UC-NRLF ! $B 3ft 37^ ■ fffSlfei THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA HENRY RAND HATFIELD MEMORIAL COLLECTION PRESENTED BY FRIENDS IN THE ACCOUNTING PROFESSION ?&?&&'* Digitized by the Internet Archive in 2007 with funding from Microsoft Corporation http://www.archive.org/details/bookkeepingbymacOOthornricti BOOK-KEEPING BY MACHINERY A Treatise on Office Economies BY Erwin W. Thompson Published By The Author 1906 NEW YORK COPYRIGHT 1906 BV EIRWIN W. THOM PSON BOOK-KEEPING BY MACHINERY. Hf & ts TS PREFACE. This book has been undertaken for the purpose of point- ing out to managers of large offices the easily possible econ- omies attainable by the use of mechanical aids to accounting. Every manufacturer of apparatus issues a certain amount of literature, describing the uses and advantages of his par- ticular devices or methods, without reference to their relation to other apparatus. It has been the Author's intention to here review, in the most impartial manner, the principal means of mechanical computation now on the market, and to describe comprehensive practical methods for the use of sets of this apparatus, each piece in complementary relation to the others; and to point out just what sorts of apparatus are applicable to certain typical conditions. It seems proper here to state that this book is not an ad- vertising medium, and that I have not received, and do not expect to receive any compensation whatever for making any statement about any apparatus or method herein described. The plates from which the illustrations are printed were made for this work, with all trade names and names of makers omitted, and no such names have been mentioned in the text. ERWIN W. THOMPSON. New York, Jan. I, 1906. M51^03 CONTENTS. CHAPTER I— INTRODUCTION. CHAPTER II— GENERAL PRINCIPLES. Multiple Operations. The Unit Document. The Uni- form Blank. Schematic Classification. Multiple Service Documents. Cross Tabulation. Transposed Headings. Required Limit of Accuracy. Decimal Points. Constant Factors. Inter-columnar Ledger Accounts. Addition. Subtraction. Multiplication. Division. Reciprocals. Hand Finishing of Machine Work. CHAPTER III— ADDING MACHINES. Listing and Non-listing Machines. Use of Listing Mach- ine for Making Permanent Entries. Split Key Boards. Frac- tional Key Boards. Multiplication and Division on Add- ing Machines. CHAPTER IV— THE ELECTRIC TABULATOR. Tabulation of Statistics in Different Groups From One Set of Record Cards. CHAPTER V— THE PLAIN SLIDE RULE. Engineering Instrument Applied to Accounting. Ap- proximate Unit Costs, Percentages and Pro-ratings. CHAPTER VI— THE CYLINDRICAL SLIDE RULE. An Instrument of Greater Accuracy Than Plain Slide Rule. CHAPTER VII— MULTIPLYING AND DIVID- ING MACHINES. Perfect Accuracy Up to Sixteen Figures. CHAPTER VIII— CALCULATING TABLES. Extended Multiplication Tables to Suit Any Desired Condition. CHAPTER IX— BILLING AND CHARGING. Machine for Making the Bill and Charge at One Opera- tion. Department Store Systems. Adding Attachment to Billing Machines. Back Order System. CHAPTER X— AUTOGRAPHIC REGISTER. Methods for Making Multiple Autographic Copies With- out Handling Carbon Sheets. Check Registers. CHAPTER XI— ADDRESSING MACHINES. Pay-roll Systems. Mailing Notices. Gas and Electric Bills. Dividend Lists and Checks. Stencil Card Index. CHAPTER XII— TIME STAMPS. Workman's Time Cards. Decimal Time Dials. Elapsed Time Recorder. Calculated Value of Time. Telephone Time Record. CHAPTER XIII— LOOSE LEAF BOOKS. Ledger Binder. Transfer Binder. Flexible Leaves. Self- indexing. Index Tabs. Card Ledger. Loose Leaf Pocket Books. CHAPTER I. INTRODUCTION. Much progress has been made in the application of modern methods to the general organization and conduct of the office as a whole; but these relate, for the most part, to methods of handling orders, bills, correspondence, &c, and have but little to do with the actual work of book-keeping. Some thought, however, has been expended on the arrange- ment of the work, cutting out of duplications, and the use of loose leaf books, which have, in the aggregate, saved consid- erable labor. Supplementary to these general methods, is a field practically unexplored, namely: the actual performance of book-keeping and auditing work by machinery, in the same sense, and following the same lines as writing letters by ma- chinery. It is the purpose of this work to point out the possi- bilities of mechanical aid to book-keeping, and to give large numbers of concrete examples, which may be taken as types, suggesting still further extension of the idea to fit special cases. Book-keeping consists principally in recording the facts of a business, as they transpire, and in so arranging and sum- marizing these facts that they may give the proprietors of the business correct and comprehensive information in regard to any phase of the work. Any method of book-keeping which tends to yield further information about the business, without the addition of undue expense, is certain to yield good re- sults. 2 INTRODUCTION. Invariably, the introduction of improved and cheaper methods of doing any one thing, increases the amount of that thing which will be performed. Stenography and type-writ- ing generate countless thousands of letters which, otherwise, would never have been. Similarly, the employment of easy methods of recording and tabulating business facts will lead to much more of this work, which, in turn, will show Proprietors more about the many sides of their business, and lead them to shape policies from day to day to suit conditions as they develop. Proprietors and heads of departments of large enter- prises have great opportunities for reducing the cost of work in their accounting and statistical divisions. Accountants, themselves, are mostly so busy with their routine work, that a halt for a few days to look into a new scheme seems to them to involve the falling behind in their duties, with no immediate hope of reward. There is always plenty of room for improvement, and wherever there is a large office force, it will be found advan- tageous to detail one skilled man to thoroughly investigate the idea of book-keeping by machinery, and to find the parts of his present work which may be better and more cheaply done by employing mechanical aids. The selling end of a business may be said to progress by steps (1 ) soliciting orders, (2) receiving and recording them in the office, (3) filling them, (4) recording and tabulating the results in a way to be easily interpreted. Most large business houses now have perfected methods of soliciting orders, and making the primary records; but many of them perform a large amount of needless work in the subsequent steps, and do not in the end reach perfection. Book-keeping traditions have a great deal to do with this condition. Book- INTRODUCTION. 3 keepers have been trained to enter transactions in a certain way on some form of journal, and tren post them to the ledg- er. Since this training leads to correct results, Proprietors generally hire enough men to perform all these operations in the conventional manner, and cease to think much more of it. One of the first things to examine in any system of labor saving, is the duplications. Wherever there is a performing of the same operation more than once, there is always some possibility of saving. This principle has been well recognized by the "system" promoters, in arranging carbons, so that at one writing there is made a number of documents, (say the order to the factory for the goods, the partial invoice, and the partial charge for same.) But there is one subtle form of duplication which usually escapes the most vigilant "system," viz: multiplying, dividing, adding, subtracting. There are books extant, which are, in effect, extensions of the multiplication table in directions to suit certain trades and conditions. In the purchase of cotton in the Southern States, these books are widely used. One of the earliest pub- lications of this sort was designed especially for this trade. A bale of cotton weighs from 300 to 650 pounds, and sells from four to twenty cents a pound, varying mostly by sixteenths of a cent. It is therefore very easy to make a book, each page of which is headed with some cent and fraction of a cent, and with one column on the page filled with pounds from 300 to 650, and another column with values of the whole bale. A cotton buyer turns to the proper page, and reads off the amount of money to pay for the bale, instead of calculating it. This same method ought to be applied to every business of magnitude. If the book is not already published to suit the particular condition, it would pay any large concern to set about making such a book for its own use. All extensions 4 INTRODUCTION. on invoices should be read out of the book, instead of being multiplied by hand, over and over again by one clerk and then checked in the same way by another. Listing-adding machines ought to be used as an integral part of book-keeping, forming original and duplicate records, and automatically making the footings, all in one operation. Monthly statements of accounts should be made in this way, and these monthly mechanical footings utilized in the ledger, and trial balances taken off with this machine. Reports on sales should be listed on this machine, according to territory, according to salesman, or according to any other desired clas- sification. They may be run through successively in any de- sired order, with great ease and rapidity, and are always self- proving. Average prices received or paid, average expenses per unit, or "per" anything, should be read from a slide rule, in- stead of duplicating the laborious operation of division. This instrument is so simple and so quickly mastered, that, once put into use, other possibilities develop and suggest them- selves, until it becomes a pleasure to instantly read off any possible "per" which may be unexpectedly required. Finally the use of the above mentioned aids, and sundry similar ones, to perform their individual functions, leads to the use of them in endless combinations to facilitate all possible book-keeping operations. Promptness in furnishing informa- tion from the books is the ultimate end; machinery is the newly recognized means. CHAPTER II. GENERAL PRINCIPLES. The universe is held in equilibrium by centrifugal versus centripetal forces. This book aims to be a centrifugal force to counter-balance the well-known centripetalism of book- keepers. It is hoped that true progress may be the resultant. Old and well-tried schemes should be maintained against all new comers, until the new comers demonstrate their advantages. But it is not wise to sit still and claim that any present method may not be improved. The only way to make headway with a new idea is to try it, and not argue against it, simply because it is new. It may require some time and patience to investigate the new, whereas the old will go along in a rut and accomplish things without much thinking. But a small amount of thinking on a new scheme may save a large amount of work over the old way. Book-keepers have vast opportunities to advance themselves if they are willing to devote some time to the subject. The man, who devises a way to save labor in an office, is not the man who is dispensed with in the saving. The men who are willing to help along the new methods are the men who will be re- tained to work them. Mechanical means of book-keeping have arrived. The young man who goes into book-keeping now cannot evade the issue : he must learn the methods in some way. He can not learn it by ignoring the literature on the subject, or by imagining that the old methods are good enough. 6 GENERAL PRINCIPLES. Many book-keepers who do work in the old way with the greatest ease, find difficulty in acquiring the use of the new methods; and they become discouraged if they cannot grasp the whole of a new idea at once, and immediately put it into execution, and save time over the old method in which they have had years of experience. This should not be expected. One must learn to read a new language. Book-keeping by machinery is essentially a matter of reading. The machine does the work, but the man must read the result. A Type- writer must learn to read the keys on the instrument, and know where to find the letters with facility. The Operator of an adding machine must learn to quickly find the keys and to read the result. These are easy, but they must be learned. Reading the slide rule is but little more trouble — it is just more unusual. Reading calculating tables is easy; but all of these things naturally require some practice, to pro- duce the most efficient result. The beginner should not be discouraged if he finds that all the schemes cannot be mas- tered in one day. It is safe to say, that after one day's faith- ful attention to any one of the mechanical devices herein de- scribed, the beginner san save time over the old methods. Every day's use brings greater facility, and finally produces the firm impression that book-keeping by hand will soon be as unusual as letter-writing by hand. The difference between "manufacturing," and simply making an article, may be said to consist in producing it in quantity, by systematic methods and machinery developed for the purpose of making duplicate parts. Manufactured articles are more uniform in quality, cheaper, and usually better than those individually made. The reason lies pri- marily in the fact that many similar articles are produced at once. GENERAL PRINCIPLES. 7 MULTIPLE OPERATIONS. Book-keeping by machinery is manufacturing work, versus plain hand work. To make such manufacturing most profitable it should be applied to large amounts of similar work, so that the greatest advantage may accrue from mul- tiple operations, or the making of many practically duplicate pieces of work under a system especially suited for doing that particular work. Small offices, doing general work, and employing from one to three men, usually equip themselves with book-keepers and appliances fitted for doing any work that comes, just as it comes. Such offices generally cannot better their condition by the use of much book-keeping machinery; but they may often make great improvements, by following up by hand, some of the general principles enunciated for machine work. Assuming that there is a large amount of book-keeping or other office work to be done, the first essential in reducing it to a manufacturing basis, is to segregate the several sets of multiple operations, and arrange to do each set in a way espe- cially adapted to itself, and by machinery designed for that class of work. In its ultimate analysis, the work to be done in book- keeping is addition, subtraction, multiplication, division; and hence these would seem to be the natural cleavage lines for the division of labor. But this is only partly true. The way in which the figures originate, and the final purpose for which the primary operations are performed, will generally deter- mine the method of differentiating the groupings. These groupings are more likely to follow the mechanical means by which the work is to be done, than to follow the primary oper- ations themselves. Therefore, the chapters of this book arc divided mainly according to the mechanisms, while the pri- « GENERAL PRINCIPLES. * mary operations are commented on in the sub-headings of this chapter. THE UNIT DOCUMENT. Bound books were formerly the unit in the book keeping system. When goods were sold, they were entered in the day-book, one bill after another, and figured out, and then copied on the invoices for the customers, and then transferred into the books of various sections or departments, and finally posted to the various customers' accounts. Then came the loose leaf book, with the implication that one leaf is the unit, with as many items as may be entered on this leaf. The leaf is distributed to departments or geographical divisions as might be required. Then came the "bill and charge" system, with the idea that the customer is the unit, and that at the same time the bill is being made against him, a carbon copy may be made and treated as the original charge against him. Then came the Department Store scheme of making every little sale slip an accounting unit, and posting these slips to a state- ment ledger, or a book of perforated leaves, so that, at the end of the month, the customer's bill is made for the entire month's business, and the carbon is the ledger record. Thus, progress is made in one direction by the consideration and the re-consideration of the question — "what is the unit docu- ment?" This question may be re-opened with advantage every time a new scheme is to be considered. In a large business, requiring many statistics, arranged variously, according to salesmen, to geographical location, to brands of goods, to months, to manufacturing branches, &c, the smaller the unit document, the more easily it may be tabu- lated under one classification after another. GENERAL PRINCIPLES. 