452 THE POPULAR SCIENCE MONTHLY. 



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 figu7*e 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 | f | |- | |- | ; and by making the addition paral- 

 lel 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, be- 

 cause 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 simj^le 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 up, 

 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 pos- 

 sible to give all the products of numbers of ten figures by other simi- 

 lar numbers. — Translated for the Popular Science Monthly from, the 

 Iteviie Scientifque. 



♦♦♦ 



THE LAKGER IMPORT OF SCIENTIFIC EDUCATIOK.* 



By J. W. POWELL, LL. D. 



THE 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. 



* From an address delivered at the inauguration of the Corcoran School of Science 

 and Arts, in the Columbian University, Washington, D. C, October 1, 18S4, 



