But there is one feature that has not been considered above, and that is a serious handicap to any effort at combining the two sciences in the high school, and this is the question of relative difficulty. It is sometimes said, in a doctrinaire fashion, that geometry is easier than algebra, since form is easier to grasp than function, and that therefore geometry should precede algebra. But every teacher of mathematics knows better than this. He knows that the simplest form is easier to grasp than the simplest function, but nevertheless that plane geometry, as we understand the term to-day, is much more difficult than elementary algebra for a pupil of fourteen. The child studies form in the kindergarten before he studies number, and this is sound educational policy. He studies form, in mensuration, throughout his course in arithmetic, and this, too, is good educational policy. This kind of geometry very properly precedes algebra. But the demonstrations of geometry, the study by pupils of fourteen years of a geometry that was written for college students and always studied by them until about fifty years ago,--that is by no means as easy as the study of a simple algebraic symbolism and its application to easy equations. If geometry is to be taught for the same reasons as at present, it cannot advantageously be taught earlier than now without much simplification, and it cannot successfully be fused with algebra save by some teacher who is willing to sacrifice an undue amount of energy to no really worthy purpose. When great mathematicians like Professor Klein speak of the fusion of all mathematics, they speak from the standpoint of advanced students, not for the teacher of elementary geometry.