9 THE UNIFORM BLANK. Paper and printing are cheaper than time and errors. No progress can be made in systematic mechanical book-keeping without recognizing the importance of standard size papers, and standard printed forms for collating and con- solidating records of a similar nature. Every office ought to fix upon a standard size sheet for loose leaf binders, and for general filing. This facilitates business, and makes the work more neat. It is possible to so arrange almost any data in such a way that it may be disposed to advantage on one or more standard sheets. This is wonderfully illustrated in the case of the United States Patent Office, where they re- quire all drawings, of whatever nature, and of whatever ob- ject, (from a pencil to a suspension bridge) to be drawn on one or more sheets 1 inches by 1 5. A good handy standard in an office is 8 1 -2 x 14 inches, which is the size of regular journal paper, and which cuts without waste from regular cap paper 1 7 x 28. When the standard size is determined upon, a large number of sheets should be ruled with vertical and horizontal lines to suit the adding machine spacings. These may then be printed with headings at the top of columns, and at the sides for various purposes in consolidating and tabulating. In the case of a Central office controlling several Branches, the names of the Branches should be printed on some forms at the head of the columns, and on some at the sides. An in- variable rule should be established to list the Branches and other important classifications in the same order on all docu- ments. This facilitates all consolidations and tabulations, whether mechanical or otherwise, and enables large amounts of work to be done by simply calling and checking b>" amounts only, no names being used. io GENERAL PRINCIPLES. A common example of this practice is the way a tailor takes measures for a suit of clothes. He takes two or three dozen different measures, and calls the inches from his tape line to his clerk, who sets them down systematically in his book, with never a hint from the tailor, as to where the meas- ures belong. SCHEflATIC CLASSIFICATION. Ledger indexes are commonly arranged alphabetically, and sub-divided after the manner of a lexicon or a city direc- tory. The introduction of loose leaf ledgers has revolu- tionized the whole subject of ledger indexing. Pages are now inserted in alphabetical positions in the book, and these positions marked with various styles of tabs. This case of classification in loose leaf ledgers has lead to other kinds of subdivisions, such as by cities, by departments, &c. Some- times, different colored leaves are used to denote certain things. One row of tabs may subdivide across the side for one scheme, say alphabetical ; across the top for another, say geographical; and colors may subdivide for something else, all without one scheme interfering with another. Schematic classification may be carried to an almost unlimited extent, in the case of the card index, where tabs, colors, notches, punchings, guide cards, and separate drawers may all be made to mean something distinctive. In making up unit documents, such as inventories, cost sheets and orders, it is often advantageous to adopt a distinc- tive color for each department of a business. MULTIPLE SERVICE DOCUMENTS. Carbon copies of invoices are quite commonly made to do duty as factory order, shipping document, &c. Pursuing this idea a step further, it is often practicable for a Branch Office to utilize, as part of their accounting system, some of GENERAL PRINCIPLES. n the documents received from Central Office, and vice versa. For example, Central Office bills out goods, from day to day, to a Branch. The most economical practice in Central Office is to file carbons of the bills until the end of the month, and then totalize on an adding machine sheet all its charges against each Branch, sub-divided and sub-totaled in such a way that the Branch may be debited by one entry for the grand total, and the various sales or other revenue accounts credited by sub-totals, as desired. A carbon copy of the adding machine sheet is sent to the Branch. The Branch files invoices as re- ceived during the month, and at the end of the month checks these against the copy of charge sheet rs^eived from Central Office. This sheet is then filed in a loos- leaf binder as a journal page, crediting Central Office for the grand total, and debiting its sundry purchase account or expense accounts with the sub- totals. Documents in transit at the end of the month and other sundry discrepancies, must of course be re- conciled and taken care of in the usual way. CROSS TABULATION. Branch Offices reporting to the Central Office, say on the costs of operating, will report one department under another in a vertical column for easy adding. But the Central Office will want to tabulate and find the total cost of all the work in each department, as well as the departmental and total cost at each Branch. This consolidation is most easily ac- complished (either by hand or machine) on a form with de- partment headings across the top of the sheet, and the names of the Branches down the side. The footings on the original sheets are checked as they stand. The items are then trans- ferred to the consolidated sheet, as above, (totals and all), when the cross-tabulation may be easily performed in vertical columns. COST SHEETS AS SENT IN FROM BRANCH OFFICES. Albany Allegheny Bing'ton Can'daig'a Catskill Delaware Logging 1486.28 810.12 1340.12 65.75 314.17 972.72 Teaming 610.18 200.05 187.10 310.60 614.70 Sawing 1207.14 1200.00 918.40 378.80 604.17 1000.00 Lathing 806.10 200.07 110.80 86.10 604.44 Shingling 116.00 740.13 84.40 36.90 Butting 59.60 100.40 110.80 37.20 75.40 50.50 Planing 907.00 217.13 317.90 578.00 110.10 296.30 Stacking 214.20 88.90 108.84 112.00 200.34 110.17 Dry Kiln 62.00 37.30 95.60 83.84 100.00 246.38 Total 5468.50 2853.97 3631.79 1637.89 1800.88 3932.11 Fig. i. GENERAL PRINCIPLES. 13 Fig. 1 shows a list of costs in vertical columns, as sent in by Branch offices. These are not to be copied on a form as this table would indicate; but the figures are made to as- sume this shape by slipping one cost sheet under another, care- fully in line, so only the figures will show. These figures are called out from the horizontal lines, to the adding machine operator, who has a sheet ruled to fit the machine, and printed with departmental headings at top of columns (in- stead of at the sides, as in the individual sheets) and the names of the Branches at the sides. As the figures are called from left to right, they are set down by the machine from top to bottom, as shown in Fig. 2. This sheet is ruled for a six column adding machine. As there are more than six depart- ments, the form is duplicated on the bottom part of the same sheet. When all the figures are called off, including the Branch totals, the whole work is proved by copying the departmental totals in another column, headed "proof." If desired, this proof column may be set down on one of the regular blanks, from the Branches. This will then show on the regular printed form, the cost by departments for the whole system. The cost sheets, sent in by the Branches are, themselves the result of consolidations at the Branch offices, of a variety of component parts, such as pay-rolls, materials, fixed charges, &c. If the theory of unit documents is carried out to the full, the workmen will have individual time cards, on which the particular work being done is marked, so that the cards may be collected and sorted according to men, and then ac- cording to occupation or department. If any of this sub- divided information is to be forwarded to Central Office, it may be forwarded on cards, so that Central Office may sort and re-sort for consolidations under various headings. COST SHEETS CROSS TABULATED FOR CONSOLIDATION. Logging Teaming Sawing Lathing Shingling Butting Albany 1486.28 610.18 1207.14 806.10 116.00 59.60 Allegheny 810.12 200.05 1200.00 200.07 100.40 Bing'ton 1340.12 918.40 740.13 110.80 Can'daigua 65.75 187.10 378.80 110.80 84.40 37.20 Catskill 314.17 310.60 604.17 86.10 75.40 Delaware 972.72 614.70 1000.00 604.44 36.90 50.50 Total 4989.16 1922.63 5308.51 1807.51 977.43 433.90 Planing Stacking Dry Kiln Total Proof Albany 907.00 214.20 62.00 5468.50 4989.16 Allegheny 217.13 88.90 37.30 2853.97 1922.63 Bing'ton 317.90 108.84 95.60 3631.79 5308.51 Can'daigua 578.00 112.00 83.84 1637.89 1807.51 Catskill 110.10 200.34 100.0U 1800.88 ! 977.43 i Delaware 296.30 110.17 246.38 3932.11 | 433.90 ! j 2426.43 1 834.45 1 1 625.12 i Total 2426.43 1 834.45 625.12 19325.14 |19325.14 Fig. 2. GKNERAL PRINCIPLES. 15 The cost sheets, as shown in Fig. 1 , might have been sent forward from each Branch on cards; one card for each department, thus enabling Central Office to sort as desired; but in cases of this particular kind, where no more than one classification is desired, the sheets as shown are the most con- venient, particularly as each Branch must in any case, make up a total for its own use. REQUIRED LiniT OF ACCURACY. It is important not to do any more work on a problem than that particular problem requires. In book-keeping, itself, the accuracy in addition and subtraction must be absolute ; but in making reports, statistics and tabulations to exhibit and interpret the results, it is fre- quently sufficient, and even desirable, to show figures to only a limited degree of accuracy. For example, percentage may be required in some cases to the nearest whole number, as 76 %, while in other cases several decimals may be required, as 76.48%. In computing such work, it is obviously unneces- sary to carry out the division to four places of decimals if only two are required. This general principle applies to work done either mentally or mechanically ; for, as a rule, the more accuracy required of a machine, the more time and skill necessary to operate it. DECiriAL POINTS. Whether work is to be done mentally or mechanically there is great advantage in learning to place the decimal point in the final result by inspection, rather than by following it through all the operations. In most cases of routine work, where the results of a series of allied operations are visibly comparative, the Oper- ator knows, within a limit of 90%, what the result should be. 16 GENERAL PRINCIPLES. For example, if he were working out the average cost per pound of the constituent expense accounts in producing factory work, he would have, say, a production of 10,897 pounds, and an expenditure of $374.78 for labor. By divid- ing, without reference to decimal points, he would get 344. By inspection, he could see at a glance that one cent per pound would have been $108.97, and hence he points off his answer in cents as 3.44. This habit soon becomes auto- matic, especially if one man is employed in working out such results continually. He would know without conscious thought that in his particular line, labor costs would not be $3.44, or 34.4 cents, or .344 cents per pound. This im- portant faculty of sub-conscious decimalization is practically universal, though often not appreciated or used. CONSTANT FACTORS. To avoid duplication of work, and to properly group problems together for advantageous solution, any calculation that is common to more than one problem should be per- formed only once, and that result applied to the various prob- lems, instead of working it out separately for each one. Of- ten, in a series of problems, there are common factors which are not immediately noticeable, on account of the fact that they do not come in the same order, or are not separately set out. For example, in importing a lot of silks, at prices vary- ing from three francs to forty francs per metre, it is required to work them all out in cents per yard. The primary method is to reduce 3 francs to cents, say 58 cents, and reduce the metre to yards, say 1 .09. Divide 58 by 1 .09, and find the price per yard 53.2 cents. This is as short as any other way for working one example. But if there are several examples involving francs and metres, the short way is to GENERAL PRINCIPLES. 17 find how many cents per yard corresponds to 1 franc per metre, say 17.75 cents; then this is a constant which may be multiplied by any other number of francs per metre, to reduce to cents per yard. This is a starting point toward a calculating table, which may be constructed for reading cents per yard directly opposite any number of francs per metre. Many problems of this kind occur in inter- national business. Sometimes interior freights must be paid on goods to the seaboard in cents per 100 pounds, ocean freight in shillings per long ton, foreign interior freight in marks per 100 Kilograms, while the foreign sale is finally made in marks per metric ton. All of this might have to be reduced for entry on the domestic books to dollars per short ton of 2,000 pounds. All of these constituent parts should be re- duced to a constant factor, so that a quotation in marks per metric ton in the foreign country, may be reduced in one operation or one reference to a table to dollars per 2,000 pound ton at the point of shipment. INTER-COLUriNAR LEDGER ACCOUNTS. Columnar cash books and special journals have become quite common, for the purpose of sorting out and aggregating certain accounts on the primary books of entry, rather than on the ledger. These books save much time in posting, and conduce to a quicker trial balance. Another convenient scheme of this sort is the columnar ledger, in which a group of allied accounts are collected under one general head. For example, the books of a General Office may show the ex- penses, sales, &c, of several Branch Offices. It may be de- sirable to show a sub-division of these expenses into, say, Office Expense, Salary, Insurance, &c. One page of the ledger may be used for all the expenses of Branch A, in the 18 GENERAL PRINCIPLES. outer column. The details may be shown in a series of spe- cially ruled inner columns. If the ordinary ledger page is not broad enough, it is perfectly proper and feasible to use the two opposite pages for one account: the left page for all debits, and the right for all credits. The expenses of Branch B are shown collected in the same way on another pair of pages. Sales may be sub-divided for various commodities or grades in the same way. This scheme is especially val- uable for handling expenses or sales which are to be pro-rated on any basis. The totals may be posted first in the outer column, and the pro-rated division distributed through the inner columns at leisure. ADDITION. Most of the problems of addition in book-keeping of the conventional sort, are on columns of figures entered in books by hand. Most good book-keepers can mentally add such columns faster than they can be done on any adding machine. Therefore where such conditions necessarily ob- tain, an adding machine would be of no great advantage. But the important point here is, do the above conditions often necessarily obtain? It will be abundantly shown in later chapters that, having a large amount of addition to do, the antecedent condition of the figures to be added may be al- tered from the traditional course so that the adding machine will be of the greatest advantage, in that it may be made to not only add the figures, but to enter them in the books them- selves. It is on loose leaf documents, and cross additions, and figures not already listed in vertical columns that adding ma- chines are of the most use. If figures originate on loose docu- ments, a machine which will list these facts on regular size GENERAL PRINCIPLES. 19 paper, and automatically add them will save the work which has hitherto been considered necessary in writing them by hand in a book, and then adding them. SUBTRACTION. There is usually no advantage in using a machine for adding two numbers, however they may be situated. Sub- traction involves but two numbers, and, while the mental operation of subtraction is considered harder than adding, it is of no general value to subtract by machinery, though it is possible to do it on an adding machine. MULTIPLICATION. Children learn the "multiplication table," and, through- out life use the units from that limited table to compute prob- lems containing the largest possible number of digits. Whenever two large numbers are multiplied together, it is rare that the same two digits are not multiplied together several times in the course of the operation. In making out invoices, it is exceedingly common to find the same unit price prevailing on many documents, and it is not uncommon to find the same quantity also; so that actually the same calcu- lation is often made, over and over again in the course of a day. Even more often, the same multiplier is used over, though on different multiplicands. These are the cases where calculat- ing tables are needed. These are books of tables, each page of which represents some unit price as a multiplier, with all necessary quantities in columns, as successive multiplicands, having the correct results set opposite. Multiplication may be performed on the adding ma- chine; but it is usually more tedious than addition, and is not commonly done. There are some expensive machines now •on the market which perform multiplication and division very 20 GENERAL PRINCIPLES. expeditiously; and they are now in limited use by some con- cerns having large amounts of such work. In statistical work, it is frequently required to have cer- tain multiplications approximate only. In these cases, the slide rule is useful. DIVISION. In routine book-keeping work, it is seldom required to do division, and hence book-keepers are not generally as pro- ficient in this operation as in addition, subtraction and multi- plication. Book-keepers, however, very often have to make up statistics involving a large amount of division, most of which is needed with only a certain amount of approximation. Examples are calculations relating to percentage, and to average unit costs. The instrument especially adapted to this work is the slide rule. Calculating tables may also be used for this work, especially in connection with reciprocals. There are also some special computing machines, which will do this work to any required degree of accuracy. RECIPROCALS. The reciprocal of a number is 1 divided by that number. For example, 1 -8 is the reciprocal of 8, and 8 is the reciprocal of 1-8 or .125. Disregarding decimal points, 8 and 125 are reciprocals. It is obvious that (disregarding decimals) multi- plying by 8 gives the same results as dividing by 1 25. There- fore, we may elect to perform the multiplication or the di- vision, according to which happens to be the easier. Division being more difficult than multiplication, it is often useful to multiply by the approximate reciprocal of a number instead of dividing by the number itself. If there are several accounts to be divided by the same number, we may find the reciprocal of the divisor, and use this as a constant GENERAL PRINCIPLES. 