Page:Popular Science Monthly Volume 26.djvu/468

452 ten slats, of which the one on the left is fixed, while the others are movable and can be changed about at pleasure. Each of the squares of the table is divided by diagonals into two triangles, in the lower one of which is found the figure of the units of each of the products, and in the upper and left one the figure of the tens. If we place by the side of the fixed bar the slats bearing at the top the numbers 7, 5, and 8, we obtain almost immediately the products of 758 by all the numbers from 1 to 9. Thus, before the 6 of the fixed bar, we find, looking horizontally, 6 | |  |  |; and by making the addition parallel to the diagonals, we have 4548 as the product of 758 by 6. The other products are got in the same manner. These slats then permit us to find rapidly—without having to know the table of Pythagoras, but by the simple addition of two figures—all the partial products by a number of ten figures. Thus, multiplication is again brought back to addition. This invention, however, has not become practical, because of the difficulty of finding the products when the multiplicand has two or more similar figures. An invention of our own gives it a more practical form. We have replaced the slats by square rules, containing four different numbers on each of the four faces, by which four tables of Pythagoras are included in the same space. But a little addition is still required for finding each of the partial products. M. Henri Genaille, an engineer of the state railroads, has devised a plan for substituting these additions by simple designs, that will permit all the partial products to be read instantly. The management of the rules is very simple, and may be learned at once. As perfected by us, this apparatus replaces the operations of multiplication and division by a simple addition, or a subtraction. With the boxes of the Genaille rules, each eighteen centimetres long, twelve wide, and one thick, we can obtain the partial products of all the numbers to twenty figures. With another disposition of the rules, on a larger scale, it will be possible to give all the products of numbers of ten figures by other similar numbers.—Translated for the Popular Science Monthly from the Revue Scientifique.



HE establishment of a School of Science and Arts at the capital of the nation, through the munificence of Washington's venerable philanthropist, is a landmark in the progress of culture and the history of education, and shows that the demands of modern culture are fully recognized. Let us briefly glance at some of the characteristics of this new education. 