work can be done with the square and cubic inch and foot. The French measures can be used exclusively, or in connection with the English. Additions and subtractions can be performed with objects of these dimensions in the same manner as ordinarily with beans and blocks. The blocks may be made of wood of different kinds. Thus at the same time and with additional interest and effect there can be taught—1. The fundamental numerical operations; 2. The recognition of the useful woods; 3. The recognition of exact dimensions and proportions.
This last would lead at once into the investigation of the dimensions of the school-room, the objects in it, the parts of their own bodies, etc. The sense of dimension and proportion, generally so poorly cultivated, so important in numerous arts and industries, would thus receive an early and full development.
The constant drawing of these forms and dimensions, crudely at first, but more perfectly with practice, would lay an early and solid foundation for both mechanical and artistic drawing.
Why should not children early learn to mix paints and adorn their squares and cubes with the principal colors and their simpler hues and tints; then, with this as a foundation, go on to represent nature's simpler colors in the plant, animal, rock, and sky?
Thus not only would color-blindness be detected, but the color sense would be thoroughly developed, and the foundation laid in the knowledge and power given for successful work in numerous lines of industry. We would, then, urge the practicability of using common industrial materials, objects of definite dimensions, weights, colors, imagined values, as the objects by means of which to develop primary conceptions of number and of numerical operations—thus adding to the interest, saving time, and imparting industrial knowledge.
For advanced work in the development and application of arithmetical principles, we would use such simple scientific apparatus as we have on exhibition, or those materials which would lead at once into some principle of political economy. It is our conviction that during the time ordinarily spent by a class upon ratio and proportion, there can be given a better knowledge of these subjects, as such, than is ordinarily given; and in the same time there can be taught, by actual experiment, the law of action of the lever, the laws of vibration of the pendulum, the number of vibrations in each note of the musical scale, and still other important scientific principles. The pupil certainly will have at the end a tolerably correct idea of the mission of ratio and proportion in the scientific and commercial worlds. He will not be likely to make those failures in the application of simple arithmetical principles to scientific and commercial problems with which (I know from experience) he is at present justly credited.
The result of such a method would be to show definitely the place of mathematical science in the progress of civilization. The whole