21 multiplier, or we may use this reciprocal as a multiplier in a calculating table. All calculating tables ought to have the reciprocals of the multiplier stated at the top of the page; but in tables where this is not the case, the reciprocals may be found from other tables, and written at the top of the multiplying tables. HAND FINISHING OF ilACHINE WORK. All work done by machinery must necessarily be in- spected and given finishing touches, and finally assembled by hand. Similarly, it must be expected that any mechanical device for office use will not absolutely finish up the whole job without intelligent supervision, and oftentimes some addi- tional hand work. The central idea in book-keeping by machinery is fhe adaptation of mechanical methods to accomplishing the bulk of the time-consuming, and error-breeding operations. The remainder must, as before, be closed up by careful indi- vidual attention CHAPTER HI. ADDING MACHINES. Primarily, adding machines were made to add. As a second thought, they were made to list, as well. Both the listing and the non-listing machines have their special uses. Fig. 3 shows a machine of the non-listing class. It has, besides the usual set of result dials, an extra set of dials to indicate the last amount added. For example, to add" 461,734.61 and 138.52. When the first amount is set up, it will appear on both dials. When the second amount is set up, this amount, 1 38.52, will appear on the upper set,, and the result 461,873.13, will appear in the lower set. This extra upper set is useful in detecting errors, and in keep- ing the place, in case the Operator is disturbed. In operating most non-listing machines, nothing is necessary but to depress the proper keys, while with a lister, it is also necessary to pull a lever. Thus a non-listing machine is usually more rapid and less laborious to operate. In many cases it is more de- sirable on this account. On the other hand, there is no way to check the result, except to do the work a second time. Some Operators claim to be able to do the work twice on this class of machine with less labor and time than it takes to do it once on a lister. In either case, the actual number of entries that can be made in a given time depends somewhat on the origin of the figures, that is, whether they are on loose slips, or scattered on a sheeet, or are called out by an assistant. It is possible in favorable cases, and with very expert Operators, to make 5,000 per hour on a non-lister, and 2,500 on a lister. Half this speed, however, is good work, and greatly ahead of mental work. NON LISTING ADDING MACHINE. fy '8, V8) © © © ' 8 .' :, (5 '(v 'ij, © © © 13 ? ' 4 s; ^ J . r >, © © © 4 ^ t> n J 4 © ©© i i ,j) !3y © © © 7 2J u 2j 7 2j © © © ^ 7 g "U '1- »iy © © © Fig. 3- ADDING MACHINES. 25 The choice of a machine must generally depend upon whether only the final result of the addition is wanted, or whether there is also required a permanent list of the items. A large part of the hard work in book-keeping consists in listing and adding. To apply machinery to this kind of work, it is only necessary to have an adding machine which will list and add on standard size sheets of paper, that may be filed in a loose leaf binder, and become a final book of record. Most of the wasted work of book-keeping — and there is a vast amount of it — is in the crowning evil of doing the same thing twice, when once is actually better. Duplicating the ordinary arithmetical problems (adding, subtracting, mul- tiplying and dividing) is the most common, and, at first sight, necessary case of this. As will be shown in other Chap- ters, it is frequently, if not generally, unnecessary to make mul- tiplications even one time — being better to read the result from a book of tables. Additions are being duplicated, first, last and all the time in all books of account, as at present kept. The book of original entry is painfully added by hand, as it were, first up and then down, to make sure. The totals are carried forward to the end of the month and posted to the ledger, where these totals are added to other entries, first up, and then down, to make sure. These totals of each account are added on the trial balance, first up and then down, and then up again, and then not sure. To apply an ordinary adding machine for alleviating these troubles, as existing in ordinary book-keeping, is to in- crease the time consumed ; for it may be assumed as a maxim that if entries are already made in vertical columns, it will require more time to add them on a machnie, than by an ex- pert, mentally. In some cases, it might be possible and de- 26 ADDING MACHINES. sirable to use an adding machine, in the hands of a cheap Operator, instead of taking the time of an expert book-keeper ; but under ordinary circumstances, this would not pay. Real assistance in this line is to be looked for from ma- chines which will list or type-write the figures as they are set up on the machine, and to do this on sheets which will form the original entry, so that, instead of first writing the entry in a book, and afterwards adding it by hand or machine, the machine does the original writing and adding at the same time. This is the general principle, and is capable of wide application, to suit the most varying conditions, covering prac- tically any business which is conducted on a scale large enough to make worth while, the consideration of any labor- saving device for accounting. In a selling establishment, the selling transaction may be said to start with the Customer's order. The route from here to the ledger is vastly different in different establishments. Typical modern cases are: 1 . Write the order with carbon duplicating sheets. Use one copy for factory shipping order, one for stock clerk, and one for the foundation of the invoice. Charge the goods in a sales journal. Post from the sales journal to the ledger. 2. Write the order with carbon duplicating sheets, one of which is bound in a book. When invoice is completed over the carbon, the bound sheet serves as a page in the sales journal. 3. Perform the foregoing operation with a billing ma- chine designed to move the bills with reference to the sales journal sheet, so that an entry may be made on every line of the page. LISTING ADDING MACHINE. Fig. 4. ADDING MACHINES. 29 The last two methods are excellent time-savers ; but fre- quently, the last method is not applicable, on account of lack of room for details. The second method requires too many pages of the sales journal, and hence a great deal of adding and carrying forward of the totals. A listing adding machine removes this objection, and renders this method nearly per- fect. It is immaterial whether the charging copy of the bill is a loose leaf, or is bound in a book, with one or more charges on a page. At the end of the month, each item is called out to the adding machine, which lists the amounts on a standard size sheet, and finally furnishes the total for posting to the credit of the sales account at the end of the month. Other information, such as invoice numbers and ledger folios, may be printed by the machine on the same sheet, or may be in- serted by hand. The sheet is put in a loose leaf binder, and forms the sales journal. The carbon charge sheets may be retained in their own bound book for reference; or, if they are loose, they may be put in a vertical file. The nature of the business must determine whether, with a system of this kind, it is better to have the charge sheets bound or loose. If it is required to compile statistics of the business, with reference, first to one thing, and then to an- other; or if it is required to post the month's sales to the credit of several different accounts according to the character of the goods, or according to departments, it is very much bet- ter to have the documents loose, one transaction on a sheet; for then there is infinite opportunity to list and re-list accord- ing to any desired classification. Fig. 4 shows a listing machine. This machine has been used for several years in banking houses for listing checks. It was at first used exclusively for listing on narrow paper ribbons. When a Customer's book was balanced for the month, his TELLER'S DAILY CASH. Bal. for'd 96,418 27 Deposits 26,491 28 Checks 10,045 35 Int. & Ex. 117 42 Exchange Drafts Balance 112,981 62 123,026 97 123,026 97 DEPOSITS DEPOSITS CHECKS CHECKS 25.00 50.00 100.00 30.28 205.00 10.20 81.31 1,728.00 327.33 100.00 5,000.00 30.00 1,060.00 10.00 424.52 20.00 125.45 1,531.00 154.20 5.08 19.90 200.00 2,000.00 273.98 1.35 1,200.06 43.65 .65 189.37 482.42 11 167.95 13.53 2,421.33 273.98 1,216.83 .65 3,056.66 1,444.98 10,045.35 67.60 1,101.34 64.42 481.80 121.50 .15 5.00 21.80 8,168.09 2,408.16 72.00 26,491.28 Fig- 5- CHECKS ADDING MACHINES. 31 paid checks were listed on the ribbon, and the ribbon, with the cancelled checks, returned to the Customer. At the present time, much more extended use is being made of the machine. Fig. 5 shows one page of a Teller's cash book, in a small bank. The upper part of the form is ruled to make the usual daily cash balance, bringing forward the balance of the day previous, and debiting with deposits, exchange, drafts and other receipts, and crediting with checks and other items paid out. The lower part of the sheet is used for listing the deposits and checks ("unit documents.") This whole sheet is filed as a permanent cash book. In large banks, this same idea has been still further de- veloped thus : the checks of each Customer are sorted in sepa- rate piles, and listed and added separately on the Teller's sheet or check register. Each lot is numbered by hand oppo- site the total, to indicate the Customer's ledger account, and the totals are posted to his debit by these reference numbers. The grand total disbursement by check for the day, is made up by summarizing and listing the Customers' totals. There are many uses made of the listing sheet by pro- gressive banks. For example, in making remittances, the letter of advice may be printed to the effect that the following list of papers are enclosed for collection and credit. The papers are then listed on the adding machine, and the carbon duplicate filed in a binder, for posting direct to the ledger. Fig. 6 shows an ingenious use of an adding machine by a Gas Co. They render gas bills, with the understanding that if they are paid at the Company's office before a certain date, a discount will be allowed. When the bills are paid, their stubs are retained in the office, showing amount of bill, and amount paid. At night, the stubs are listed on the add- COLLECTION SHEET. Net Amount Collected. Gross Amount of Bill. 225, 002.50 110, 001.23 79, 000.87 310, 003.45 238, 002.65 135, 001.50 217, 002.41 168, 001.87 108, 001.20 207, 002.30 486, 005.40 61, 000.68 222, 002.47 275, 003.05 132, 001.47 243, 002.70 90, 001.00 99, 001.10 112, 001.25 126, 001.40 405, 004.50 224, 002.49 45, 000.50 72, 000.80 126, 001.40 199, 002.20 270, 003.00 247, 002.75 180, 002.00 5,411, 060.14 Fig. 6. ADDING MACHINES. 33 ing machine: the net amount collected being set on the left (apparently as hundred thousands) and the gross amount of the bill on the extreme right. The appearance of the record is somewhat peculiar, by reason of the fact that the machine automatically prints the intervening ciphers. But by having a black line ruled on the blank to separate the net to the left, it becomes clear; as for example, $2.25 net, $2.50 gross. On a nine figure machine, care must be taken in a case of this kind, not to list so many before taking the total that the total of the net part will exceed the capacity of that half of the machine, that is, $99.99. This sheet is filed in a loose leaf binder as a page of the cash book, crediting Ac- counts Receivable with the gross, debiting Cash with the net, and debiting Discount with the difference. Fig. 7 shows how a monthly statement of account may be made on the adding machine. The blank should be printed with dates for every day of the month, spaced to suit the machine. The debit amounts are listed by dates, and totaled in the first column. The credit amounts are listed by running the sheet through a second time. The difference may be determined mentally, and set down by the machine. An incidental advantage of this scheme is, that if the state- ments are made up promptly at the first of the month, the adding machine totals on the statements may be used for pencil footings on the ledger, for drawing the trial balance. Fig. 8 shows a blank made by listing the deliveries for a month on a milk route. The tickets are listed each day from each driver, to show amount and kind of goods deliv- ered on each route. At the end of the month, the lists for each route are listed by days on the sheet shown in Fig. 8, and the totals shown for each kind of goods. The sheet is run through the machine for each designation. The sheet MONTHLY STATEMENT OF ACCOUNT. Dr. Cr. Balance For'd. 17.40 i 15.00 2 75.01 3 34.89 4 22.10 5 42.00 6 23.00 7 8 9 193.45 IO 4.11 ii 4.33 12 77.54 13 "4 15 89.54 16 22.00 17 53.44 18 52.33 19 20 21 11.01 143.00 22 23 8.95 34 9.38 25 42.79 26 75.00 27 32.52 78.00 28 24.55 29 11.00 30 3.87 31 58.76 1,003.97 221.00 221.00 Balance Due 782.97 Fig- 7- ADDING MACHINES. 35 shown is a copy of one in actual use. It happened, in this case, that the capacity of the machine used was for six sepa- rate columns, while there were seven designations required. The last column was "split," to show two designations, sim- ilar to the gas bill adaptation in Fig. 6. The punctuations were those in a regular machine for listing dollars and cents. The delivery on the first day is to be read 456 quarts, al- though it is punctuated 4.56. Adding machines are used more for dollars and cents than otherwise, and hence the standard method of arrange- ment and punctuation is for this purpose. The keys of a nine figure machine are generally colored as in Fig. 4, namely: one key white for the million, the next three black, the next three white, and the two for cents black. The punctuation is 9,999,999.99. But the machine may be ordered with any desired coloring and punctuation. In fact, the colors may be changed in some makes of machine by simply pulling off the keys and transposing them. Fig. 9 shows a key-board for simultaneously adding two columns of related matter, such, for example, as freight and drayage, or debits and credits for a trial balance. A line is drawn in the engraving to show the separation, and to in- dicate how the sheet should be ruled to receive the work. The punctuation is arranged for two sets of dollars and cents, as for example, $999.99 $99.99. The amounts here ex- pressed would be the limits of addition for the twin columns. Hence in using such a combination, it is necessary to take off the totals before they accumulate beyond these amounts. Fig. 1 shows the work of an ordinary nine figure ma- chine, with key-board split, and with the cipher types ex- tracted in two of the columns. This was specially arranged for recording the gross and tare weights of oil in barrels. The MONTHLY SUMMARY OF MILK ROUTE. DAY MILK CREAM BUT MILK (Quarts Pints Quarts Pints y 2 P'ts ^P'ts Quarts I 4.56 4.55 55 1.20 3.44 45, 005.55 2 3.40 3.31 74 1.30 2.21 32, 000.44 3 4.50 2.21 54 1.03 4.31 43, 000.45 4 2.30 76 65 1.04 3.21 43, 002.34 5 3.44 87 31 1.40 2.21 22, 003.44 6 3.45 65 22 1.66 2.44 24, 000.56 7 5.53 1.20 24 87 2.55 24, 000.67 8 4.32 1.30 22 98 2.32 20, 003.45 9 3.21 53 42 87 4.32 20, 002.34 IO 3.50 65 5 79 3.21 54, 002.33 ii 3.66 76 54 69 3.40 65, 000.55 12 3.70 4.03 22 2.01 2.46 66 13 3.07 3.02 42 1.60 2.77 54, 003.55 M 3.04 2.01 43 1.40 2.56 32, 000.34 15 3.40 2.33 21 1.33 4.43 32, 000.23 ■6 3.50 1.33 12 1.40 3.21 32, 002.44 17 3.30 3.21 32 1.05 3.67 21, 002.30 18 3.20 4.32 33 1.66 3.78 32, 000.77 19 3.32 5.03 20 1.55 3.67 43, 004.66 20 3.43 6.54 30 1.54 3.06 64, 000.45 21 3.43 74 10 1.43 3.45 64, 003.05 22 3.31 4.43 30 1.42 3.40 65. 002.44 23 3.20 3.21 34 97 3.03 54, 002.44 24 3.21 1.44 35 87 3.30 43, 000.00 25 3.32 1.55 32 76 20 43, 000.45 26 3.44 3.32 31 1.56 2.70 43, 003.55 27 3.55 53 20 1.67 2.80 54, 002.04 28 3.55 6.64 27 87 2.78 43, 003.55 29 30 3i 98.84 70.47 9.22 34.92 84.89 1,111, 055.04 Fig. 8. KEY-BOARD OF ADDING MACHINE SPLIT FOR ADDING TWO SIMULTANEOUS COLUMNS. D@@® 8) (8 VIZ D©@ © S@® SO® 3 ## 2 ®@ 5 2 1 ®®® Fig. 9 . WEIGHT SHEET 100 BARRELS OIL. 466 68 473 80 468 80 483 73 468 70 485 81 485 78 457 74 478 70 478 73 488 69 467 70 468 73 468 70 477 73 485 73 467 73 484 68 485 62 484 74 468 70 468 69 468 90 468 64 466 70 484 69 466 71 489 75 499 79 488 70 501 69 467 69 486 71 467 60 478 71 468 69 478 72 464 59 468 75 468 74 478 74 468 70 465 68 468 70 469 71 468 75 478 72 466 70 488 70 478 70 468 73 474 80 467 70 477 69 488 72 458 70 466 70 486 73 468 70 483 73 486 75 484 68 475 72 485 75 466 69 468 67 488 73 476 64 501 71 485 68 468 70 501 75 487 71 465 83 484 59 475 73 468 71 464 70 501 71 468 66 478 63 464 62 464 68 500 79 466 67 466 75 488 70 476 68 468 69 457 75 466 73 466 69 466 69 468 73 468 71 488 70 466 68 473 72 467 76 469 71 47508 7117 40391 7117 Fig. ro. ADDING MACHINES. 39 machine is placed near the scales where the oil is to be weighed, and as a man rolls the barrel on the scale and bal- ances the beam, the Operator reads the beam for gross, and reads the tare from the mark that is already on the barrel. Both of these weights are set up at once in the proper columns (which in this case are differentiated by colors) and the handle pulled, thus recording, say, 468 68. When the entire lot is recorded, a total is shown up to 99999 9999. As the average unit shipment and billing is 100 barrels, the to- tals come easily within the range. The machine, with the ciphers cut out, as above, may still be used with perfect ac- curacy for other work. It would record $9,900,000.99 as 99000 99. Fig. 1 1 shows the use of an ordinary machine for mak- ing weight sheets of cotton. It records 550 pounds as 5.50. Fig. 1 2 shows the key-board of a machine arranged for adding fractions. Such a machine is well adapted for weight sheets of cloth. Fig. 13 shows the kind of record which is made for shipping every bale of cloth from a mill. This record was made with a machine with a key-board like Fig. 12, having ciphers cut out of five columns, and having the first column to the left arranged to repeat. The first 1 is set up, as indicating the number of pieces of cloth corresponding to each number of yards, as set up to the right. When the total is taken, the left hand figures indicate the number of pieces in the bale. It is convenient to make up a weight sheet or bale ticket in carbon triplicate, one copy being packed in the bale, one sent with the invoice, and one filed in the office. Fg. 1 4 shows a special adaptation of a 1 3 figure machine for use in the office of a car accountant of a Railroad, for making up the monthly report of "per diem" and "penalty" on foreign cars. The first seven figures at the left are reserved 4 o ADDING MACHINES. for car numbers, and marked by colors on the key-board. This machine is so arranged that it will not record the total of this set when the totals are taken off for the other sets. The cipher is cut out of the next row after the car numbers. The next two figures are for per diem. The cipher is cut out of the next row, and the last two figures are for days pen- alty. As the number of days per diem or penalty can never exceed 31 (probably averaging 15) the two sets of two fig- ures each for these columns, will always be sufficient. The totals of these two columns may record 999 each, so that it is possible to arrange the ruling for such a sheet to hold 30 or 40 lines. It is convenient to have the bottom of such a sheet ruled for summarizing and making the final calculations at the agreed rate of per diem and penalty. These sheets are to be made up in duplicate : one to be sent to the foreign road, and one to be filed in a loose leaf binder as a permanent record. Fig. 1 5 is a sheet for use by a Railroad when forward- ing coal in large quantities for a mine. Duplicates of this sheet are furnished the Mine at stated intervals, to collect freights, and to furnish the Mine with weights for use in their own billing. This sheet is made on a nine figure machine, with carriage arranged to automatically feed side-wise for three columns, and then vertically for one space. The ma- chine is specially arranged to avoid recording the totals of any but the last column, which is the one showing the weights. Fig. 1 6 shows the use of a plain machine for collecting and recording comparative statistics for two years. A proper form is printed for recording the same corresponding fact for two years, one above the other. The statistics for one year are first recorded and totaled, and then those for the next year. WEIGHT SHEET 100 BALES COTTON. 