Page:Popular Science Monthly Volume 3.djvu/798

774 the attention of students of language and mythology, traces this as well as older allied meanings from the original meaning of στοιχείον in classical Greek, as the shadow on the sun-dial, acutely observing that the moving shadow would seem to the natural man far more alive and mysterious than the fixed rod.

There are several matters dealt with in special chapters by Mr. Fiske which we must put off with little more than allusion: the book is indeed a small one, but so full of interest that choice among its contents is not easy. An essay on "The Descent of Fire" treats of the divining-rod and other talismans endowed with the faculty of rending open rocks and revealing hidden treasure, which all appear to be symbols, sometimes obvious, sometimes remotely and fancifully derived, of the lightning which breaks the cloud and lets loose the treasures of the rain. There is also a chapter on the mythology of non-Aryan tribes, showing the difference between the vague resemblance of these to Aryan myths and to one another, and the close family likeness which leads to the certain conclusion that the great mass of Aryan mythology came from a common stock.—Spectator.

a late number of this journal is an excellent article by Prof. Alexander Hogg, of the Alabama Agricultural and Mechanical College, entitled "More Geometry—less Arithmetic," that contains various suggestions worthy the thoughtful attention of teachers. It was a favorite idea of the late Josiah Holbrook, which he enforced upon educators on all occasions, that rudimentary geometry should be introduced into all primary schools j but he insisted with equal earnestness upon his theory of their order, which was embodied in his aphorism, "Drawing before writing, and geometry before arithmetic." The priority of geometrical or arithmetical conception in the unfolding mind is a subtle psychological question, into which it is not necessary for the teacher to go, the practical question being to get a recognition of the larger claims of geometry, and this is the point to which Prof. Hogg wisely directs the discussion. The fact is, mental development has been too much considered in its linear and successive aspects, and the theories that are laid down concerning the true order of studies have been hitherto too much confined to this idea. Starting with inherited aptitudes, mental development begins in the intercourse of the infant mind with the environment, and, while it is true that there is a sequence of mental experience in each increasing complexity, it is equally true that many kinds of mental action are unfolded together. Ideas of form are certainly among the earliest, and therefore should have an early cultivation. To all that Prof. Hogg says about the need of increasing the amount of geometry in education we cordially subscribe, and we think he is equally right in condemning the excess of attention that is given to arithmetic, which is mainly due to its supposed practical character as a preparation for business. But neither is geometry without its important practical uses. The professor says:

"Let us see, then, what a pupil with enough arithmetic and the plane geometry can perform. He can measure heights and distances; determine areas; knows that, having enclosed one acre with a certain amount of fencing, to enclose four acres he only has to double the amount of fencing; that the same is true of his buildings. In circles, in round plats, or in cylindrical vessels, he will see a beautiful, universal law pervading the whole—the increase of the circumference is proportional to the increase of the diameter, while the increase of the circle is as the square of the diameter. . ..

"Thousands of boys are stuffed to repletion with 'interest,' 'discount,' and 'partnership,' in which they have experienced much 'loss' but no 'profit;' have mastered as many as five arithmetics, and yet, upon being sent into the surveyor's office, machine-shop, and carpenter-shop, could not erect a perpendicular to a straight line, or find the centre of a circle already described, if their lives depended upon it. Many eminent teachers think that young persons are incapable of reasoning, and that the truths of geometry are too abstruse to be comprehended by them. . ..

"Children are taught to read, not for