*CALCULATING-MACHINES.*

formance of the machine. With this instrument, which my children learned to use when they were seven years old, the product of two numbers of ten digits can be obtained in half a minute; and it is used in numerous offices and institutions in France, the average sale of it being a hundred a year.

About a half a century ago, Charles Babbage undertook the construction of a universal calculating-machine, which should give the successive terms of arithmetical progressions of different orders; but, having devoted the latter part of his life, and all of his fortune and income to it, died without finishing it. George Scheutz, of Stockholm, and his son, Edward Scheutz, exhibited a machine at the Paris Exposition of 1855, which was bought by a citizen of the United States and presented to the Dudley Observatory in Albany. It is shaped like a small piano, and by simply turning the handle gives out the successive terms of arithmetical progressions, not of the first order only, but of the second, third, and fourth orders.

John Napier, the inventor of logarithms, suggested an ingenious method of performing the operations of multiplication and division. The table in Fig. 13 represents the table of Pythagoras dissected into