5.50 5.13 5.04 4.50 5.65 4,60 5.06 4.05 5.42 5.03 5.40 4.92 5.54 4.86 5.55 4.69 6.00 5.27 6.03 5.52 5.60 5.63 5.54 5.57 5.05 5.01 5.03 4.59 5.35 4.35 5.40 4.56 5.42 5.32 5.52 5.50 5.54 5.01 5.60 6.04 5.40 5.60 5.53 4.04 6.44 4.06 6.04 5.09 4.50 4.76 4.52 4.73 5.40 4.62 4.56 4.99 4.74 5.45 4.85 5.60 4.39 6.40 4.48 6.03 4.57 5.45 4.35 4.56 5.52 6.21 4.68 5.23 6.03 5.34 4.55 5.09 5.67 5.49 5.08 5.71 6.07 5.64 5.57 5.84 6.23 4.70 6.49 5.22 5.08 5.23 5.40 5.21 4.05 5.43 4.62 5.67 5.21 5.06 4.72 6.02 521.70 Fig. II ® KEYBOARD WITH FRACTIONS. @®®®©@® ®®®®d ®®@©@®®®# ®@®®®@® ® ©€ @®S ©d ®®a 1 D®@ 4 3 2 Fig. i2. BALE TICKET FOR COTTON MILL. 20 54 46 1-2 51 51 53 3-4 54 53 54 3-4 53 1-2 48 1-2 54 53 1-2 53 1-2 65 53 55 50 53 55 52 1-2 1,064 1-2 Fig, I 3- RAILROAD PER DIEM AND PENALTY REPORT ON FOREIGN CARS 1 S 3 z u s a £ s u S Pu u ,5 s 3 U U S u - 1 e 3 s s u 0) "(3 s 1,130,914 34,214 42,614 11,314 8,733,714 6,835 11 17 7 3 18 54 5 1 8 14 Fig. 14. 44 ADDING MACHINES. Special machines may be made for many different uses. A most valuable adaptation is for exporting houses where considerable business is recorded in English money. An adding machine designed for this purpose, will produce cor- rect totals of pounds, shillings and pence with as much facility as with decimal currency. It might happen that records are wanted in bound books or on sheets too large for the adding machine. In these cases, it is quite feasible to list the items on a ribbon and cut up the ribbon and paste it up in any shape desired. All makers of adding machines claim that their machines will also subtract, multiply and divide. This can be true only in a certain sense. Strictly speaking, an adding machine can only add. It can be made to record the result of subtrac- tion by the subterfuge of adding the complement. For ex- ample, subtract 375 from 510. The complement of 375 is 625. This added to 510 gives 1 135, which is 1000 more than the correct answer. In reading the answer on the add- ing machine, the left hand 1 may be disregarded, and the answer read 1 35. By working this out carefully, it is possible to become expert in subtraction. But, except in cases where a very large amount of subtraction is to be performed con- tinuously, it is usually easier to do the work mentally than on the machine. By the subterfuge of continually adding a number to itself, the effect of multiplication may be produced. To mul- tiply, say, 1 55 by 7, set up 1 55 on the machine, set the repeat key, and pull the handle seven times and take the total. To multiply by 97, pull seven times, as above, and then set up 1550 and pull nine times, and take the total. Except in small numbers in the multiplier, an adding machine is not par- ticularly useful for multiplying. It is of no practical use for STATEMENT FURNISHED TO A MINE BY A RAILROAD CO. SHOWING COAL FORWARDED FOR THE MONTH. Date W'ybill Car No Weight 1,215 4,665 56,000 6 6,540 65,000 7 3,080 67,000 8 7,540 50,000 9 4,688 50,000 20 13,056 100,000 1 6,054 76,000 2 5,007 75,000 3 608 80,000 4 8,864 66,000 5 7,044 65,000 6 7,640 66,500 7 7,076 65,400 881,900 Fig 15- INSURANCE COMPANY'S COMPARATIVE STATEMENT OF EX- PENSES. Head office Agencies Totals Commission 1904 4,444.30 45,505.00 49,949.30 1905 5,066.00 44,400.00 49,466.00 Bonus 1904 345.00 50,666.00 51,011.00 1905 300.00 45,500.00 45,800.00 Physicians 1904 77.60 455.00 532.60 1905 56.60 400.00 456.60 Salaries 1904 1,908.00 1,330.00 3,238.00 1905 1,300.00 1,200.00 2,500.00 Totals 1904 6,774.90 97,956.00 104,730.90 1905 6,722.60 91,500.00 98,222.60 Fig. 16. ADDING MACHINES. 47 division, although it is possible to get the result by subtracting the divisor from the dividend as many times as possible. For example, divide 500 by 10. Ten may be subtracted from 500 fifty times. Small electric motors are now being supplied for adding machines. This greatly increases their speed, and renders them more nearly practicable for multiplication. It is probable that a machine might be designed with nine special keys, so connected with the electric circuit that when the multiplicand is set up, the special key corresponding to the multiplier, say, 5 is depressed, and causes the machine to start up, repeat five times, take the total and stop. Non-listing machines cost from $125.00 to $200.00, according to capacity. Listing machines cost from $300.00 to $500.00. CHAPTER IV. THE ELECTRIC TABULATOR. In cases where statistics must be collected and tabulated in numerous forms, with reference to different material facts, the theory of "Unit Documents" applies to the fullest extent. If, for example, the record of sales consists of one bill for each sale, it is possible to arrange all the sales in the entire system with reference to any number of controlling factors: say, by salesmen, by locality, by purchasers, by kind or class of goods, and so on indefinitely. Fig. 1 7 shows an automatic electric tabulating machine, which is very useful for adding and re-adding statistics, ac- cording to classifications. It is operated by an electric motor, and is controlled in all its mechanism by electricity. One or more adding machines are located in the upper part of the case, where the dials may be easily read. A frame, carrying a gang of vertical needles is hinged on the desk leaf in front. When the frame is pressed down (by hand or by electricity) the needles make electric contacts with points on the table, thus operating the dials on the adding machines. The figures to be added or tabulated are punched on a card similar to the cards used for Jacquard looms or automatic pianos. When a card is fed to the machine, and the needle frame de- pressed, only such needles as pass through the punched holes can make electric contact. Hence, only those needles which are thus automatically selected will operate their respective dials in the adding machines. ELECTRIC TABULATOR. Fig. 17. THE ELECTRIC TABULATOR. 51 Fig. 1 8 shows a card for operating this machine. The punchings may be easily read. This card represents a bill of goods sold 1905, August 27th, serial number 846, class 35, sold to customer number 912, (or if desired, any number ending in 912, say 350,912), in territory 65. The bill con- sisted of 152 units, billed at $1,582.46. Suppose a corporation, operating a number of Branch Offices, desires to tabulate statistics of sales. The facts on every bill sold are punched on cards. These cards may be sorted in accordance with any desired classification, say, for goods sold in the month of August. This sorting of the Au- gust cards out of a large lot of all dates, may be easily done by sticking a knitting-needle through the figure 8 in the second column. When these selected cards are drawn out and stacked up, the selection is easily verified by looking through the 8-hole. If it is obstructed when the cards are even, there is something wrong. When the cards are fed through the machine, it will add the amounts of the bills, and also, if de- sired, add the number of units of goods at the same time on the second dial. The machine may be so set that, if by acci- dent, a card belonging to any other month than August should be inserted, the whole machine will stop. Other discriminative tabulations are accomplished in the same manner. For example, if it is desired to know the total goods sold of class 35, all cards punched 35 in the "class" column are sorted together and fed through. An automatic electric sorting machine may also be had with this system. By setting it to sort a certain classification, say, the month of September, all the cards may be fed to it indiscriminately, and it will throw out all the September cards. After these are used by feeding through the tabulator for totals, they are returned to the pile, and again fed, with 52 THE ELECTRIC TABULATOR. all the other cards, through the sorter, which is now set to select some other classification, say, for goods sold in territory No. 47, and so on for all the different classifications desired. Special cards may be designed for recording any kind of facts that may be expressed by figures, and for elaborating to any required detail. All that is necessary is to construct a table giving each designation its own characteristic number in its own class column, and punch the cards accordingly. These machines may be had with any desired number of dials, to simultaneously add any number of co-ordinate facts, as for example: number of units, weight or quantity, cost, selling price. The cards may be printed in different colors, to assist in certain classification, such as yellow for ordinary sales, pink for credits on goods returned, &c. Each Branch Office might have its own designating color or combination of colors, as well as its distinctive number to be punched on all cards from that Branch. Most elaborate cost systems may be maintained by the use of this machine. An Operator may sit in front of the machine, with his cost ledger, and record or post the various totals as they appear on the dials as totals of each tabulation. There need be no fear of any kind of final error in this scheme; by reason of the fact that the machine will stop rather than add a wrong card in any given classification. The cards are added so many times in different orders that there will always be several grand totals. If any of these dis- agree, it is easy to repeat the operation and discover the trouble. Department stores could make good use of this machine. A card would be punched for each sales slip for the day, showing date ; salesman's number ; class of goods ; department 54 THE ELECTRIC TABULATOR. number ; whether cash or charge sale ; and if charge sale, the number of the personal ledger to which it will be posted; amount of bill; cost of goods (in case a system of cost marks is used on sales slips.) At the end of each day all cards would be run through the machine, indiscriminately, to show the grand total of all sales for the day. If the cost system is used a double dial machine would be used and the cost and selling price would be simultaneously totaled on every tabulation. Cards would then be sorted and run through the ma- chine successively ( 1 ) to show amount sold by each sales- man, (2) amount in each department, noting the state of the dials at the end of each sub-division for class of goods. (3.) amount sold for cash, (4) amount sold to be charged, noting the state of the dials at the end of each lot to be posted to a given ledger, (5) any other classification desired. Entries would be made in the books of account by direct reading from the dials at the end of each subdivision. For example, the general ledger clerk would at once post from the readings of the dials, (no journal entries) to the credit of the proper department, the amount of sales as shown for that department. He would post from the dials, to the debit of each personal ledger, the total of all sales that would be indi- vidually posted to the debit of the customers in that ledger. He would post to the debit of Cash the total of cash sales. The total of all the debits thus posted to the general ledger each day would thus necessarily equal the total of the credits. After the use of the cards as above, they could be sys- tematically filed until the end of the month, when they might again be run through to prove the trial balance, and then they might be destroyed, to save room. Fig. 19 shows the punch which is used in making the PUNCH FOR ELECTRIC TABULATOR. Fig. 19. THE ELECTRIC TABULATOR. 57 cards. It has an automatic feed, so that when the card is inserted, it is fed forward just the right amount for the next column. One of these punches may be supplied to each Branch Office or Department. Reports may then be punched on cards, instead of writing them. These cards, after being passed through the tabulator, may be filed in classified cabi- nets, as original records, always accessible for re-tabulation, if desired. If the cards have been punched in duplicate, they may be filed according to two classifications, thus saving the time which might be required to classify again, in case it is likely that such information might be often necessary. Orders originating at a Central Office, to be filled at the Branches, may be punched in duplicate, on these cards, and sent out to the Branches, instead of sending the written orders. The cards are thus ready for tabulation without extra labor. Infinite other uses for this system will readily suggest themselves to any office which handles a large amount of statistical work. The makers of these machines do not sell them, but rent them to users, and supply the cards, properly printed to tabulate any kind of work. The rental price is so different for each case that no regular list is available, each case being priced according to the requirements. CHAPTER V. THE PLAIN SLIDE RULE The slide rule was invented for engineers, and its use in work of this sort is very general; but for purposes of ac- counting, it is practically unknown. One reason for this is, that it is not for sale among office supplies; another is, that at first sight it seems to be such a complicated affair, that a book-keeper hesitates to try to learn it. As a whole the in- strument is capable of performing a vast multitude of intricate calculations, and in this sense, it may be said to be compli- cated. But for the simple operations of multiplying and dividing, for approximate results, it is simplicity itself. An ordinary carpenter's square is full of figures, which might make this common tool seem complicated, except for the fact that a carpenter generally pays no attention to any figures except the plain graduations for inches and fractions. Likewise, on a slide rule, it is necessary to learn to disregard all the figures except the ones being used. When this is ac- complished, the instrument will prove itself most valuable for working up data on reports and statements. Its general func- tions are to multiply and divide. It is, of course, impossible to learn much about such an instrument from any book, without having the actual in- strument in hand. Instruction books usually come with the instruments; but these instructions relate altogether to engi- neering calculations. There is no book which explains the application of the slide rule to accounting problems, and hence be THE PLAIN SLIDE RULE. 61 this chapter will be devoted to such explicit instructions for its use in accounting, that any beginner may take the rule in hand and follow the examples given, and become proficient in a few hours. Great expertness will of course come only after considerable use under actual conditions. The greatest advantage in the use of the slide rule will appear when there is a large number of similar operations, particularly if there is a constant multiplier or divisor. Such cases would be : find- ing some given per cent of a number of amounts (the use of a constant multiplier) : finding what per cent each of a series of numbers is of the sum of the numbers (the use of a constant divisor) ; the finding of unit costs of production in a factory. In this last case, the amount of output, (tons, yards, &c.,) would be the constant divisor, while the amount of each ex- pense account would be the varying dividend. TO MULTIPLY. Set the index (1 or 10) on the slide, to the multiplier on the rule. Find the multiplicand on the slide and read the answer opposite on the rule. TO DIVIDE. Set the index (1 or 10) on the slide to the divisor on the rule. Find the dividend on the rule, and read the answer opposite on the slide. Nothing could be simplier than these two rules. Note that the setting is the same, whether for multiplication or di- vision. The only difference in the whole operation is, that in multiplying, the answer is read on the rule, while in dividing, the answer is read on the slide. The only reason for going further into the subject is to show how to read the scales. Fig. 20 is a general view (about one-third size) of a 20-inch slide rule. The main body of the instrument is desig- 62 THE PLAIN SLIDE RULE. nated as the "rule," the central sliding portion, seen extending to the right, as the "slide," and the dark pointer near the centre, as the "runner." There are two complete sets of scales from 1 to 1 on the upper part of the "rule," and two exactly similar sets of scales on the upper part of the "slide," so that in the figure, if 1 on the slide is opposite 1 on the rule, 2 on the slide will also be opposite 2 on the rule, and so on. On the bottom part of the rule there is one complete scale from one to ten, and an exactly similar set on the lower part of the slide. Hence the graduations on the lower part of the instrument are twice as long as those on the upper part, and may therefore be read with greater accuracy. READING THE SCALES Fig. 2 1 shows a portion of the instrument to exact size. The lower scale has been concealed, so that no confusion may result when discussing the figures. The figures visible on the body of the rule are from 1 to 3.3. These are read with- out regard to decimal points; that is, 1 may stand for .001, .01,-1, 1 ., 10, 1 00, &c. The figures on this part of the rule read as printed, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,20, 30, 35. The intermediate amounts, or digits of third degree, are read by the graduations, thus, 101, 102, 103, 104, 105, (designated by a longer graduation line) 106, 107, 108, 1 09, 1 1 0, (which is the same as II, and is indicated by the small figure 1 , printed following the large figure 1 at the start) 111, 112, 113, 114, 115, (designated by a longer graduation line) 116, 117, 118, 119, 120 (which is the same as 12) and so on to 200, which is designated by the figure 2. Digits of the fourth degree may be estimated with a fair degree of accuracy on this part of the scale. For ex- bo THE PLAIN SLIDE RULE. 65 ample, find 6 1 on the slide ; the corresponding amount on the rule is nearly 1 1 00, and may be estimated as 1 098. From 2 to 4, the intermediate figures for digits of the second degree are not printed except for 25 and 35; they are to be read by the long graduation lines. Digits of the third degree are read by the short graduation lines, two points at a time. Referring to the engraving, the left edge of the runner is set to 222 on the rule. The right edge is at 265, that is, it is about half way between 264 and 266. (As the runner covers part of the space from 2 to 3, the reading 265 is ar- rived at by glancing ahead to 300, and counting back.) Only three digits may be relied on for this part of the scale, though by care the fourth may be estimated with some ac- curacy. From 4 to 10, no more intermediate figures are printed. Digits of the second degree may be read by the medium length graduations, one point at a time. Digits of third degree may be estimated with considerable accuracy. The shortest graduations are half points. This part of the scale is visible on the slide. Find 1 2 on the rule ; the corresponding amount on the slide is about half way between 665 and 670, and may be estimated as 667. Beginners experience some difficulty in remembering the varying values of the graduations, some lines being read for 1 point, some for 2, and some for one half. But it is not necessary to remember it; the eye will soon become accus- tomed to these valuations, by glancing ahead. In parts of the scale where a graduation stands for one point, there are ten divisions between the long marks ; in parts where it stands for two points, there are five divisions between the long marks. 