VINNOW VO

EQUATIONAL ARITHMETIC,

APPLIED TO QUESTIONS OF

INTEREST, ANNUITIES, LIFE ASSURANCE,

AND

GENERAL COMMERCE;

WITH

VARIOUS TABLES

BY WHICH ALL CALCULATIONS MAY BE GREATLY FACILITATED.

By W. HIPSLEY.

LONDON:

JOHN WEALE, 59, HIGH HOLBORN.

970

PREFACE.

ALTHOUGH many Treatises on Arithmetic are already before the public, they are, for the most part, open to this objection, that they seek rather to invent labor for the student, by multiplying rules and examples, than to economise it by the most concise methods. The present work, which is not intended exclusively for a school book, nor yet to supersede the more useful of the elementary works already published, will, it is confidently believed, afford advantages to the accountant, merchant, and private student, which are not to be found in any other.

It is said, "that railways have been used in this country for more than two centuries:" the recent and rapid extension of the system is a proof that the practical application and improvement of well-known arts is often of more value than an absolutely new invention. In like manner, the simplest form of fractional arithmetic, that of decimals, though so ancient, and to the present day so universal a branch of school-boy lore, has so unaccountably fallen into disuse as to be all but forgotten in after years.

Another powerful motive for increasing in the public mind an interest in this mode of calculation is, that we thereby diffuse a knowledge of the great commercial benefits to be derived from an universal decimal scale of money, weights, and measures. Thus, we may ultimately obtain some parliamentary enactment which may rescue this country from the disgrace of being behind some other nations in the practical application of general principles.

By giving only one or two examples, as a formula for each kind of calculation, we are enabled so to extend the work as to include Compound Interest, Annuities, Life Assurance, and almost every computation that comes within the sphere of ordinary arithmetic; thus comprising in one small volume, of which the tables alone are worth the cost, what has hitherto been diffused through many large and elaborate works, at a proportionally large expense.

Every calculation in this work is reduced or reducible to one form—that of a simple equation; it has been the aim of the writer so to elucidate this method, that the accountant shall find no difficulty in applying the principle to any question whatever, though its formula be not found in these pages. By means of the decimal tables alone, which have never before been published at a moderate price, a vast amount of labor may be saved. All fractions of English money and time are already reduced to decimals in Tables I. and II., to which is added a new table of the decimals of the hundredweight, and the usual tabular values of compound interest and annuities at various rates per cent. The facilities of the decimal system may thus, in some degree, be anticipated.

These advantages, together with that of reducing the innumerable rules of common arithmetic to the simple form of an equation (without assuming the merit of a new discovery), form, at least, an unique combination, affording all the facilities that could reasonably be expected, even from a new calculus, applicable to the ordinary purposes of commercial and scientific investigation.

The great extension of prudential assurance against death and the various contingencies of life, which has recently taken place, renders a knowledge of this philanthropic subject almost a necessary part of a liberal education. It is, moreover, desirable to prepare the public mind for the discussion of the great question of financial reform, forced upon

us by the necessities of the times; this can be accomplished only by popular treatises on the higher branches of calculation, of which it is hoped the present work will prove neither the last nor the best.

It is disgraceful to our boasted civilization, that pauperism and destitution should be the lot of any but the incorrigibly vicious and criminal; for it is well known to those accustomed to the calculation of annuities, that the poor rates might be entirely extinguished by an extension of its principles to the labouring classes.*.

The profitable employment of the masses is now an European question. Though, on the Continent, the attempts to realize it may assume the distorted forms of "socialism” or communism, in themselves impracticable, it requires little sagacity to predict that the true solution of the problem, the universal scheme of co-operative labor and economy of capital, must ultimately be founded on principles developed from those of life assurance and annuities.

The unprecedented success of the Industrial Exhibition of 1851 is a striking illustration of the wonderful effects of cooperative labor, or capital, which is the result of labor, when judiciously applied to a useful end.

The art of arithmetic and the art of war, are, unfortunately,

very closely connected. When money has been demanded for the purpose of destroying our fellow men, under the plea of avenging national honor, restoring the balance of power, natural enemies, or any vulgar delusion of the day, there has hitherto been little difficulty in raising loans to any required amount, to be repaid in any way, or in no way, as posterity might think proper. There can be no greater proof than this of financial ignorance, equalled only by moral imbecility; for a mere tithe of those enormous sums, which have been utterly wasted by an art which belongs to barbarous ages,

*See "Arithmetic of Annuities," by Edward Baylis.