approximation, has led me incidentally to show the advantages of a decimal system of coins and measures, with particular reference to what may be called MilMetric Arithmetic. The adoption of the Metric System and a Decimal Coinage would simplify Arithmetic enormously, and I am hoping that the new method of decimalising money at sight adopted in this book, and the treatment of many other questions, will show the student that we have a coinage ready made to our hands, with the radical coins as the £, florin, cent, and mil (each being of the preceding); in other words money expressed in £ and decimals of a £ to three places. The great practical advantage of this coinage is that the sovereign is untouched. Any proposal with the penny as basis necessitates a world-wide revolution, whereas our immense foreign trade would be unaffected as long as the sovereign remains the integer. It is true that our internal trade would be to some extent disturbed by a change in the smaller coinswhich would not occur if the penny was made the basis; but this disturbance would be nothing in comparison with that caused by altering the sovereign. The Methods of Approximation and their Developments, the Methods of Prediction, have been systematically employed throughout the book, and though care and practice are required to prevent errors, not only is there an immense saving of time and labour in their use, but they are the only scientific methods of ensuring absolute accuracy in intricate operations. It has been AUTHOR'S PREFACE. vii the custom in Engineering Text-books, etc. to accept certain approximations as practically absolute, thus commencing with errors, the precise effect of which cannot altogether be foreseen. The Methods of Prediction show clearly the limits of error at almost every stage of the process, and produce results accurate to the exact degree required. The information in the book is a prominent feature, and every endeavour has been made to secure accuracy. My obligations to Tate's Modern Cambist will be recognised as very great by those who know that standard work, but many of the facts have been verified or corrected by personal informants. The Danish Ambassador (M. de Bille) with great courtesy wrote me an exact statement of the condition of the Danish weights and measures, and many London and Provincial Bankers, Stock-brokers, Marine Insurance Agents, Merchants and Brokers have kindly volunteered aid. I wish specially to acknowledge the kindness of Mr. Samuel Montagu, M.P., the well-known financier, in criticising and improving the Section on Exchanges and Exchange operations one of the longest and most important chapters in the book. From other written sources I have naturally derived great help. De Morgan's Methods of Approximation and their Developments have been employed throughout the book. The method of stating a Proportion sum like a pair of scales is derived from Mr. Frusher Howard's Art of Reckoning, and the Method of Linkages is a modified form of that given in D. O'Gorman's Compendious Calculations. Mr. Moxon's monograph on Banking practice has been of great use in the Exchange Section. In conclusion I have sincere pleasure in gratefully acknowledging the encouragement and kindness I have received from Dr. Gow in a somewhat arduous task. S. JACKSON. NOTE. Answers have not been supplied in order that students may follow the well-established commercial plan of doing calculations in two ways to secure correct results. If, however, any schoolmaster or student desires the answers they will be supplied separately in March, price 1/-. Any corrections and suggestions communicated to the Author or Publishers will be gratefully received. The old-type figures in the Courses of Exchange (§ X.) are variable quantities. In Art. 5°, page 23, the number of figures in the divisor should be one more than the rule gives. |