66 THE PLAIN SLIDE RULE. To multiply 18 by 123. Set the index point of slide (this is usually 1 , but may also be 1 0, as shown in the engrav- ing) to 1 8 on the rule. Find 1 23 on the slide, and read the answer opposite on the rule. This is about three-quarters of the way between 220 and 222 (where the runner is set,) and may therefore be estimated at 2215. The correct an- swer, of course, is 22 1 4 ; but this part of the scale is not to be relied upon for the fourth figure, within one or two points. Great expertness with the instrument would in a case of this sort lead to reading it 2214, because it may be readily seen by inspection that the last figure must be 4, (3x8 being 24.) To divide any amount, say 222 by 18. Set the index point of slide to 1 8 on the rule, as before. Find 222 on the rule. (It is convenient to use the runner as a marker, both in multiplication and division) and read the answer opposite on the slide. This is a little more than 12.30; it might be read 12.31 to 12.33. The correct answer is 12 1-3. A large number of examples in multiplying and divid- ing by 1 8 may be worked by reference to the engraving. PERCENTAGE. A stock of goods consists of Shoes $11,475.20 Hats 2,818.40 Clothing 3,440.17 Notions 268.30 Total $18,002.07 Set the index of slide to the total or divisor 18,002.07 on the rule, say 18, as per engraving; opposite the value of each stock on the rule read the percent on the slide. These read 637, 157, 191, 149, respectively. The decimal points THE PLAIN SLIDE RULE. 67 must be supplied by inspection. It may be seen at once that the shoes form more than half the stock, and hence that per cent must be 63.7. (It would be unreasonable to call it 6.37.) Likewise, we read hats 15.7, clothing 19.1 and no- tions 1 .49. (This could not reasonably be called 1 4.9 per cent, because it is seen at a glance that 1 per cent would be $ 1 80, and hence $268.30 must be less than 2 per cent.) The above list of per cents add up $99.99. The figures may now be adjusted to make 1 00. per cent, say by calling the notions 1.5. RULE — To find what per cent a small number is of a large one, set to the large number. Find the small number on the rule ; read the answer op- posite on the slide. UNIT COSTS. It is required to find the cost per unit (of manufactured goods) of each of the elements which enter into the total cost. For example a cotton mill turns out in a week 1 8,000 pounds of yarn. The various items of cost are: Labor $ 318.45 Supplies 1 94.62 Repairs 296.82 Fixed charges 222.00 Total 1,031.89 Set the index to the production, 1 8, as in Fig. 2 1 . Opposite 318 on the rule, read unit cost on slide, 1 77. We know by inspection that $360 woud be 2 cents per pound, hence we read this answer as 1 .77 cents per pound for labor. Opposite 195 read 1.08 for supplies. Opposite 297 read 1 .65 for repairs. Opposite 222 read 1 .23 for fixed charges. 68 THE PLAIN SLIDE RULE. These add up 5.73. Check the result by looking opposite the total cost, 103 for the total unit cost. This reads 5.73, and proves the results. Work on unit costs in this manner is so easy and rapid that it conduces to a more searching inquiry into this subject, sub-divided into finer classifications than would be the case if the work were more laborious. Such calculations as the above require on the slide rule about 12 seconds per opera- tion while the average time for making long divisions by the usual method would be 20 to 30 seconds, so that the rule easily saves half the time. Only one setting of the slide (namely to the production) is necessary to find the unit cost of any number of expense accounts for the same production. RULE — To find unit costs : Set to the amount of pro- duction (pounds, tons, bushels, gallons.) Find the amount of each expense account on the rule, read the unit cost opposite on the slide. All of the above examples have to do with a constant multiplier or a constant divisor. It sometimes happens that we have to deal with a constant dividend and varying di- visors. For example, in the cotton mill problem above, sup- pose the fixed charges (salaries, taxes, insurance, &c.,) would remain the same, whether the production is 18,000 pounds or more, and suppose all other costs would vary substantially with the production. It is required to find how much the cost would be successively reduced by increasing the pro- duction in 1 000 pound steps. Set the index to 18 (the pro- duction, as before.) Move the runner to 222 on the rule. This is the fixed charges. Read the cost per pound 1 .23 at the runner on the slide. Leave the runner stationary and set the index to 1 9 for an increase in production of 1 000 pounds and read the answer on the slide at the runner. Set the index THE PLAIN SLIDE RULE. 69 to 20, and read the answer on the slide at the runner, and so on. Thus the cost per unit for fixed charges corresponding to any possible production may be quickly found by setting the runner once for all at the fixed charges on the rule, setting the index successively at the various productions, and reading the corresponding answers at the runner on the slide. PRO-RATING. It is required to pro-rate an amount of fixed charges over each department of a factory according to the produc- tion of that department. For example $2,222.00 in the proportion of: 6,750 7,820 9,160 3,120 26,850 Oneway to work this is to set the index to the total 2,685, and opposite each of the amounts, 675, 782, &c, on the rule, read the per cents 25.1, 29.1, 34.2, 1 1.6 on the slide. Then set the rule to 222 and multiply it by the various per cents as above, by reading opposite 25.1, 29.1, &c, on the slide the various answers on the rule: $557, 646, 759, 258, total 2,220. The above method requires 10 operations. A shorter method is to set the runner to $2220. on the rule, bring 2685 on the slide, up to the runner, then opposite 675, 782, &c, on the slide, read the answers at once on the rule. This requires only 6 operations. RULE — For pro-rating a fixed amount over several departments in the ratio of the production of the respective departments: Find the fixed amount on the rule; mark it with the runner; find the total production on the slide and 7 o THE PLAIN SLIDE RULE. draw it under the runner; opposite each production on the slide, read the pro-rata on the rule. RULE OF THREE. Set the runner to the second term on the rule ; bring the first term on the slide under the runner; opposite the third term on the slide, read the answer on the rule. The example under pro-rating may be stated under the rule of three thus : 2685 :222 : .67 J : All of these are, of course only approximations, but they are usually close enough for pro-rating. If there are odd cents involved, they may be distributed in a way to make the sum of all the different divisions exactly equal the total. Too much time is frequently consumed in trying to make such calculations as these exact to the cent. No good pur- pose is served by it, because the basis of the pro-rating is itself generally somewhat theoretical, and a few cents varia- tion one way or the other makes no material difference. FRACTIONS. To operate with fractions or with any numbers contain- ing fractions, express them decimally, and proceed as with the whole numbers. For example, 4 3-4 x 3 1 -4 : Consider the problem 4.75 x 3.25. To reduce any fraction to a decimal, divide the numer- ator by the denominator, that is, set to the denominator, and opposite the numerator on the rule, read the answer on the slide. For example, reduce 1 3- 1 8 to a decimal. In Fig. 2 1 , one rule is set to 1 8. Opposite 1 3 on the rule, read .722 on the slide. CLOSER APPROXIMATIONS. In cases requiring a closer approximation than may be gained by the scales on the upper part of the slide rule above THE PLAIN SLIDE RULE. 71 described, the scales on the lower part may be used. This should not be attempted until after complete familiarity with the upper scales. The reading is done in exactly the same manner, and the general principles and rules are the same; but, on account of the scale not being in duplicate as on the upper part, it is necessary to make the setting sometimes with the slide drawn out to the right and sometimes to the left. Fig. 22 shows a portion of the instrument to exact size, with the upper scales concealed, so that the lower scale may be discussed without confusion. The slide has been drawn out to the right until the index 1 is set to 4. These scales are read as printed: 11, 12, 13, 14, 15, 16, 17, 18, 19,20.... to 50. The intermediate amounts, or digits of the third de- gree are read by the graduations, as 101, 102, 103, &c, as on the upper scales. Digits of the fourth degree, as 101 1, 1012, 1013, 1014 to 2000 may be estimated with fair accuracy, while amounts, whose fourth figure is 5, as 1025, (This on the slide opposite 41 on the rule) may be placed accurately by the middle graduations. From 2000 on, the third figure is easily read by the graduations, while the fourth may be estimated, though with less and less accuracy toward the end of the scale. A great many examples of multiplying and dividing by 4 may be worked by reference to the engraving. To multi- ply 4 by 18, find 1 8 on the slide and read the answer oppo- site on the rule 72. To divide 465 by 4 find 465 on the rule and read the answer opposite on the slide 1 16.25. One setting of the rule will always suffice for working any problem of percentage or unit costs on the upper scale, because one of the two series of numbers is always in range, while in using the lower scale, (which has only one series,) there will be occasions when some numbers will be out of 72 THE PLAIN SLIDE RULE. range with one setting. For example, to divide 4 into 385. In the setting shown in the engraving, the 385 is out of range on the rule, being at the left of the index. In a case of this kind, it becomes necessary to re-set, by using the index at the right hand of the slide, by pulling the slide out to the left. After some practice it becomes easy and natural to set it the right way for any example. RULE — For division with the lower scale. If the divisor is smaller (disregarding decimals) than the dividend, draw the slide to the right; if larger, draw to the left, and proceed as with the upper scale. In multiplying with the lower scale, it is easier to notice by inspection which way to draw the slide, than to follow any rule for it. In either multiplication or divison on the lower scale, the only point to be observed, is to set the index so that it is possible to find the answer on the slide opposite the problem on the rule, or vice versa. OTHER PROBLEHS. The slide rule is adapted to infinite problems involving combinations of multiplication and division. Methods for working such problems will be apparent to any one who has become familiar with the examples above cited. The top scale bears a definite relation to the bottom one, so that in some cases it is convenient to use both scales together. All the quantities on the top scale are the squares of those on the bottom, and the bottom quantities are, there- fore, the square roots of the top ones. For example, 3 on bottom of rule is opposite 9 on the top, &c. A twenty inch slide rule costs about $12.50. Slide rules are also made 1 inches and 5 inches long. These have correspondingly shorter graduations, and hence less accuracy. These smaller rules are not recommended for accounting purposes. < U z 8 _ U a, s H - i a bo E CHAPTER VI. THE CYLINDRICAL SLIDE RULE. For problems in multiplication and division requiring closer approximations than are obtainable by the plain slide rule, the cylindrical slide rule is well adapted. Fig. 23 is a general view of this instrument. In effect, it is one long slide rule, divided into 20 sections on trianpular bars, placed side by side around a cylinder. On a plain slide rule, the distance from 1 to 2 on the bottom scale is about 6 inches, while on the cylindrical rule, this distance is about 9 feet, hence the graduations are about 18 times as long, and the results may be read vith corre- spondingly greater accuracy. The same general principles govern the use of this as the plain rule. To multiply, set the index to the multiplier, find the multiplicand on !he slide (that is the cylinder) and read the answer opposite on the rule. To divide, set the index to the divisor, find the divi- dend on the rule, read the answer opposite on the slide. But there are some details in regard to the setting and reading which are worth further consideration. The index is 1 00 or 1 000, instead of 1 or 1 with the plain slide rule. There are several series of figures on the triangular bars; but for accounting purposes only two series are to be considered, namely one on the front of the triangular bars, close down to the cylinder, and one series on the back of the triangular bars close down to the cylinder. When the instrument is revolved toward you to read this back series, they appear on the top of the triangular bars. 76 THE CYLINDRICAL SLIDE RULE. There are two series of figures on the cylinder, corresponding to the two on the bars, as above described. Fig. 24 shows a portion of the cylindrical slide rule to exact size. The cylinder has been drawn out to the left and set to about 35864. The front of the particular triangular bar containing the figures where the instrument is now set, is so placed in the engraving as to be most easily read. The two bars above this one appear to run together in the engrav- ing. The bars in the centre naturally show both sides, the front and the back, with the figures somewhat distorted. The bars below the centre show their backs, with figures fairly clear. In using the instrument, it is revolved to such a position that the required number is easily legible, either on the front or the back of a bar. There are three indexes on the slide (cylinder) : 1 00 at the left, 1 000 in the centre and 1 000 at the right. These may be easily found by the heavy black spots. For purposes of setting, one or the other of the end indexes is used, the middle index being merely used as a check. Find the desired number for the setting on the front of the bar. If this number appears nearer the left than the right of the instrument, use the left index on the cylinder; if the number appears nearer the right hand end, use the right in- dex on the cylinder; if the number is approximately in the centre, either index will answer. The object in this discrim- inative setting is, like the setting for the bottom scale of the plain slide rule, to make sure that the answers to the problems will always be in range. Example: Set to 35864. Revolve the entire instru- ment until the number 358 is found on the front of a bar, close down to the cylinder. This appears nearer the right ^^^^L. 04 IN JU!| THE CYLINDRICAL SLIDE RULE. 81 hand end. Draw out the cylinder to the left, and revolve it (meanwhile firmly holding the body of the instrument with the right hand) until 1 000 at the right hand end of the cylin- der comes into view. There are two of these 1 000 indexes, side by side, belonging to two separate series; always use the one nearest to you. Bring this index 6 points beyond 358, then move it on nearly half way to the next graduation to read 35864. To check this setting and see that it is cer- tainly correct, revolve the whole instrument toward you about a quarter of a turn, and see that the centre index, 1 000 on the cylinder, is also set to 35864 on the back of the bar. Be careful to notice in all cases that the real index point is not the large black spot (which is only to attract the eye), but the hair line directly at 1 00 or 1 000. Example, multiply 35864 by 972. Set to 35864, as in the engraving. Find 972 on the cylinder (toward the upper left hand corner of the engraving,) read the answer opposite on the front of a bar, 34,860,000. The correct an- swer is 34,859,808. This is as near as the instrument will read in this part of the scale. Example, multiply 35864 by 146. Set to 35864, as before. Find 1 46 on the cylinder (toward the left centre of the engraving) read the answer opposite on the back of the bar, 5,236,100. The correct answer is 5,236,144. It will be noticed that in the part of the scale above 500, the grad- uations stand for two points. This is easily seen by counting the divisions, say between 5230 and 5240. There are only 5, and hence must represent 2 points each. Example, divide 35864 into 39750. Set to 35864. Find 397 on a bar, and look 5 graduations beyond, read the answer opposite on the cylinder, 1 . 1 084. This is correct to the nearest fifth figure. 82 THE CYLINDRICAL SLIDE RULE. In accounting, this instrument has its greatest usefulness in determining averages, unit costs and percentages: that is, those examples involving the dividing of a number of quant- ities by the same divisor, where the answer is required to be correct only to the fourth or fifth figure. It is convenient in using the instrument, both for setting, and for determining the answers, always to read the first three figures first, independent of the real decimal point. This is because three of the figures of any number are always printed on the instrument. For example, to deal with $27.45, you would read 274 first, and then find the fifth point beyond. Likewise in dealing with $274.50, or $2. 