^4 ?^.^a! IMAGE EVALUATION TEST TARGET (MT-3) fe I A / 1.0 I.I 1.25 l^|28 |£0 *"■ iLo mil 2.0 2.5 2.2 1.4 1.6 i CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions Institut Canadian de microreproductions historiques 1980 Technical Notes / Notes techniques The Institute has attempted to obtain the best original copy available for filming. Physical features of this copy which may alter any of the images in the reproduction are checked below. D D □ D Coloured covers/ Couvertures de couleur Coloured maps/ Cartes gdographiques en couleur Pages discoloured, stained or foxed/ Pages ddcolordes. tachetdes ou piqudes Tight binding (may cause shadows or distortion along interior margin)/ Reliure serrd (peut causer de I'ombre ou de !a distortion le long de la marge intdrieure) L'Institut a microfilm^ le meilleur exemplaire qu'il lui a 6t6 possible de se procurer. 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Les images suivantes ont 6t6 reproduites avec le plus grand soin, compte tenu de la condition et de la nettetd de I'exemplaire film6, et en conformity avec les conditions du contrat de filmage. The last recorded frame on each microfiche shall contain the symbol -^^ (meaning CONTINUED"), or the symbol y (meaning "END"), whichever applies. Un des symboles suivants apparaltra sur la der- nidre image de cheque microfiche, selon le cas: le symbole — ► signifie "A SUIVRE", le symbols y signifie "FIN". The original copy was borrowed from, and filmed with, the kind consent of the following institution: National Library of Canada L'exemplaire film6 fut reproduit grSce & la g6n6rosit6 de I'dtablissement prdteur suivant ; Bibliothdque natior.dle du Canada Maps or plates too large to be entirely included in one exposure are filmed beginning in the upper Inft hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes ou les planches trop grandet> pour dtre reproduites en un seul clich6 sont film^es d partir de Tangle sup6rieure gauche, de gauche d droite et de haut en bas, en prenant le nombre d'images ndcessaire. Le diagramme suivant illustre la mdthode : 1 2 3 1 2 3 # » 6 L SH TH T ADVANCED SYSTEM -FOR- Liocatirxg Errors Witlioiit Re-ClieckiDg or Copying Entries. / BY HENRY GOLDMAN, AUTHOR OF "the arithmetical C2TECTOR." "new systems for PROVING CALCULATIONS WITH ENGLISH CURRENCY^" SHORT METHODS FOR COMPUTING INTEREST AND DISCOUNT." "new method for averaging ACCOUNTS," THE EXPERT CALCULATOR," " IMPROVED TIME CALCULATOR," "combination discount CALCULATOR," GOLDMAN'S instantaneous INDEX, ETC., ETC. MONTREAL & TORONTO: Ofpick Men's Record 189*. BEWARE OF IMITATORS ! The exclusive right of introducing this Copyrighted System is reserved by the author for himself and his authorized agents, who are supplied with Books of Instruc- tion and Credentials, bearing the date of the CURRENT MONTH. Others claiming to represent me or offering for sale information of the nature described in my circulars are pirates and impostors, and anyone who will promptly notify the author of their appearance, names and whereabouts, will receive, gratuitously, instructions by mail. Also, do not be deceived by brainless imitators, who literally copy my circulars and advertisements, in order to dispose of their worthless fabrications. Infringements of this Work will be vigorously prosecuted, and anyone attempting to communicate its contents to others, in order to reap a pecuniary benefit, exposed. A special warning to "Authors," who are in the habit of advertising as their own "discov- eries," what they discover in other publications. It is expected that those who acquire the knowledge, embodied in this volume, will not willfully deprive the author of the results of his labors. Entered according to Act of Parliament of Canada, in the year 1892, by Henry Goldman, at the office of the Minister of Agriculture. WITH VALUABLK ADDITION* PROr NEW SYSTEMS FOR PROVING CALCULATIONS WITH ENGLISH CURRENCY. Copyrighted, 1884, by Henuy Goldman. Ppeface. OFFERING this new system, in addition to the great number which have been devised for the same pur- pose, the author feels convinced that it occupies a hitherto vacant phice in the science of accounts, being complete wherever others are deficient, and facilitating the most important task which double entry book-keeping makes necessary. The principal faults of other systems, either requiring a great amount of additional labor during the month, or leaving room for numberless mistakes with- out a single rule or hint for their detection, have been overcome or avoided in my "Advanced System," which, embodying all the valuable contributions of theory and practice, will readily demonstrate its usefulness and su- periority. The information embodied m this work is not a stale compilation of old and commonplace rules, which may or may not prove of service, or a plan of subdividing the ledger into artificial sections of 100 or 200 pages, or a blank book scheme, necessitating a complete change of Ledger, Journal, Sales Book, etc., in order to gain a questionable advantage, but a simple and complete system, based on an entirely new and original idea, which accomplishes the seemingly impossible, requiring no change of book or book- keeping, no additional books, no carrying of totals during the month, no special division of the ledger, no copying of amounts, no slips, blanks, or forms of any kind, etc. It removes all difficulties, generally' experienced with the trial balance, and without entailing extra labor practically reduces the routine work of the office, as all postings, foot- ings and balances are proved witliout comparing amounts, re-cliecking or re-figuring. With its aid an itemized trial balance can be taken in half the time generally consumed by book-keepers, a great saving of time at a time when time is most valuable, avoiding entirely th«^ delay in com- mencing the posting for the current month. Considering the importance of the information offered, the facility of its application, and the many advantages derived from its use, no intelligent and progressive book-keeper can afford to