312 Old-time Schools and School-books
out of the subtrahend and note the excess as before; lastly cast the nines out of the remainder, and add the excess last found, and the excess of the subtrahend together, and if the sum of both be equal to the excess found in the minuend the work is allowed to be right.
An efficient force in raising the standard of mathematical instruction was the publication of Warren Colburn's Intellectual Arithmetic in 1821. Previously all arithmetic had been scarcely intelligible ciphering; but Colburn gives a multitude of simple problems to be done mentally. These cultivated quick comprehension and accuracy, and made it easy to apply what was acquired to the affairs of everyday life. The best teachers lost no time in putting the book into use, and it determined the character of all subsequent text-books. From the very first, its sale was prodigious, and during the next half century more than two million copies were circulated.
Among the books patterned more or less closely after Colburn's was a little volume called the Franklin Arithmetic, Springfield, Massachusetts, 1832. This had a moral purpose, and proposed to improve on the other works then in vogue by the use of " questions, the solution of which will convey to the mind some important truth. It seems rather out of place for a teacher to sit down with a pupil to calculate the gain or loss on the sale of gin, or lottery tickets. In one of our excellent and popular books on mathematical science, there are two or three questions which the scholar cannot solve without knowing