8 1 4 THE POPULAR SCIENCE MONTHLY. 



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 recogni- 

 tion of the useful woods ; 3. The recognition of exact dimensions and 

 proportions. 



This last would lead at once into the investigation of the dimen- 

 sions 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 arith- 

 metical 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 cer- 

 tainly 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 arith- 

 metical 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 



