that wherein unity or 1 and 0 are only used.—This was the invention of M. Leibnitz, who shows it to be very expeditious in discovering the properties of numbers, and in constructing tables: and Mr Dangecourt, in the history of the royal academy of sciences, gives a specimen of it concerning arithmetical progressionals; where he shows, that because in binary arithmetic only two characters are used, therefore the laws of progression may be more easily discovered by it than by common arithmetic. All the characters used in binary arithmetic are 0 and 1; and the cypher multiplies every thing by 2, as in the common arithmetic by 10. Thus 1 is one; 10, two; 11, three; 100, four; 101, five; 110, six; 111, seven; 1000, eight; 1001, nine; 1010, ten; which is built on the same principles with common arithmetic. The author, however, does not recommend this method for common use, because of the great number of figures required to express a number; and adds, that if the common progression were from 12 to 12, or from 16 to 16, it would be still more expeditious.