AN EXPERIMENT IN PRIMARY EDUCATION. 473 



a clearly intellectual life on any other subjects, it attains a very defi- 

 nite power to distinguish the square, the circle, the oval, the spiral ; and 

 also to recognize the rhythm of verse and music. Out of space and 

 time arise through the suggestions of the material world three princi- 

 pal sciences : geometry, arithmetic, algebra. In considering space we 

 are led to imitate the act of the Divine Intellect, which has geome- 

 trized from eternity. Geometry is the earliest and simplest of all pos- 

 sible sciences." The writer proceeds to point out that " the earliest 

 abstraction from the idea of form is that of number, and out of this 

 idea is evolved the earliest of the truly abstract sciences, namely, arith- 

 metic. But because this science is based upon an abstraction, and not 

 upon a direct perception, it should be made to follow, and not, as is 

 usually the case, precede geometry." Again, " the earliest suggestions 

 of motion reveal to us time as well as space. But space is external to 

 the mind ; time enters into our spiritual consciousness, and measures 

 our flow of thought." 



To this might be added the anatomical consideration that the for- 

 mation of space conceptions is the function of the cerebrum, from the 

 impressions furnished by the optic nerve ; while the conceptions of 

 time are elaborated in the cerebellum from the experience in succes- 

 sions of events furnished by the auditory nerve. Space conceptions are 

 objective, static ; time conceptions, from the beginning subjective, are 

 at first successive, then become progressive, finally causal, dynamic 

 when the conception of cause arises from consideration of the sum of 

 antecedent events. Thus this second series of conceptions soon im- 

 pinges upon moral considerations ; the first remains within the sphere 

 of perceptive intelligence. To space, or optic nerve conceptions, be- 

 longs symmetry ; to time, or auditory nerve conceptions, belong har- 

 mony and rhythm. 



These ultimate ramifications of the primary psychic phenomenon 

 must be held in mind at the moment of beginning to systematize the 

 visual and auditory perceptions which lie at their basis. 



All object-teaching may be made useful as a means of training to 

 independent observation. But the study of ordinary, i. e., of complex 

 objects, is necessarily empirical, whereas geometric forms can be at 

 once submitted to scientific generalizations, can therefore at once initi- 

 ate the child into scientific method. Dr. Hill recommends the study 

 of geometry to be begun at the age of eight. The child upon which 

 my own experiment was performed began the study of geometric ele- 

 ments before she was four. Some details of her education may per- 

 haps be quoted as the best way of illustrating certain abstract princi- 

 ples. At the age of four and a half she had learned the following 

 elements : straight, curved, slanting, and half-slanting lines, also to 

 distinguish perpendicular and horizontal lines, and to draw either 

 straight or curved lines parallel to each other. She was well acquainted 

 with all forms of the triangle, equilateral, isosceles, right angle, and 