74, or $274,590.60, it is convenient to think of, or read, or call, 274 first. Unit costs, percentages, pro-rating, rule of three and all similar problems, are worked on the cylindrical slide rule in the same manner as with the plain slide rule. The instrument shown costs about $35.00. Larger ones of the same kind may also be had for about $75.00. CHAPTER VII. MULTIPLYING AND DIVIDING MACHINES. Fig. 25 shows a machine designed particularly for mul- tiplication and division, but also adapted for addition and subtraction. It is made in several sizes, the most common of which has a capacity of eight figures in the multiplier, eight in the multiplicand, and sixteen in the product. The opera- tion is very simple and rapid, especially for multiplication. If it is required to multiply, 69,317,563 by 64,795, move the knob to M for multiplication, set up the multipli- cand with the knobs in the upper part of the machine, as shown in the engraving. The figures will then show in the row marked "divisor." Now move the left hand indicator crank successively to 6, 4, 7, 9, 5, and turn the upper right hand crank one revolution every time the indicator is set. The whole multiplier will then appear in the middle row of figures, as shown, and the final result will be in the lower row. Other operations are performed very quickly, in the same gen- eral way, division being the most difficult. This machine is especially adapted for use in railways. Insurance Companies and large manufacturing plants, and for all cases where percentages or unit costs are required to very great accuracy. In the last named cases, the ordinary method would be to use a constant divisor and numerous varying divi- dends. But the easiest way in connection with this machine, is to first find the reciprocal of the divisor (which can easily 84 MULTIPLYING AND DIVIDING MACHINES. be done on the machine, itself), and set this up as a constant multiplier. If the results determined by this machine are to be tab- ulated and added, it is convenient to have the sheet for the results ruled to fit a listing adding machine, and record the results on the adding machine, as fast as they are read off from the multiplying machine. When the calculations are concluded, as for example, in percentage, the results will have been recorded and added, to prove the 1 00 per cent. The price of the machine shown is about $400.00. Fig. 26 shows another machine designed for the same purpose. It is somewhat simpler than the other, but not quite so rapid. To multiply, set the little levers on the top rounded sur- face to the figures of the multiplicand, (say 640,245,480.) Set the lower carriage back to the left, so that the arrow (which is now seen in the engraving pointing at 4) will point to 1 . This machine is then ready to multiply by units. One turn of the crank from you will multiply by 1 , and the multi- plicand will be seen in the dial at the right, and 1 will appear in the dial at the left. Four turns will multiply by 4, the re- sult appearing in the dial at the right, and the figure 4 at the left. Now move the carriage one place to the right, so that the arrow will point to 2 (showing that it is multiplying by a figure in the second or ten's place.) Turn the crank twice, move the carriage to the fourth place and turn the crank 7 times. You have then multiplied by 7024, as shown in the dial at the left, and obtained the result 4,497,084,251,520, shown in the dial at the right. Division is performed in the reverse manner, by turning the crank toward you. If a mistake is made in turning the bio E b& s MULTIPLYING AND DIVIDING MACHINES. 89 crank too many times one way, it may be immediately cor- rected by turning it back. This machine may also be used for addition and sub- traction, but it is not so rapid for this purpose as a regular adding machine. The size machine shown in the engraving costs about $250.00. CHAPTER VIII. CALCULATING TABLES. Whenever there are calculations to be made, involving multiplying a number of different amounts by a constant fac- tor, a calculating table is useful. A most common example of this condition is in making out invoices. Fig. 27 shows a sample page from a book of calculating tables. This is for 2.78 cents per pound, per yard, &c. All invoices to be calculated at this price are sorted out, and the extensions read from this page. For example, 287 pounds $7.98. For quantities over 1000 pounds in this book, two readings are necessary. For example, 96,898. Find 96,000, $2,668.80. Find 898, $24.96. Add these two results, $2,693.76. A great variety of these books are made, covering a wide range of work. In selecting a book of tables, it is best to define the range of work, and get a book as small and as little complicated as will answer the purpose. There are some books published which cover practically an infinite range of prices, in one volume. But in a business handling, say sugar, bacon and lard, ranging by 1-16 cent, from 4 to 1 5 cents per pound, it is more convenient to have one small vol- ume of tables covering only this range, than to have a large volume, covering every possible range. At the top of the sample page will be noticed the re- ciprocal, 359712. The next page 2.79 would have the re- ciprocal 358425.. These reciprocals are not habitually printed at the head of calculating tables, but they are fre- quently valuable, and can be easily determined and marked SAMPLE PAGE CALCULATING TABLE: "RECIPROCAL 359712. PORTIONS OMITTED. ( 1078 1 178 *l _ — 078 n078 ■1 U A .100 200 ZToo ■Uz I 03 101 .2 81 201 5 59 90T 25 05 2.000 56 60 c 06 102 2 84 202 5 62 902 25 08 3,000 88 40 3 08 103 2 86 203 5 64 903 25 10 4,000 111 20 4 11 104 2 89 204 5 67 904 25 18 5.000 139 00 5 14 105 2 92 205 5 70 905 25 16 6,000 166 80 6 17 106 2 95 206 5 73 906 28 19 7,000 104 60 7 19 107 2 97 207 5 75 907 25 21 8,000 222 40 8 22 108 8 00 208 5 78 908 25 24 9,000 250 20 9 25 109 8 03 209 5 81 909 28 27 10,000 278 00 10 28 110 3 06 210 5 84 910 25 30 1.1 ,000 805 80 11 81 111 8*09 211 5 87 911 25 33 12' 000 833 60 12 33 112 8 11 212 5 89 912 25 85 13,000 861 40 13 86 113 3 14 213 5 92 913 25 88 14,000 389 20 65 1 81 165 4 59 265 7 37 66 1 88 166 4 61 266 7 39 67 1 86 167 4 64 267 7 4-2 68 1 89 168 4 67 268 7 45 69 1 92 169 4 70 269 7 48 70 1 95 170 4 78 270 7 51 71 1 97 171 4 75 271 7 58 72 2 00 172 4 78 272 7 56 73 2 03 173 4 81 273 7 59 74 2 06 174 4 84 274 7 62 75 2 08 175 4 86 275 7 64 76 2 11 176 4 89 276 7 67 77 2 14 177 4 98 277 7 70 78 2 17 178 4 95 278 7 73 79 2 20 179 4 98 279 7 76 80 2 22 180 5 00 280 7 78 81 2 25 181 5 03 281 7 81 82 2 28 182 5 06 282 7 84 83 2 81 183 5 09 283 7 87 84 2 34 184 5 IS 284 7 90 85 2 36 185 5 U 285 7 92 86 2 39 186 5 17 286 7 95 87 2 42 187 5 20 287 7 98 88 2 45 188 6 23 288 8 01 89 2 47 189 5 25 289 8 03 90 2 50 190 5 28 290 8 06 91 2 53 191 5 31 291 8 09 92 2 56 192 5 84 292 8 12 93 2 69 193 5 37 293 8 15 94 2 61 194 5 39 294 8 17 95 2 64 195 5 42 295 8 20 96 2 67 196 6 45 296 8 23 97 .2 70 197 5 48 297 8 26 98 2 72 198 5 50 298 8 28 99 2 75 199 5 53 299 8 81 100 2 78 200 5 56 300 8 34 965 26 83 66,000 1834 80 966 26 85 67,000 1862 60 967 26 88 68.000 1890 40 968 26 91 69,000 1918 20 969 26 94 70 000 1946 00 970 26 97 71.000 1978 80 971 26 99 72,000 2001 60 972 27 02 73.000 2029 40 973 27 05 74,000 2057 20 974 27 08 75 000 2085 00 975 27 10 76,000 2112 80 976 27 13 77.000 2140 60 977 27 16 78,000 2168 40 978 27 19 79.000 2196 20 979 27 22 80,000 2224 00 980 27 24 81,000 2251 80 981 27 27 82,000 2279 60 982 27v30 83.000 2307 40 983 27 33 84.000 2386 20 984 27 36 85; 000 2868 00 985 27 38 86 000 , 2390 80 986 27 41 87.000 2418 60' 987 27 44 88.000 2446 40 988 27 47 89,000 2474 20 989 27 49 90,000 2502 00 990 27 52 91 .000 2529 80 991 27 55 92.000 2557 60 992 27 68 93 000 2585 40 993 27 61 94,000 2613 20 994 27 63 95 000 2641 00 995 27 66 96,000 2668 80 996 27 69 97,000 2696 60 997 27 72 98,000 2724 40. 998 27 74 99,000 2752 20 999 27 77 100,000 2780 00 1.000 27 80 200.000 5560 00 Fig. 27. 92 CALCULATING TABLES. by hand on the top of each page of the tables. In case of finding average costs per unit of production, or in any case where one divisor is constant for several dividends, this con- stant divisor may be found as near as may be among the re- ciprocals at the tops of the pages ; then, opposite the amount in the table, may be read the unit cost. For example, the production of a factory is 3597, and the cost of fuel $29.87. Opposite 299 on the page shown in the engraving is 83 1 . It may be seen by inspection that the cost is less than a cent a pound, hence we read in cents .83 1 . If this result is not suffi- ciently accurate, by reason of using 299, instead of 2987, find 2000 in the table, and read opposite, 5560. Now find 987, and read opposite, 2744. Add these two readings and the answer is .8304 cents. This same style of calculation may be used to find the respective percents which any number of constituent parts form of a whole. For example, what percents are 30,000, 5,000, 971, of the whole 35,971. Opposite 30,000 on the page shown in the engraving read 83.4%; op- posite 5,000, 13.9%; opposite 971, 2.7%. Fig. 28 is a sample page from a potato and grain calcu- lator. This page shows the value of any number of pounds of potatoes or wheat @ 85 cents per bushel, 60 pounds of these commodities being a bushel. This table may also be used for a variety of other commodities, as indicated at the top of the page. Fig. 29 is a sample page from an interest computer, of which there are many kinds, arranged to suit various require- ments. This particular book is arranged for six per cent, and for every day in the year. It has a key for converting the re- sult at any other rate than six. The publishers of this book have discovered another SAMPLE PAGE CALCULATING TABLE : PORTIONS OMITTED. 3 2 Lbs. Oats at 3 .45'/3 . PerBu. \ 34 M Malt at .48,16 + " 1 48 ** Barley at .68 • 4% *■ .5 5 " Turnips at 6 " Corn at 5 M •• of .77,91 H- M ■ .99,16 + .02 .06'4 1 UK ft The Calculations on 5 6 7 7 I | I OjCi This Page are Also Applicable to j .. .. 2 .. 5 " " at at 1 at 1 •; ( For Potatoes and Wheat at •« " at .13$ • 60 Lbs. to Bushel* Freight and Hay at 1 .41% Per 100 Lbs. J at 28.33ft " Ton. / 1 01 101 143 1010 14 31 2010 23 474 3010 42 64 4010 56 81 5010 70 974 2000 28 33 2 03 102 1 444 1020 14 45 2020 28 62 3020 42 78 4020 56 95 5020 71 12 3000 42 50 3 04 103 1 46 1030 14 59 2030 28 76 3030 42 924 4030 57 09 5030 71 26 4000 56 67 4 06 104 1 47 1040 14 73 2040 28 90 3040 43 07 40S0 57 23 5040 71 40 5000 70 83 s 07 105 1 49 1050 14 874 2050 29 04 3050 43 21 4050 57 374 5050 71 54 6000 85 00 8 084 106 1 50 1060 15 02 2060 29 18 3060 43 35 4060 57 52 5060 71 68 7000 99 17 7 10 107 1 52 1070 15 16 2070 29 324 3070 43 49 4070 57 66 5070 71 824 6000 113 33 8 11 108 1 53 1080 15 30 2080 29 47 3030 43 63 4080 57 80 5080 71 97 S000 127 50 I 9 13 109 1 54 1090 15 44 2090 29 61 3090 43 774 4090 57 94 5090 72 11 10000 141 67 j 10 14 110 1 56 1100 15 53 2100 29 75 3100 43 92 4100 58 08 5100 72 25 11000 155 83 1 11 16 111 1 57 1110 15 724 2110 29 89 3110 44 06 4110 58 224 5110 72 39 12000 170 00 12 17 120 170 1120 15 87 2120 30 03 3120 44 20 4120 58 37 5120 72 53 13000 184 17 13 13 130 1 84 1130 16 01 2130 30 174 3130 44 34 4130 58 51 5130 72 674 14000 198 33 14 20 140 1 98 1140 16 15 2140 30 32 3140 44 48 4140 58 65 5140 72 82 15000 212 50 15 21 150 2 12i 1150 16 29 2150 30 46 3150 44 624 4150 58 79 5150 72 96 16000 226 67 16 23 160 2 27 1160 16 43 2160 30 60 3160 44 77 4160 58 93 5160 73 10 17000 240 83 17 24 170 2 41 1170 16 574 2170 30 74 3170 44 91 4170 53 074 5170 73 24 180C0 255 00 18 254 180 255 mo 16 72 2130 30 88 3180 45 05 4180 59 22 5180 73 38 19000 269 17 19 27 190 2 69 1190 16 86 2190 31 024 3190 45 19 4190 59 36 5190 73 524 20000 283 33 20 28 2on 2 83 I2C0 1/ 00 2230 31 17 3200 45 33 4200 59 50 5200 73 67 21030. 297 50 21 30 210 2 97A 1210 17 14 2210 31 31 3210 45 471 4210 59 64 5210 73 81 22000 311 67 22 31 220 3 12 1220 17 28 2220 31 45 3220 45 62 4220 59 78 5220 73 95 23000 325 83 23 33 230 3 26 1230 17 4>4 2230 31 59 3230 45 76 4230 59 924 5230 74 09 24030 340 00 24 34 240 3 40 1240 1/ 5/ 2240 31 73 3240 45 90 4240 60 07 5240 74 23 25CC0 354 17 25 35 250 354 1250 1/ 71 2250 31 874 3250 4i 04 4250 60 21 5250 74 374 26000 368 33 26 37 260 3 68 1260 1/ b5 2260 32 02 3260 45 18 4260 60 35 5260 74 52 27000 382 50 i 27 38 270 3 82i 1270 17 99 2270 32 16 3270 46 324 4270 60 49 5270 74 66 28000 396 67 i 28 40 280 3 97 1280 18 13 2280 32 30 3280 46 47 4280 60 63 5280 74 80 29000 "10 &3 60 85 600 8 50 1600 22 67 2600 36 83 3600 51 00 4600 65 17 5600 79 33 61000 864 17 61 86 610 864 1610 22 81 2610 36 974 3610 51 14 4610 65 21 5610 79 474 62C08 878 33 62 83 620 8 78 1620 22 95 2620 37 12 3620 51 28 4620 65 45 5620 79 62 63000 892 50 63 89 630 8 924 1630 23 09 2630 37 26 3630 51 424 4630 65 59 5630 79 76 64000 906 67 64 91 640 9 07 1640 23 23 2640 37 40 3640 51 57 4640 65 73 5640 79 90 65000 920 83 65 92 650 9 21 1E50 23 374 2650 37 54 3650 51 71 4650 65 874 5650 80 04 66000 935 00 66 934 660 9 35 1E60 23 52 2660 37 68 3660 5185 4660 66 02 : . cso 80 18 67000 949 17 67 95 670 9 49 1670 23 66 2670 37 824 3670 51 99 4670 66 16 5670 80 324 68000 963 33 68 96 680 9 63 1680 23 80 2680 37 97 3680 52 13 4680 66 30 5680 80 47 69000 977 50 69 98 690 9 77J 1690 23 94 2690 38 11 3690 52 27i 4690 66 44 5690 80 61 70000 991 67 70 99 700 9 92 1700 24 08 2700 38 25 3700 52 42 4700 66 58 5700 80 75 71000 1005 83 71 1 01 -710 10 06 1710 24 224 2710 38 39 3710 52 56 4710 66 724 5710 80 89 72000 1020 00 1 72 1 02 720 10 20 1720 24 37 2720 38 53 3720 52 70 4720 66 87 5720 81 03 73000 1034 17 ' 73 1 03 730 10 34 1730 24 51 2730 38 674 3730 52 84 4730 67 01 5730 81 174 74000 1048 33 I i 74 1 05 740 10 48 1740 24 65 2740 38 82 3740 52 98 4740 67 15 5740 81 32 75000 1062 50 75 1 06 ;750 10 62i 1750 24 79 2750 38 96 3750 53 124 4750 67 29 5750 81 46 76000 1076 67 76 1 08 760 10 77 1760 24 93 2760 39 10 3760 53 27 4760 67 43 5760 8160 77000 1090 83 77 1 09 770 10 91 1770 25 074 2770 39 24 3770 53 41 4770 67 574 5770 81 74 78000 1105 00 78 1 10} 780 11 05 1780 25 22 2780 39 38 3780 53 55 4780 67 72 5780 81 83 79000 1119 17 79 1 12 790 11 19 1790 25 36 2790 39 524 3790 53 69 4790 67 86 5790 82 024 80000 1133 33 80 1 13 800 1133 1800 25 50 2800 39 67 3800 53 83 4800 68 00 5800 82 17 81000 1147 50 81 lit 810 11 474 1810 25 64 2810 39 81 3810 53 974 4810 68 14 5810 82 31 82000 1161 67 82 820 11 62 1820 25 78 2820 39 95 3820 54 12 4820 68 28 5820 82 45 83-300 1175 83 83 1 18 830 1176 1830 25 924 2830 40 09 3830 54 26 4830 68 424 5830 82 59 84000 1190 00 84 1 19 840 11 90 1840 26 07 2840 40 23 3840 -64 40 4840 68 57 5840 82 73 85000 1204 17 85 1 20 850 12 04 1850 26 21 2850 40 374 3850 54 54 4850 68 71 5850 82 874 86000 1218 33 86 122 860 12 18 1860 26 35 2860 40 52 3860 54 68 4860 68 85 5860 83 02 87000 1232 50 87 123 870 12 324 1870 26 49 2870 40 66 3870 54 824 4870 68 99 5870 83 16 88000 1246 67 88 1 25 880 12 47 1880 26 63 2880 40 80 3880 54 97 4880 69 13 5880 83 30 89000 1260 83 89 1 26 890 12 61 1890 26 774 2890 40 94 3890 55 11 4890 69 274 5890 83 44 90000 1275 00 90 1274 900 12 75 1900 26 92 2900- 4rra 3900 55 25 4900 69 42 5900 83 58 91000 1289 17 91 1 29 (910 12 89 1910 27 06 2910 41224 3910 55 39 4910 69 56 5910 83 724 92000 1303 33 92 1 30 920 13 03 1920 27 20 2920 41 37 3920 55 53 4920 69 70 5920 83 87 93000 1317 50 93 1 32 930 13 174 1930 27 34 2930 41.51 3930 55 674 4930 69 84 5930 84 01 94000 1331 67 94 1 33 940 13 32 1940 27 48 2940 4165 3940 55 82 4940 69 98 5940 84 15 95000 1345 83 95 135 950 13 46 1950 27 624 2950 41 79 3950 55 96* 4950 70 124 5950 84 29 96000 1360 00 96 '136 960 13 60 1960 27 77 2960 41 93 3960 56 10 4960 70 27 5960 84 43 97000 1374 17 97 137 970 13 74 1970 27 91 2970 42 074 3970 56 24 4970 70 41 5970 84 574 98000 1388 33 g -139 980 13 88 1980 28 05 2980 42 22 3980 56 38 4980 70 55 5980 84 72 99000 1402 50 140 990 14 024 1990 28 19 2990 42 36 3990 56 524 4990 70 69 5990 84 86 100000 1416 67 109 142 1000 14 17 2000 28 33 3000 42 50 4000 56 67 5000 70 83 6000 85 00 "200009 2833 33 Fig. 28. 94 CALCULATING TABLES. somewhat peculiar use for this table. Most oils are sold at a certain price per gallon, but are weighed, to determine the number of gallons. Linseed, cotton seed, and many other kinds of oils weigh 7 1 -2 pounds per gallon. These interest tables are adapted for calculations on oils of this weight. All that is necessary is to mark the proper price on each page. For example, the page shown, 296 days, corresponds to oil at 37 cents per gallon. Opposite 300 on this page is $1 4.80. This is 300 pounds of oil or 40 gallons @ 37 cents. The next page of this table would be 297 days and would corre- spond to 37 1-8, and so on, varying by 1-8 cent. The page for 8 days would give the value of any number of pounds of oil @ 1 cent per gallon, or it would give the number of gal- lons in the pounds stated. The page for 80 days gives the same thing by pointing off one decimal. For example, oppo- site 310 is 413, which may be read 41.3 gallons. It is not usually necessary to state the gallons on an oil invoice, but the information is frequently desirable. Incidentally, it may be interesting to state that pounds may be converted into (7 1-2 pound) gallons by adding 1-3 to the pounds, and pointing off one decimal. Also gallons may be converted into pounds by moving up the decimal place and deducting 1-4 from the gallons. Adding to 310, 1-3 of 310 (103) gives 413. Point off one decimal and we have 41 .3 gallons. Deducting from 413, 1 -4 of 41 3 ( 1 03) gives 3 1 pounds. In any large business requiring the same line of calcula- tions to be done repeatedly every day, it is profitable to use calculating tables. If there are none published which exactly fit the case, it is very easy and profitable to construct a set of tables to suit. The tables, as illustrated here, are reduced from the large tables as published in the calculating books, by cutting out some of the matter, instead of by reducing the size of the type. SAMPLE PAGE INTEREST TABLE: PORTIONS OMITTED. 74(? 75* 76* 77* 78* 79* 80* 81* 82* 83* 84* 85* 86* 87* 88* 89* 90* 91* 92* 93* 94* 95* 96* 97* 98* 99* 100* 9 MONTHS AND ' 3 % Interest; on basis of A n 360 days to a year. /H 6D ATS I 26 DAYS. 296 ^r ■ L ' 11 1 Mi ii $o oo 1 05 101 4 98 ] 901 44 45 2,000 98 67 2* 3* 4* 5* 6* 7* 8* 9* 10* 11* 12* 13* 14* 15* 16* 00 ^2 10 102 6 03 [ 902 103 5 08f 903 44 50 3,000 148 00 00 3 15 44 "55 4,000 107 83 00 4 20 104 5 13 904 44-60 5,000 246 67 00 5 25 105 5 18 -905 44 65 6,000 296 00 00 6 30 106 5 23 906 44^70 7,000 845 33 00 7 85 107 5 28 907 44 75 8,000 894 67 1 00 8 39 108 5 33 908 44 79 9.000 444 00 00 9 44 109 5 38 909 44 84 10,000 493 33 oo 10 49 110 5 43 910 44 89 11,000 642 67 01 11 54 111 5 48 911 44 94 12,000 592 00 01 12 59 112 5 53 912 44 99 13,000 641 33 01 13 64 113 5 57 913 45 04 14,000 690 67 01 14 89 114 5 62 914 46 oo 15,000 740 00 01 15 74 115 5 67 915 45 14 16,000 789 83 01 16 7'.) 