, to use a mechanical term, "files off the sharp edges" of studies hitherto deemed difficult, must be of service to them. Euclid (a book which, by some means or other, has been sadly misplaced in modern school studies) has been taught as "Elements of Geometry" to mere children, whose young minds have not been in any way prepared either to comprehend the practical constructions, or to appreciate the consecutive and comprehensive reasoning contained therein; further (and whoever would write honestly, must write plainly), the poor little victims have been even more mystified by the system on which geometry has been taught in most schools; for instance, a roughly-drawn un

equal-sided quadrilateral figure has been sketched on the black board, and the pupil has been called upon to believe that "of four-sided figures, a square is that which has all its sides equal, and all its angles right angles." He is told that the diagonals of a square or other rectangle will be equal. He sees they are not so on the board; he is mystified, but he learns the definition, and sometimes a page of reasoning.

A figure something like the one on page 62 is drawn by the teacher, and the pupil is told that "all straight lines (ie., the radii) drawn from a certain point (ie., the centre) are equal to one another." The poor child would believe it if he could, but he sees that no two of the radii are alike. But he must "say" the lesson, as Topsy was compelled to "fess," so he says it. But is not that child's faith in geometry weakened?

He remembers that when he first learnt arithmetic, his mother (after all, the best teacher for a child), when she told him "two and two make four," and using perhaps Mr. Butter's "Tangible Arithmetic," counted out firstly two little blocks of wood, and then another two; and when he counted both groups, they did, together, make four, he believed, and had faith in the instruction.

Now, why do not our teachers teach as demonstratively as mothers?

The answer is simple. The mothers teach from the heart, knowing, or rather feeling, that what comes from the heart, goes to the heart; and, therefore, affection smooths the way-the rugged way to knowledge. Further, they are not bound to teach from any particular book, nor are they compelled to have their pupils "up" in any subject by a given date, and can therefore calmly and deliberately watch the development of the young minds, and repeat or vary the lesson as circumstances may require.

Our teachers, on the other hand, honest, hardworking, and zealous, are bound by routine to teach from the book, and Euclid has for centuries past been considered the book, so they teach it, but too early; and therefore, one of the objects I have humbly aimed at in this little work, has been to place in their hands a book which shall introduce the subject in a simple form to the children, so that their first impressions of geometry may be pleasurable, and having thus acquired some of the elementary principles, they may be enabled subsequently to read a more advanced book with interest.

But the question will no doubt be put to me

here, as it has often been before, "Why not begin to teach children geometry or rather geometrical drawing with instruments at once?" There are numerous objections to such a plan.

Firstly, As far as National schools are concerned, the difficulty of obtaining a case of instruments, however cheap, for each pupil in the class, and the short time which such a cheap case lasts, owing firstly, to their necessarily fragile construction, and secondly, to their liability to get out of order, by the loosening of the joints, or by the loss of the screws.

Secondly, The pupils learn in using instruments to depend on the mechanical power rather than on the eye, and the experience of twenty years has shown me that the children who are taught drawing with instruments, before they have acquired a certain amount of power in drawing by hand and eye only, are the most difficult to teach free-hand drawing, having no confidence in their own judgment, unless assisted by rule and compass, and thus all their subsequent efforts become timid, formal, and cramped; whilst, where the elementary study of free-hand drawing has been based on exact or rigid forms, the eye is able to appreciate and the hand to execute the graceful and undulating forms seen in nature and copied in design, with accuracy