The volume contains a more than ordinarily thorough and full treat ment of the processes of Literal Arithmetic, viz., the Fundamental Rules, Fractions, Involution, Evolution, and the Calculus of Radicals. It is in these processes that pupils usually find the most difficulty; and in them comparatively few become proficient, especially in the Calculus of Radicals. Yet no one can become an algebraist, and, if not an algebraist, not a mathematician, without being perfectly mas ter of these processes. Hence they are treated so much at length and with so much care and thoroughness. It is idle to deceive the pupil with the notion that he is mastering the subject of algebra by obtain ing a superficial acquaintance with the nature and uses of some of the more simple forms of the equation. The pupil who cannot. Attain a good degree of familiarity with the literal arithmetic, cannot appro ciate mathematical reasoning, or profit much by this study.