11.6 5 72 916 45 10 17,000 888 67 17* 18* 01 17 '84 117 6 77' 917 45 24 18,000 888 00 01 18 89 118 5 82 918 45 29 19,000 937 33 19* or 19 94 119 5 87 919 45 34 20,000 986 67 20* 01 20 99 120 5 92 920 45 39 21,000 1036 00 21* 01 21 1 04 121 5 97 921 45 44 22,000 1085 33 .22* 01 22 1 09 122 6 02 922 45 49 23,000 1134 67 23* 01 23 1 13 123 6 07' 923 45 53 24,000 1184 00 74 3 r,r, 174 8 18 1974 48 05 75.000 8700 00 75 3 70 175 8 63 j 975 « «» '976 48 10 76,000 3749 33 76 3 75 176 48 15 77,000 8798 67 11 3 80 177 B 73 977 48 20 78.000 3848 00 78 8 85 178 8 78 978 48 25 79,000 8897 83 79 3 90 179 8 K3 979 48 80 80.000 3946 67 80 81 3 95 180 8 K8 980 48 35 81,000 3996 00 4 00 181 8 03 981 48 40 82,000 4045 83 8 00 CO CO CO CO ; 4 05 182 8 98 982 48 45 83,000 4094 67 4 09 183 9 03 983 48 49 84,000 4144 00 4 14 184 9 08 984 48 54 85,000 4193 83 4 19 185 9 13 985 48 59 86,000 4242 67 4 24 186 9 18 986 48 64 87,000 4292 00 4 29 187 9 23 987 48 69 88,000 43 11 83 89 90 91 92 93 94 95 96 97 98 99 1100 4 34 188 9 27 988 48 74 89,000 4390 67 4 39 189 9 32 989 48 79 90,000 4140 00 4 44 190 9 37 990 48 84 91,000 4489 33 4 49 191 9 42 991 48 89 92,000 4538 67 4 54 192 9 47 992 48 94 93,000 4588 00 4 69 193 9 52 993 48 99 94,000 4637 33 4 64 194 9 57 994 49 04 95.000 4686 67 4 69 195 9 62- 995 40 09 96,000 4736 00 4 74 4 79 4 83 4 88 4 93 196 9 67 996 49 14 97,000 4785 33 197 198 199 200 9 72 9 77 9 82 9 87 997 998 999 1000 49 19 49 23 49 28 49 33 98,000 99,000 100,000 200.0CO 4834 67 4884 00 4933 33 9866 67 Fig. 29. CHAPTER IX. BILLING AND CHARGING. It is self evident that the charge against a customer's account should be identical in amount with the invoice. It is equally evident, that if the charging is one separate opera- tion, and billing another, there is a chance for a difference, such chance depending upon the accuracy and fidelity of the particular individuals who do the work. The only absolutely certain method is to make the in- voice and the charge at one operation. This may be accom- plished by the use of carbon sheets. There are certain other documents that have on them the same information as the in- voice, in a greater or less extended form. These are: office shipping order, factory shipping order, stock sheet, dray re- ceipt, railroad bill of lading, packing list, duplicate invoices for branch offices, &c. With a proper arrangement of papers, it is possible to make all these documents at one operation, thus ensuring accuracy, and saving time. A type-writing machine is not an absolute necessity for making duplicate carbon documents; but it is a good con- venience, and is conducive to neater and more compact and legible records. Fig. 30 shows a flat writing or billing machine, well adapted to this kind of work. The types strike down on a hard flat surface, and may be struck hard enough to produce a dozen copies. Fig. 3 1 shows a machine equipped with a roll of carbon % u. s 00 DUPLICATE DOCUMENTS MADE BY BILLING MACHINE. 5^^^ Fig- 32. BILLING AND CHARGING. 103 paper, which may be used in some cases to avoid the neces- sity of handling carbon sheets. Fig. 32 shows a number of duplicate invoices, and a tripli- cate sales record, all made at one operation for each set. One sales record may be filed in a loose leaf book for the per- manent sales journal, whence the posting may be done, indi- vidually to the debit of the customers, and by totals to the credit of the sales accounts. If a bound record is preferred, the invoice blanks may be bound alternately with the sales records, and detached when desired. If the adding machine record is preferred, the invoices may be padded instead of bound. The original is sent to customer; and the account is posted from the carbon copy, which is then placed in a vertical file until the end of the month, when it is listed on a permanent sheet in the adding machine. The monthly totals may be posted from this list to the credit of the Mer- chandise accounts. Fig. 33 shows an adding attachment to the writing ma- chine which has recently been perfected. With this attach- ment, the work of billing and charging becomes merely a question of accurate copying, to be done by a good machine operator, without regard to his ability as a book-keeper. Fig. 34 shows the billing machine with the type-writing part removed from the flat platen, to exhibit the various de- vices for holding different kinds of sheets. Broad sales record sheets may be put down first and held, say on the left hand edge by studs through the binder post holes. Then the office order, factory order, bill of lading, invoice and other docu- ments may be laid down with carbon sheets between. If some papers are narrower than others, the steel nbbon, as shown in the engraving, may be adjusted to hold them in 104 BILLING AND CHARGING. place. When one side of sales sheet is filled, it may be turned over and fastened to the binder posts on the right hand edge. If any part of the information on the invoice is unneces- sary or undesirable on any of the underlying documents, these documents may be made shorter or narrower ; or the carbon sheets immediately above the document may be cut shorter or narrower; or an extra sheet of paper may be inserted, hav- ing slits cut in it, to expose just such parts as are wanted and suppress all other parts on any given document. Standing straight up in Fig. 34 is seen the sliding bill holder. The bill is fastened to the sliding clamp, by which it may be moved along from top to bottom of underlying sheets. With this device it is possible to make out a complete bill, containing all the details desirable, and yet, by suppress- ing all but the date, customer's name and amounts on the un- derlying sales sheet, this information will be recorded on one line of sales sheet. The bill may be slipped along with the bill holder, so that as it is made, there will be recorded the date, customer's name and amount, on the next line of the sales sheet, and so on. This one sheet of sales journal may record for posting some thirty or forty bills. This same scheme may be used to advantage for check writing, in cases where a large number of checks are to be written for charge to the personal account of the payee, or for charge to one representative account (Salaries or Com- mission, for example). In these cases, only one line is neces- sary for the record; namely, date, payee, and amount The checks are printed so that these facts may be written on one line. They are put up in pads, consecutively numbered. They have short stubs, which are perforated, and punched to fit the bill holder. The check record, (which takes the place of the record made on the stubs in the usual style of check book) be bib E BILUNG AND CHARGING. 109 may be a loose leaf or a bound book. Each line is numbeied consecutively to correspond with the check numbers. The check is put on the bill holder, over a carbon sheet over the check record; the date, payee and amount is written, the next check is inserted and slipped along, so that the carbon writing will appear on the next line of check record, and so on. Thus, thirty to forty checks may be recorded on one page, instead of five to ten written in any other way. A great deal of unnecessary sacredness is cherished about checks and check books. It has been quite generally believed that it was essential to have checks bound w ith then- stubs in a book, so that the check and its stub have to be sep- arately written. The stub is then copied in the cash book, making three entries of the same transaction, whereas one would be better. With proper precautions, it is quite as safe to have numbered checks in pads as in books. In either case, a check may be abstracted, and equally in either case the missing number would expose the fact. Even with bound checks and stubs, the stubs may serve as a cash book, for posting direct to the ledger, instead of through the medium of a cash book. There is a prejudice against filling out checks with a typewriter, based on the fear that they might be easily raised. This fear will pass away when it is considered that ink ribbons are available which are practically indelible. It is practicable, too, to have a machine with special type, covered with points, which will partially perforate the check, while writing. Fig. 35 shows a most ingenious system for handling "back orders," that is, goods which cannot be shipped at once. A pad of order blanks is made up, marked succes- sively: Original, and A, B, C, D, E, &c. Carbon sheets no BILLING AND CHARGING. are interleaved. The original order, as sent in, is checked and approved, and passed to the machine operator, who copies it in the column, headed "Quantity Ordered." The original, or top copy is sent to the stock room, where the goods are "laid out,*' as far as possible to fill the order that day. The quantities are entered with pencil in the column headed A, and the blank is returned to the office. When the goods are ready to be boxed, the packer makes his count and enters it on the sheet marked A. This sheet is in turn sent to the office, and there compared with the original and entirely independent count, and then becomes the basis of the bill and charge. When the next installment is ready to go, the shipping clerk "lays out" the goods, and enters quantities in the B column of the original sheet, which goes back to the office. The packer makes his independent count and enters it on the sheet marked B, which goes to the office for comparison with column B on the original, and for billing, as before. This routine is continued until the entire order is filled. The Office knows at all times by reference to the original order sheet, just what may still be due at any time on any order. This same scheme may be used for inter-company or- ders and memorandum invoices. For example, a Branch House sends the order to Factory in multiple on these forms; the factory fills out the goods in duplicate on the successive blanks, A, B, C, and uses one copy for the memorandum charge to Branch Office, then Branch Office uses the same sheet for checking, and for crediting the factory and debiting it's own stock. In the engraving, the top, or original order sheet (which is the same size as the others) is folded under at the bottom, ! o o u u. «., | ! 9 § Sj B ? Six | tt -5 f . 8 - qpf j i § | i \. SJ3S sas DEPARTMENT STORE MONTHLY BILL AND CHARGE. Marshall In 1.1) & Company. Importers. Retailers. M VXIIVACTI i KHS W K-llllS.. f.V K-.N ,„.,.. iAWahasi g Chi <:.\< O.Apr 1 19« Mra willlaa D«»ina 283 Wabatar A»a 2/7°6 .»__.. -"KT 615 i 4 Dreaa Oooda 6 oo 1 h.»t Challle 1 35 3812 1 carver 3 25 10 60 2602 5 1 Coraat 1 50 404 1 1 1 Murn«r 2 25 2 50 2 50 «75J 2114 7 1 3 oo»n M 1 00 1 SO j ChaaUaa 1 50 4 OO! l Rant CbalUe 1 Cor sat 3504 10 J Ox KOU 4 00 1 00 U15 U • tUuKlna 2 ,•0 3 TJaa 6 25 I 13 1 Walat 6 oo & 1 Pr aiotaa S«»l sun Co.' 45 1 7^ 35 50 90 1 64 72 6 oo 64 1 ^ 35 >6o» 2. So6 27 1 HO) 7g 2 J J 2 1 1 9 2 1 Co* Pr & • Sll. Da Handh Raaaant I* BNM Tda Planaal 2 • rjabrolti«ry Pig- 3 6 - ( NOTE. — The items returned, aggregating 2.85 and 6.35, are made in red by the Bill- ing Machine.) BILLING AND CHARGING. 115 to show the underlying copies. The first one seen is copy A. The other copies B, C, D, &c, are drawn out to the left. Fig. 36 shows a method much in vogue in department stores, and other large retail houses. The underlying part of the sheet is somewhat wider than the top, and is punched for filing in a loose leaf binder as a permanent record. This folded sheet is inserted in the billing machine, and held in place by studs which fit in the post holes in the sheet. Entries are made from the sales tickets each day; and the sheet is removed each day and put in a vertical file. At the end of the month the customer's bill is all made out, ready to be de- tached along the right hand perforated edge. If the number of customers is not too large, the carbon sheets may constitute leaves in a loose leaf ledger. In this case, all the carbon leaves for the month are listed by totals, on the adding machine sheet, and the total of all the sales posted from this sheet to the credit of the (one or more) sales accounts. This retains the double entry system almost wholly without hand work. If the business is so large that the ledger kept in this manner would be cumbersome, the carbons of customers' bills are listed by totals on the adding machine sheets, each customer's account number being recorded (by keys on the extreme left of the machine) at the same time. The total of each customer's bill for the month is posted from this sheet to customer's account on the ledger, and the total of all sales posted from this sheet to the credit of the sales account. Un- der this system, the personal accounts on the ledgers need have only twelve debit entries in a year, and hence one page of the ledger would last several years. In cases of dispute, the carbon copies of the bill are always available in their binders or folders. 1 16 BILLING AND CHARGING. Large department stores have a general ledger which is used for all representative accounts. In this ledger each department is credited each day with the amount of its sales. The corresponding debits are made against a series of ac- counts with personal ledgers, dividing the alphabet into con- venient sections, depending upon the number of customers, say, A to C, D to E, &c. The method of handling the sales tickets, and finally posting them to the individual accounts in the sectional per- sonal ledgers, is as follows: 1 . The charge tickets for the day are sorted according to departments, and listed on an adding machine sheet, show- ing a total for each department (and sub-total for sub-depart- ments, if desired), and finally a grand total for all sales for the day. 2. The tickets are sorted alphabetically, without re- gard to departments, and then separated into sections corre- sponding to the personal ledgers, say A to C in one lot, D to E in another, &c. These lots are listed on the adding ma- chine sheet, showing a total for each ledger, and finally a grand total for the day. This grand total must, of course, equal the grand total, as shown when the tickets were listed according to departments. 3. The amount of the sales made in each department, as shown by the adding machine sheet, ( 1 ) , is posted direct from the sheet to the general ledger to the credit of that de- partment. 4. The amount of the sales which have been allotted to each personal ledger, as shown by the adding machine sheet, (2) is posted direct from this sheet to the general ledger to the debit of that personal ledger. 5. Sales tickets, being already alphabetically arranged BILLING AND CHARGING. 117 and sorted according to personal ledgers, are now distributed in this order, to the clerks who write them up with the billing machines, making the customer's bills and charges at the same time, as shown in Fig. 36. The daily total is extended in every case. 6. The daily totals for each personal ledger are listed on the adding machine sheet, and agreed with the amount which has been charged on that day against that ledger on the general ledger. 7. The monthly total on each customer's bill is posted to the debit of the customer in the proper personal ledger. 8. At the end of the month, the totals for each per- sonal ledger are listed on the adding machine sheet and agreed with the debit balance against that ledger on the gen- eral ledger. This method automatically makes a daily and monthly trial balance. The sale tickets have been listed in two differ- ent orders ; and if the totals for the day are the same in both cases, there is small chance for error. The most open chance for an error in the entire chain, is in extending the daily totals on the customers' bills. Even this chance is practically elimi- nated by the use of the adding attachment to the billing machine. It will be seen that the above system of double entry accounting on the general ledger treats a whole personal ledger as the debtor, versus the Department as the creditor. The Personal Ledger makes no attempt at double entry, but merely itemizes the daily charge, which is made against it on the general ledger. Goods returned are put on a different colored ticket, and this follows a course similar to the charge ticket. The credit tickets are assembled and credited on general ledger 1 18 BILUNG AND CHARGING. to the respective personal ledgers, and charged to the re- spective departments. The tickets are entered as a credit (usually in red ink) on the customer's bill, and the monthly totals posted to credit of customer's account on personal ledger. Totals are reconciled monthly with general ledger. Cash received on account, as currency, passes through the cash register. Carbon copies of the receipts given the payers are sorted alphabetically at the end of the day's busi- ness and assembled in groups corresponding to the divisional personal ledgers. These are listed in regular order on the adding machine sheet. The tickets are then taken up in the same order, and the names entered opposite the amounts with a typewriter (if the typewriter has an adding attach- ment, of course one operation accomplishes the whole pur- pose.) The completed sheet now forms a leaf of the cash book, from which postings are made. Checks received are sorted as above, and listed in car- bon duplicate. The original forms a leaf of the cash book, and the duplicate may be used as a deposit slip. In this case, the duplicate sheet may be cut narrower than the original, so that the names of the payers wili not appear, this being unnecessary on a deposit slip. Currency received for cash sales is passed through the cash register. The sale tickets are sorted according to de- partments, listed in that order on the adding machine sheet, and summarized and balanced with the cash register. The adding machine sheets are filed in a loose leaf binder to make cash book, whence the proper credits are posted to the re- spective departments. The billing machine, as shown, costs about $200.00. The adding machine attachment costs $160.00 extra with one set of dials, and $220.00 with two sets, as shown in Fig. 33. CHAPTER X. THE AUTOGRAPHIC REGISTER. Multiple copies of documents are a prime necessity in all modern offices. These may be made by inserting carbon sheets between the blanks, and writing by hand, or may be made with a type-writing machine of regular or special pat- tern. They may also be made by hand, with the assistance of the autographic register. Fig. 37 shows one form of register, in which special stationery is provided on rolls, in such a manner that carbon sheets are interleaved, as the stationery is drawn out for use. These machines are arranged in a variety of styles, to suit particular conditions. If it is required to produce two or more simple copies for immediate use, all the copies are drawn out and torn off. If one copy is required, say as a bill to a customer, and one copy as a shipping order, shipping ticket or bill of lading, the blanks are properly printed for these various purposes, and the first two copies are torn off as made, while a third copy is rolled up inside the machine as a permanent record. This record may be perforated at stated intervals, say 1 4 inches, for the length of a page, and when removed may be filed in a loose leaf binder as a sales journal. Fig. 38 shows the original copy of a weighing ticket for the purpose of seed cotton, on which is written all the necessary informaton, including the gross, tare and net weights. Fig. 39 shows a record of this and several other similar i2o THE AUTOGRAPHIC REGISTER. transactions, which was rolled up in the machine, as made. The mechanism for feeding the rolls of paper is so con- structed that when the full width of a ticket (say 3 inches) is pulled out for the customer, the duplicate or record roll is advanced just enough for one line in the journal. This is a very desirable arrangement for making sale slips or original invoices, and making the entry in any desired detail in the sales journal at the same time, and leaving the record compact for easy addition. This same scheme may be used for writing checks, especially where a large number must be written for charging to either the personal account of the payee, or all to the same account, as Salary, Commission, Dividend. Many other adaptations will suggest themselves to the user of the machine. The carbon sheets are slowly fed from a continuous roll at one side of the machine, across and between the docu- ments, and wound up on a roll on the other side. This keeps the writing surface of the carbon fresh, and avoids the neces- sity of handling carbon sheets. These machines cost about $25.00, when fitted as shown in the engraving. an s TICKET FROM AUTOGRAPHIC REGISTER. ORIGINAL. ' rnplioate Not Negotiable. } One Load Seed Cotton. Tird Ticket No.