Though uniform in height and appearance, we do not deem the modern figures an improvement on the variously-lining figures formerly in vogue, and now happily coming again into use. The latter can be caught by the eye with greater ease and certainty, just as lower-case letter can be read with more facility than continuous lines of capitals. In the new style the 3 and 8 may easily be mistaken for each other, and so with the 6, 9, and 0; but in the old style figures such errors are quite unlikely to happen, as some of them occupy the centre of the body only, and others are ascending or descending characters. The example here given will show the justice of our remarks: ~1~ ~2~ ~3~ ~4~ ~5~ ~6~ ~7~ ~8~ ~9~ ~0~ 1 2 3 4 5 6 7 8 9 0 SCRATCHED OR CANCELLED FIGURES 1̷ 2̷ 3̷ 4̷ 5̷ 6̷ 7̷ 8̷ 9̷ 0̷ Are used in arithmetical matter when certain figures require to be crossed over in an operation. FRACTIONS. Common Fractions, or broken numbers in arithmetic, are cast solid to all sizes of type. A great improvement has been introduced by casting the numerator and denominator separately, on bodies of half size, with the line on the under figure, so that odd fractions of any amount may be readily formed, thus: ¹ ² ³ ⁄₂ ⁄₃ ⁄₄ ½ ⅔ ¾. SIGNS. COMMERCIAL SIGNS. ⅌ _Per_, each. @ At or to. % Percentum. ℀ Account. ¢ Cent. $ Dollar or dollars. £ _Libra_, _libræ_, pound or pounds sterling. / _Solidus_, _solidi_, shilling or shillings. MATHEMATICAL, ALGEBRAICAL, AND GEOMETRICAL. + _plus_, or _more_, is the sign of real existence of the quantity it stands before, and is called an affirmative or positive sign. It is also the mark of addition: thus, _a_+_b_, or 6+9, implies that _a_ is to be added to _b_, or 6 added to 9. − _minus_, or _less_, before a single quantity, is the sign of negation, or negative existence, showing the quantity to which it is prefixed to be less than nothing. But between quantities it is the sign of subtraction: thus, _a_−_b_, or 8−4, implies _b_ subtracted from _a_, or 8 after 4 has been subtracted. = _equal_. The sign of equality, though Des Cartes and some others use this mark, ∝: thus, _a_=_b_ signifies that _a_ is equal to _b_. Others use the mark = to denote identity of ratios.