do without it I The claims presented are so broad and exhaustive that some may look upon the attempt of demonstrating their truthfulness with a feeling of doubt and suspicion, but anyone who approaches the knowledge offered without bias or prejudice will be thoroughly convinced that the assertions made are fully substantiated. That the proof furnished by this system is not absolute, but simply covers the errors which are likely to occur in book-keeping, no one endowed with an ordinary amount of common sense will take occasion to find fault with. The absolute being beyoid human reach, the work of a single day could not be proved absoluteh' in a whole month. But even errors which the trial balance does not discover, as for instance counter-balancing mistakes in different accounts, or on different pages of original (mtry, are readily located to the very accounts with the aid of my "Advanced System." While it is possible to find combinations of errors, which this system will not immediately discover, these are so re- motely probable that a book-keeper could go on for years and years in the use of the system without experiencing any difficulty, and if, after all. errors of this kind should occur, enough time and labor would have been saved to prompt the cheerful performance of the work, which would have to be done every month without the system. I do not pretend for a moment that, for a consideration in h proo mak( and Trial Af enab as til comp confic neces mista conn( of spt the s.^ so th speak suppl assisti tion t< Am p«'rst)r aband as a r thing, while in hijE tion t< almos an en while going withd avoid( throuj mounts. Jed trial )nsumtHi le when in com- sidcrin*;' cilitv of • from its n att'ord tivo that ng their !ion, but without that the he proof ly covers Ding, no on sense t(i being ould not n errors instance >. or on 1 to the ystem." which re so re- or vears • :ing any should iuved to which svstem. leration in hand paid. I can make book keepers absolutely error proof I What \ am oti'ering is a valuable aid, intended to make Trial Balance Trials exceptionally rare occurrences, and to reduce the labor generally recjuired to balance the Trial Balance to a possible minimum. After a few days' use of the system, book-keepers are enabled to post just as fast, if not faster, than without it, as the necessity of repeatedly " looking backward " and comparing amounts is entirely avoided. The feeling of confidence gained, the assurance that there will be no necessity for the practically useless labor of searching for mistakes, and the absence of that dull monotony, generally connected with copying amounts, are additicmal elements of speed. The increased attention required in applying the sj'stem is m itself a valuable preventive against errors, so that many a mistake will be discovered, paradoxically speaking, before being made. My "Advanced System" supplies the book-keeper with the services of a trustworthy assistant, whose work principally consists in calling atten- tion to errors as soon as they occur. Among the large number of book-keepers, whom I have perst)nally instructed, there are very few who have ever abandoned the application of the system, and these were, as a rule, persons of doubtful ability, too lazy to learn any- thing, or too careless to care for accuracy in their work; • while those who have given the sj'stem a fair trial speak in highest terms of its value, consider it an essential addi- tion to their knowledge, and would not do without it for almost any price. The writing of a single figure at the time an entry is made does not increase the work nceptibly, while at the end of the month it is materially decreased, the going over innumerable additions and subtractions, while withdrawing the balances from the ledger, being completely avoided. I firmly believe that no one Avho has gone through the experienci^ of a month's work with the aid of -6 this system, would be inclined to jro back to the old uncer- tainty. If it only proved the accuracy of postings it would bo invaluable, if it only verified footings and balances it would be of great assistance, if it only prevented omissions and forwarding wrong totals it would be worth using, but my "Advanced System " surrounds every step in book- keeping with a safeguard, and therefore amply repays for the effort required in its application. It has been often stated by trial balance sufferers, that the inventor of a practical system, which will remove this bane of a book- keeper's life, the difficulties experienced with the trial bal- ance, would make himself a benefactor of the human race. This system is now an accomplished fact, and anyone who is neither too smart nor too skeptical, may take advantage of it. . ' ,- ^ , ': • •, The r^rice of my "Advanced System," being no equiva- lent for the actual service rendered (as many a book-keeper would be inclined to spend $10 for straightening out a single Trial Balance), but merel}- a compensation for the effort of completing and disseminating the knowledge, does not include the right of communicating its contents, which is reserved for myself and my authorized represent- atives. In placing certain restrictions upon those who purchase my work, I not only aim to protect mj' own inter- *ests, but at the same time the interests of those who acquire the knowledge, giving me the means of direct communi- cation with the users of mv "Advanced Svstem," and enabling me to give them the benefit of my most recent investigations. It is with regret that I am compelled to note here that office men, filling positions of trust, and business houses, who stand high in the estimation of mer- cantile agencies, after having faithfully promised to protect my interests, have deliberately given the information to others, so that many firms and individuals at the present time derive a benefit from the use of my "Advanced Sj's- —1. tern for Locating Errors," without having rendered airj* compensation to its originator. Others, still h)wer on the moral scale, have taken advantage of my established