^li2 A. Newtown ^JILoMliL 190.L Tare k CONSECUTIVE CHECK: M 971 Consecutive No. Ill A/wv 4(r>uA Net Weight S o o o Price d~ AMOUNT. /So oo Received from JONES cV CO t OwftwhAMdtyfM Dollars, off POOP LBS. SEE D COTTON, at/ . A in payment .per ioo pounds I imby certify that I bare tul have this day Mid aad delivered to JONES & CO 01* and that I *h autaoriied to acll aald cotfcm. Fig. 38. SUMMARY RECORD FROM THE AUTOGRAPHIC REGISTER. S\\ow \- * o EXPERT'S BILLIARD ROO Jj < CM If) a o \- UJ cc a O cc 0. I H z I o -a d z i en 1 u. v Y | 2\ ,•■% o 6 2 < CD - > w o tr < _» CD o o a cc < CO cc < o O _» < h O i ^4^^-^w Ld 2 LU < H 5 A. .••% 2 o _J to z ^•'xi -# o _J X o ■J QQ bi £ S X^S. ^ >l »- o u CO £ < <^ *o> Cb O K>' 3 ^ Ul o ^o *o ss *o Ul < \ \\ On CO Q to _j < CO _J o o Q. < CO o: < o o < i- o 1- . 1 vl B( ;-^ 3= *\ I /* 1 i xi ^ - •< l * (fc * ) / / -** s> >- * C Pi ft E- g i E- < -^MINUTE i bo 156 TIME STAMPS. erally used to show the time of commencing an operation. Another set stamps the dial at the commencing, and the other set stamps the hand at the end of the operation over the im- pression of the dial, and thus shows the elapsed time. Fig. 52 is a card printed for use in a billiard hall. It shows that table No. 6 began at 2 :27, and shows the position of the elapsed dial at that time. Fig. 53 is the same card, stamped with the elapsed hand over the elapsed dial at the end of the game. It is arranged to compute the value of the time, instead of the actual time, itself. Fig. 54 is a record made from a machine used in a long distance telephone office. It shows that a conversation com- menced about 9:45, and continued 5 1 -4 minutes. Fig. 55 is a record from a decimal dial in a printing office. The blank is printed to show all the operations likely to be performed on a job. Any particular operation which is to be timed is ticked or punched. This card shows that workman No. 37 was on job No. 520, beginning 9:45, and working 2.85 hours on "imposition." Any number of different workmen or jobs may be timed on one machine, without in any way confusing one with the other, and without regard to the consecutive order in which they are stamped. This is a most excellent machine for keeping pay-rolls and distributing costs. The blank cards may be printed in endless variety, including color schemes, to indicate certain departments or other divisions. The cards may be first sorted according to workmen, and run through an adding machine, and then sorted according to the job, and again run through the adding machine to determine the cost of the job. They may then again be sorted according to departments or to oper- \\.J!...f 2 V 6 si ** 5 XI tt'& ,o\'« 1^ Composition Proof Proof Reidini Corrections Author's Alterations 2d Proof 2d Reading Make-Up Imposition ^J Foundry Press Waitin g Printinp- Slip-Sheeting Cutting Folding Binding Packing Shipping be Making Ready " 158 TIME STAMPS. ations or to customers or in any other way desired. The grand totals of all the time must of course be equal on every set, and this makes an absolute check on the accuracy of the work. These machines cost from $1 00.00 to $300.00, accord- ing to requirements. CHAPTER XIII. LOOSE LEAF BOOKS, Economy and accuracy demand that the original sheet produced by the adding or billing machine, be made the book of permanent record. This implies loose leaf binders. The introduction of such books for this purpose leads on to an ex- tended field of usefulness for the general principle of loose leaf accounting. The card index was a fore-runner of this system. It provided the means for putting records of any kind — gener- ally names — in any desired position with reference to the others. An index which might start with 1 inch for A, and 2 inches for B, could without attention, expand to 1 inches for A and 3 for B, and meantime, provide unlimited sub- divisions and schematic classifications. Classification of accounts in book-keeping has developed along these lines, until the loose leaf binder is recognized as the modern form of book, allowing the greatest elasticity from every stand-point. The sales book, built up from machine made records or otherwise, may by this means be divided and sub-divided into as many departments as desired, always pro- viding exactly enough room for each division, no matter to what extent it grows. Statistical records of all kinds are the most accessible, and the least bulky under this system. A loose leaf ledger may always be kept free from inac- tive accounts, and always with the live accounts assorted in the desired order, and always self-indexed, ready for the most immediate reference, without consulting an index. i6o LOOSE LEAF BOOKS. Fig. 56 shows one form of loose leaf book, expanded to receive a new leaf. These books are so constructed that a leaf may be taken out or inserted at any time in any part of the book. Much time is saved in posting to a ledger with self- indexed accounts, because the book may be opened at any given account in less time than would be required to look up the name in an ordinary ledger index, and find the page in the ledger. When an account has been closed, or has become in- active, the leaf may be removed from the current ledger and placed in its proper order in a transfer binder, where it may be retained indefinitely for reference, or where it may be found for replacing in the current ledger at any time that it might be required for re-opening the account. Thus the account with any individual may be kept on consecutive pages for any number of years, and at the same time the leaf may be kept from interfering with current business during such pe- riods as the account might remain inactive. In making trial balances, the book-keeper is not obliged to turn large numbers of useless leaves. He knows he must take a balance from every leaf in the current ledger, and hence the result is more rapid and more accurate. Indexing may be according to any desired system, but what is known as the "directory" system is the most conven- ient for ordinary use in a ledger. Under this plan, the names are arranged in the same alphabetical order that they would naturally occur in a city directory. In a large business, the personal accounts are usually kept in one or more "accounts receivable" ledgers, distinct from the representative accounts, and they are disposed in the directory order, Aa, Ab, &c. The representative ac- INDEX DIVISION SHEET. • PtflDi ■»••>• Mae 1 1 Mad. Mae. Maf 2 Mag. Mah 1 jj Mar f Ma*. Mat. Mau • Mav. Maw. Mm • 1 McC 12 MrD. McE.McF 13 M MrP. 14 MrK IS § McL 17 McM •• McN.McO.McP 1" McQ. McR. Mc8 20 McT. McU. McV 21 McW. McX. McY 22 Mil si i Mim. Min. to Mis 32 Jj Mon. Moo. to Moq »« Mor. Mot.Mot Mou. Mor. Mow 37 3 Mua. toMuk 40 Mul. Mum. Mun 41 Muo.Mup.Muq 42 Mur. Mul. to Muz 43 M* 44 Fig. 57- 164 LOOSE LEAF BOOKS. counts are in another ledger, likewise disposed in directory order. In a small business, where all accounts are kept in a single ledger, the loose leaf self-indexing plan is quite as ac- ceptable. The representative accounts are kept in one part of the ledger, disposed in the desired order, and the personal accounts are kept in their own directory order, without regard to the arangement of the other part. Fig. 57 shows a convenient division sheet for assisting in the index plan. It is one leaf for the letter M. All ac- counts beginning with the letter M are inserted behind this sheet, in the order indicated. All accounts, for example, with McKay, McKee, &c, are numbered 16, and all with Martin, Marvin, &c, are numbered 7. Each letter of the alphabet has a similar sheet, with an extended tab, as shown, making it easy to first turn to the proper initial, and then to find the sub-division by reference to the numbers on the sheet. It is sometimes desirable, for statistical purposes, to ar- range personal accounts in groups of cities or states, or in ter- ritories covered by certain salesmen, or by other controlling circumstances. This may be accomplished by division sheets, carrying reference tabs placed on the bottom, while the indi- vidual leaves in each group are arranged in separate directory order, each group being provided, if necessary, with its own set of alphabetical index sheets, carrying tabs on the side. Thus, if it is desired to find the account of Wm. Johnson, of Williamsport, Pa., the tab on the bottom of the sheets will indicate Pa., or perhaps Williamsport. The J tab on the side will lead to the initial sheet, and there, under Joh, will be found the number, say 13, which will lead to a group of a few leaves carrying that number, one of which will be the LOOSE LEAF BOOKS. 165 desired account. With a very large collection of accounts which are wanted with this style of sub-division, it is some- times more convenient to keep & separate book for each sub- division, instead of making them all in one book. One of the advantages of the loose leaf system, is that a scheme of this kind may be started with sub-divisions all in one book, and, as it outgrows this method, it may be, from time to time, turned into as many books as necessary, by the simple expe- dient of transferring the leaves to other binders, without re- writing any of the records. It might happen that an account, kept in the territorial manner, is wanted, when it is not known what territory it oc- cupies. If this contingency is likely to often arise, the proper remedy is a card index, arranged in one continuous directory order without reference to territory. This index would be consulted for Wm. Johnson, under the one division for J. Still another method, though usually not so desirable, is to attach a small initial tab to each sheet, at the top, with all the A tabs in a line, one behind the other, and all the B tabs in the next row, and so on. It is very easy to pursue a system of this kind too far, so that by its cumbersomeness, it makes more work than it saves. Proper judgment must be exercised to find just the right point for maximum economy. This point is not always apparent at the very first, for the reason that any new system needs time to get into action, and thus the time-saving fea- tures of a new scheme must not be judged from the first day's work. Figs. 58 to 6 1 show the use of various kinds of tabs, as applied to loose leaf books and card indexes. Fig. 62 shows one form of loose leaf binder, generally used for a transfer binder. It is cheaper than the style shown APPLYING TAB. TABS ON END AND SIDE. Fig. 58. Fig. 59. DIVISION TABS. Fig. 60. CARD INDEX. Fig. 61. S LOOSE LEAF BOOKS. 169 in Fig. 56, and is not so convenient to handle on a desk; but it is capable of greater expansion, and hence is suitable for holding documents used principally for reference rather than for daily book-keeping. The back of the binder shown in Fig. 56 is round and smooth, like an ordinary bound book, while Fig. 62 has projecting knobs. When this binder is apparently full, the stems may be lengthened by screwing on the extension posts shown in the engraving, thus making the book as thick as desired. The leaves of the book shown in Fig. 56 have linen edges pasted on the paper, to make a flexible hinge. This is expensive, but it makes a book very flat and easy for writ- ing. There are other and cheaper schemes for making these books flat opening. They mostly consist in crimping or cor- rugating or punching the sheets near the edge to make them more flexible at that point. Most makers of lose leaf binders, supply with them spe- cial sheets, ruled and printed to suit the requirements of the user. At the present time these sheets are usually made more elaborate and expensive than is actually necessary. Printing headings on the pages of a loose leaf ledger is no more neces- sary than in a bound book. It is usually quite sufficient to have the page ruled, leaving the headings to be understood by the user. The ruling is done by a ruling machine, while if printing is required, the sheets must all be run through a printing press after being ruled. This often doubles the cost, without materially adding to the usefulness. Numbering the sheets is done on a special numbering machine without great expense. A small numbering machine in the office is often quite useful for numbering sheets in a loose leaf book, for dif- ferent sets or series. Some objections have been raised to loose leaf books in i 7 o LOOSE LEAF BOOKS. general, and to loose leaf ledgers in particular, on the ground that a leaf might be fraudulently extracted without detection. This same objection applies to any lot of loose documents, such as drafts, checks and invoices. The same safe-guards may be made to protect the one as the other. Formerly, all checks were made attached to their stubs, and bound in a book, but of late, some of the most progres- sive offices have abandoned this system, and are now using a check register for writing down the history of a check, on con- secutive, numbered lines, so that 40 or 50 may be recorded on a single page. The checks are made up in pads, wholly independent of the register. Consecutive numbers, every number being accounted for, constitute the safe-guard of this system. Similarly, a series of registered numbers may be made to safe-guard the loose leaf ledger. At first sight, this seems incompatible with the central idea of the loose leaf scheme, namely the indiscriminate use of the leaves, without regard to consecutive order of numbers. But it may be ac- complished by placing the consecutive numbers on the lower left hand corner of each sheet. In this position, the numbers do not confuse the book-keeper, and he need pay no atten- tion to them. The proprietor, or responsible head of the office, issues a certain number of leaves, say 500. At any time that it is desirable to check over the leaves, to see if they are all accounted for, the auditor has a sheet printed with 500 consecutive numbers; and, beginning at the first page of the ledger, checks off the sheet number on the list. The first page may be 1 74, while the next may be number 1 2. The num- bers are easily found on the checking list. When the ledger is thus checked through, the unused blank leaves must be pro- duced, and the entire 500 accounted for. Another safe-guard for a loose leaf ledger is the use of CARD LEDGER— WIDE PAGE. Fig- 63 CARD LEDGER— LONG PAGE. Fig. 64. £ 3 LOOSE LEAF POCKET MEMORANDUM BOOK. I CWutet hr JhluO I lOuS. 7JU*. cuk Jiott Fig. 66. CASE FOR POCKET MEMORANDUM LEAVES. Fig. 67. 176 LOOSE LEAF BOOKS. locks on the binder. The binder in Fig. 56 has a metal strip which slides over the hole through which the clamping device is operated. This strip may be locked in place, and the key kept by the responsible head of the office. Other styles of binders have the clamping device itself operated by a Yale lock and key. The card ledger is one manifestation of the loose leaf theory. The ledger is made up of cards, instead of leaves. The cards are filed in cabinets instead of binders. There is no essential difference in principle between the card ledger and the loose leaf ledger ; the difference is one of adaptability to the work in hand. Card ledgers have not attained the ex- tensive popularity enjoyed by looseleaf ledgers. Fig. 63 shows a drawer of cards from a card ledger cabinet. This contains cards 3 inches wide by 5 inches long. They may be had in all sizes. Fig. 64 shows a drawer of cards 5 inches wide and 8 inches long. This drawer came from the cabinet in Fig. 65, which is designed to act also as a desk, on which the posting may be done. Figs. 66 and 67 show an ingenious adaptation of the loose leaf principle to the daily pocket memorandum book. The little book contains a lot of record cards, arranged be- tween guide cards, according to date or other controlling factor. The filing case is kept on the desk. At night, or at the end of the week, those cards containing temporary mem- oranda, for which there is no further use, are destroyed, those for further attention are retained in the book, while those wanted as a permanent record are filed in the case behind appropriate guide cards. tn desk from which borrowed. ■tfajStt* LIBRARY Ui MG - 8 1958 iAUTOWSCOEC 5 '86 «|W DEC 22 GENERAL LIBRARY -U.C. BERKELEY Booosiseae M513303