Four Classics on the Theory of Double-Entry Bookkeeping (RLE Accounting)

Richard Brief

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781134606085
• Edition: 1
• Topic: Business
• Subtopic: Accounting
• Index: Business

Although each of the pieces included in this collection has been cited as an outstanding contribution to the literature on the subject, they are not available in most libraries. Each of them is a classic on the theory of double-entry bookkeeping. Of the nine articles reprinted in this volume originally published in 1984, those by Ladelle, Hotelling and Anton are recognized as being the classic articles on the depreciation of a single 'machine'. Each of these articles was published in a journal that is often not accessible and reprinted here has brought them together in one place. For many years accountants have dealt with depreciation and capital maintenance as a static problem. This volume recognizes its dynamic aspects.

The Algebra of Accounts.

(Written expressly for THE BOOK-KEEPER.)

BY CHARLES E. SPRAOUE.

SCARCELY any art or science can be presented to the mind in more phases than book-keeping. Not only does its application to different kinds of transactions and different branches of trade give rise to an almost infinite variety of forms, all governedned by the same fundamental laws, but those laws themselves appear to different minds in altogether different lights. The laws of debit and credit, by which all book-keeping is carried on, have been stated from a different point of view by almost every writer who has treated upon them. In the practical application of these laws there is not the slightest variation in principle; but in formulating them and stating them to others, we find the atmost diversity. And this is not a hindrance, as might be supposed. The most perfect idea of a statue can be formed by looking at it from all sides, and there is a like benefit in shifting our stand-point in regard to a principle or law in science.

I propose, then, to work out still another way of looking at the principle of debit and credit. Treating the science of accounts as a branch of mathematics (which it is), I reduce it to an algebraic notation: I constantly interpret the algebraic results into common language, and also into the technical, conventional, but often convenient notation used by book-keepers. I show this last to be as truly algebraic as the first; and I teach that no matter what particular form is employed in the presentation of facts, if the equation is preserved, implicitly or explicitly, it is true book-keeping.

But a very limited knowledge of algebra will be needed to follow this explanation. The theory of simple equations is more than enough.

I will now state and demonstrate my proposition.

Thesis. All the operations of double-entry book-keeping are transformations of the following equation:

What I have + what I trust = what I owe + what I am worth or symbolically written.

H + T = O + X.

1. Book-keeping is a history of values.

2. The mathematical side of this history consists in certain equations, in which addition and cancellation are the only operations employed.

3. History and Annals. Annals or chronicles merely relate facts which have occurred; but true history groups together facts of the same tendency, in order to discover, if possible, the cause of happiness and misery, prosperity and rain; so tree book-keeping, being a history, should group together similar values in its equations to discover the causes and effects of Loss and Gain.

4. What is Sought. In the equations of accounts the answer sought or "unknown quantity" is

"What I am worth."

We will represent it by the letter "X."

5. Simple Proprietorship. If I, the subject of the history, trust no one and owe no one; then I am worth all that I have, no more, no less; or

(Equation 1.) H = X.

what I have is the measure of what I am worth; the property actually in my possession is all mine and I claim nothing more· These readings all convey the same idea: but none of them express it as definitely and precisely as the algebraic formula

H = X.

6. The state of things denoted by Equation 1 seldom exists. Usually, or at least frequently, a value-transaction, or exchange of values, is not all completed at the same instant. We buy to-day and pay to-morrow; we sell to-day and receive payment hereafter; we make profits and losses but do not immediately realize them;we "trust"(Credimus) other people are are "owed;" we "owe" others (Debemus), or "get trusted." But we believe that we shall receive our dues from others, and know that we must pay those whom we owe; hence, these debts and credits, these postponed receipts and payments, are all elements in our state and cannot be disregarded. What we trust others with, as well as what we have, is part of our worth, a positive element; what we owe is a deduction from our worth.

7. Proprietorship with Credit. If I trust others with part of my wealth but owe no one, equation 1 becomes

(2.) H + T = X

That is, what I have, added to what is owing me, equalt what I am worth; my wealth is composed of the valuables in my possession, together with what I claim and expect to receive from others, my debtors.

But I may also owe other people, my creditors. Then H + T is not all really mine; I am holding part of it as a trustee (in the literal sense) for those who trust me; this part must be subtracted from H + T to give the true value of X. Let 0 represent the amount of my debts to others; then we have a third equation.

(3.) H + T = O + X

Here we have introduced a negative or minus quantity.

It has been found by experience that it is more convenient to avoid subtraction, whenever it is possible, in book-keeping. It is plainer always to add; when we see two numbers together, we know they are to be added together, and can make no error by choosing the wrong operation. But how shall we get rid of the negative quantity? The answer is, by transposing or removing it to the opposite side. For instance, if this equation is true: 5 - 3 = 2, then it will also be true that: 5 = 2 + 3. That is, we may transpose a minus quantity from either side of the equation to the other, if we make it a plus; or we may transpose a plus, changing it to minus.

Returning to equation 3, let us transpose the "— O" from the left to the right side of the equation, changing its sign to +. We then have.

(4.) H + T = X + O,

which is the fundamental equation,

"What I have + what I trust = what I owe + what I am worth."

8. This fundamental equation gives a mode of representing the financial status of any individual or concern at any fixed time. The mode of representing changes will be considered later.

9. Balance-Sheets.—A statement to the effect

"H + T = O + X."

is called in book-keeping a balance-sheet, or exhibit. It is made in various practical shapes to suit different cases. We will illustrate this with numerical examples. Suppose

H = 10,000 (the dollar being unity); T = 5,000; O = 6,000. Then solving the equation by the rule of algebra, we find

X - 10,000 + 5,000 - 6,000 - 9,000.

The practical way of writing the equation as a balance-sheet would be

H	10,000	O	6,000
T	5,000	X	9,000
	15,000		15,000

That is: We write the specifications of the values in two colu...

Table of contents

• Cover
• Title
• Copyright
• Original Title
• Original Copyright
• Contents
• Preface
• Introduction
• "The Principle of Equilibrium," Double Entry By Single (London, 1818), Chapter III.
• "On the Main Principle of Book-Keeping," The Elements of Arithmetic (London, 1853), Appendix VII.
• "The Algebra of Accounts," The Book-Keeper, July 20, 1880, August 3, 17, 31, 1880.
• The Principles of Book-Keeping by Double Entry, (Cambridge, 1894).