with nodal points of synthesis, which may be called the very breathing-rhythm of the scientific discoverer.
But to make this exercise of any use there must be no copying from diagrams; the value of it depends on the child evoking a curve, watching it growing, under his fingers, from mere obedience to a law.
When children are introduced by any such method as the foregoing into the laboratory of the great creators of scientific thought, three classes of comments are made by adults who do not quite understand what is going on. The first takes the form of a congratulation on the cleverness of children at the present day. 'I did not know what a conic section was when I was sixteen.' The second, of alarmed remonstrance. 'Isn't it dangerous to worry little children's brains with such learned subjects? It is far better for a child of seven to be stitching round the outline of an animal or a house on the ordinary kindergarten cards, or even working a sampler as our grandmothers did, than to be stimulating his brain with abstract mathematics.' The third comment is one of scornful incredulity. 'Now, do you believe those children understand what a parabola is? Somebody must have shown them how to work it; the teachers are only showing off.'
