Genaille’s rods

In 1885 the engineer Henri Genaille was made aware of the tens-carry problem with Napier’s rods by the mathematician Edouard Lucas. This led to his invention of new rods for multiplication or division. The rods shown are for division, which is done as follows. One juxtaposes the rods with their top numbers corresponding to the dividend. At the right is the index rod. One begins by choosing the divisor in the right-hand column of the index rod. Everything now takes place in this horizontal section alone. Go to the top number of the far left rod and then follow the line from left to right across the section, ending with a number on the index rod. These numbers yield the answer, e.g. divide 98281 by 4. Then one starts with 2 and follows the lines: 4, 5, 7, 0, 1, giving the answer 24570, remainder 1.