me from all quarters of the world during years, touching the prospects of its speedy a should augur for it a wider popularity than have yet written. The questions propounde engineers and others, in consequence of the o in the preface to my 'Catechism of the Steam 1856, to endeavour by my explanations to difficulties as impeded their progress, have ha of showing more clearly than I could otherwis ceived what the prevalent difficulties of le been; and I have consequently been enabled explanations in the present work as appeared lated to meet those difficulties for the future. To several of my correspondents I have to myself indebted for the correction of typogra in my several works, and also for valuable su various kinds, which I have made use of in which they were available. I may here take occasion to notify that prepared an Introduction to my 'Catechism of Engine,' which reviews the most important improvements of the last ten years; and which, for the convenience of persons already possessing the Catechism, may be had separately. These three works taken together form a body of engineering information so elementary as to be intelli gible by anybody, and yet so full that the attentive student of them will, I trust, be found not to fall far short of the most proficient engineers in all that relates to a knowledge of the steam-engine in its most important applications. J. BOURNE. BERKELEY VILLA, REGENT'S PARK Road, LONDON: 1865. CONTENTS. Nature and Properties of Fractions Addition and Subtraction of Fractions To Reduce Fractions to a Common Denominator Multiplication and Division of Fractions Squares and Square Roots of Numbers Cubes and Cube Roots of Numbers On Powers and Roots in General |