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ARITHMETIC

JN

THEORY AND PRACTICE

LONDON: PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE AND PARLIAMENT STREET

A TREATISE

ON

ARITHMETIC

IN THEORY AND PRACTICE

WITH AN APPENDIX

CONTAINING AN INTRODUCTION TO MENSURATION

BY

JAMES THOMSON, LL.D.

LATE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW

SEVENTY-SECOND EDITION

EDITED BY HIS SONS

JAMES THOMSON, LL.D., F.R.S.

PROFESSOR OF ENGINEERING IN THE UNIVERSITY OF GLASGOW

AND

SIR WILLIAM THOMSON, LL.D., F.R.S.

FELLOW OF ST PETER'S COLLEGE, CAMBRIDGE
PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY OF GLASGOW

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PREFACE

ΤΟ

THE SEVENTY-SECOND EDITION.

THIS Edition has been edited by Professor James Thomson, F.R.S., Professor of Civil Engineering in the University of Glasgow, and Professor Sir William Thomson, F.R.S., Professor of Natural Philosophy in the University of Glasgow and Fellow of St. Peter's College, Cambridge, two sons of the Author. They have taken greater liberty with the original text than other editors would have been entitled to take. Considerable changes and additional explanations have been introduced by Professor James Thomson in the earlier chapters of the work, up to Discount. Several of the later and less important chapters have been abridged. In the chapter on Annuities new information has been introduced, to bring it up to date, according to the practical experience of modern life offices. The chapter on Exchanges, which had been revised many years ago, after the gold discoveries, by Dr. W. Neilson Hancock, formerly Professor of Political Economy in the University of Dublin, has been again revised by him for changes consequent on the depreciation of silver. The whole work has been edited by Professor Sir William Thomson.

UNIVERSITY, GLASGOW: 1880.

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