616 THE POPULAR SCIENCE MONTHLY. 



The necessity for precision in the use of terms, thus initiation into 

 scientific terminology, was enforced incidentally on another occasion. 

 A playfellow much older than the child picked up a piece of mica and 

 called it isinglass. This conventional inaccuracy I strongly rebuked, 

 and, procuring a piece of real isinglass, led the child to note its differ- 

 ence, and to condemn in private and without malice the slovenly lan- 

 guage of her presumably untaught comrade. Now, the child had a doll 

 called Rosa, and was in the habit of illustrating any absurdity by pre- 

 tending that Rosa was guilty of it. Some time after the conversation 

 on the isinglass she was watching a stream of water falling in the sun- 

 light from a hose. She exclaimed : " See the beautiful silver water 

 coming from the old gray hose. Rosa would have called that mica ! " 



When the box of wooden geometric models was thoroughly mas- 

 tered, after about six months' study, I procured for the child a set of 

 models of crystals, such as are used for studying mineralogy. About 

 half of these proved too complex for study, but the child easily learned 

 to recognize and distinguish twenty-six, partly simple, partly compound 

 forms. As each face of the crystal showed some plane figure which 

 she had already learned, and as she was also familiar with the Greek 

 numerals from three to twelve, it was generally easy for the child to 

 devise the name of the crystal, even when apparently so repelling as a 

 scalenhedron, rhombic dodecahedron, right rhombic pyramid, etc. It 

 was interesting to notice her capacity to discern the general outline of 

 a crystal and thus its generic features, and afterward to distinguish 

 the secondary divisions of its sides, or the specific characters ; thus in 

 a four-faced cube, a three- or six-faced tetrahedron, a three-faced octa- 

 hedron, etc. The forms in the four systems of crystallization were 

 learned by repeated handling of the models, until the child's percep- 

 tions had become saturated with them, and she could, for instance, 

 discover for herself four-faced cubes in the curved molding on stair- 

 cases. Then, at the beginning of the second year, the crystals began 

 to be copied in clay, and opportunity then afforded for studying their 

 axes, or the basis of their classification, by means of long pins thrust 

 through the soft model in appropriate direction. 



Arithmetic, the second science in Dr. Hill's category, was begun 

 several months after the first studies of form and outline. Instead of 

 the beans so frequently recommended, the child used sticks of differ- 

 ent sizes and colors. For two or three months she studied such num- 

 bers as seem almost to form natural complex entities, and hence have 

 often been sacred numbers, thus : four, nine, ten, twelve, twenty-four, 

 thirty-six. The child was exercised in dividing these up into symmet- 

 rical groups, whose resemblances she was trained to tell at a glance by 

 the eye, before enumeration. Thus she learned to form groups of 

 threes, fours, and sixes, and to unite them in as many fantastic combi- 

 nations as could be invented. The object was to effect the transition 

 from the perception of form to the conception of number by a series 