rep- utation, b}' representing themselves as my authorized agents, or going so far as to introduce my system under different titles, compelling me to expose their names, and to enter proceedings against them. A few of these, most brazen of all, after advertising themselves as "Teach- ers of the Goldman Check System," securing references by pretending to be my authorized representatives, intro- ducing themselves under my name, or claiming to have improved my system, offer, under the guise of a copyright of later r^ate, some printed sheets which do not contain one fiftieth part of the information embodied in my books, and. being crude and incomplete, naturally throw dis- credit upon the value of their deficient substitutes. I do not wish my work confounded with their spurious efforts. There are also some know-alls in every community, who, after an information has once been elaborated, pretend to have known it for 25 years. Why did they keep it as a sacred secret? Why did they not make use of it them' selves ■ The answer to these questions is plain. I do not claim having revolutionized the science of mathematics, or the discovery of the Decimal System, but that I have made a new and original application of a wonderful prop- erty of numbers, that I have formulated it into a complete system, and presented it in such a form, as to bring it within easy reach of every book-keeper in the land. The Author. COflTE^lTS. Introduction 10 ADVANCED SYSTEM —FOR— Locating Errors '.i ■ -'■•■' ,'...•.•■■ Without Re-checking or Copying Entries. Proof-Number Checks 15 Self-checking Posting 18 Original Entry ^Checks 21 Ledger Checks 30 Drawing Off Balances 34 Trial Balance Checks 39 Detecting Errors of Previous Months 42 Prevention of Mistakes 44 Scientific Principles 46 Review 50 Advantages of the System 52 WHAT IT DOHSI 1. It locates an en'or in posting to the imery account without referring to the ledger, re- checking or copying entries , and almost instantaneously. 2. It indicates dirtctly t?ie account in which an entry has been omitted, and poir^ls out the repetition of an entry. S. It offers a safeguard against posting to the wrong side of an account or to a wrong account, as well as against double and counter-balancing erroi's. U. It proves the totals in the books of original entry, without requiring a second footing. 5. It detects errors of forwarding totals or balances without comparing the amounts carried. 6. It verifies the footings of each account in the Ledger toithout going over the additions. 1. It proves the correctness of every balance without repeating the operation, and locates an error immediately to the account in which it occurred. 8. It prevents the omission of a balance in the Trial Balance, ruling off accounts which should be left open, and mistakihj tJie pencil- footings of preceding months. 9. It discovers the transfer of a wrong balance from the Ledger to the Trial Balance, embracing all classes of errors, transpositions, translocations, transplacements, etc. 10. It proves the footings of the Trial Balance and indi- cates the page and account in which an error has been made, no matter if the totals are carried forward or recapitulated. APPENDIX. Foreign Currencies 04 Mixed Numbers GO Other Check Systems 67 Condensed Trial Balances 70 INTRODUCTION. Between the crude methods of hunting for mis- takes, still commonly employed by book-keepers, and my ''Advanced System for Locating Errors," which is embodied in this work, lies an extensive field of investigation and improvement. Innumer- able attempts have been made to facilitate the de- tection of errors in book-keeping, and it will be well, at the outset, to touch upon the different systems, which mark the evolution of the subject. First in order came collections of special rules for the discovery of certain classes of errors, the division of the difference by nine, in case of trans- position, by 2, to detect the posting to the wrong side of an account, etc. Trying to answer the question: What? the nature of the error may be the more important answer to the question: Where? it is to be found, was entirelv overlooked. A step forward is represented by the systems, which attempted the location of errors within cer- tain sections of the ledger, to the general or in- dividual accounts, to the debit or credit side, etc. But these also were found insufficient, as the divis- ions could not be made small enough to reduce the work materially. These systems were all remedial in their nature, aiming to accomplish the ■11 difticult task of removing in a single day or hour the errors accumulated during a month's work. An effort in the right direction were the systems based on the idea of copying the entries on slips, etc., the division of the ledger into artificial sec- tions of 50 to 100 pages, and the carrying of foot- ings during the month. Though entailing a great amount of additional labor during the month, these systems were appreciated by many, as they at- tacked the trouble at its root, and simplified the work of correcting the trial balance. These systems, offered under different names and with slight variations, were followed by a class, which may best be designated as " Blank Book Systems," necessitating a complete change of books and book-keeping. Many of the claims made for these systems are entirely without foun- dation, as for instance, that it is impossible to make a counterbalancing error that will not show itself, that errors of posting are located to page and account, that they are beyond the reach of falsification, etc., and the necessity of opening a new ledger every year, as well as the scattering of entries, the carrying of balances, which sacrifices the condensed condition of the accounts, are seri- ous objections. The results produced, while sat- isfactory in some respects, do not justify the heavy expenditure of time, labor and money, which is invariably connected with their adoption and — 12- proved an effective obstacle against the successful and general introduction of these systems. My '< Advanced System for Locating Errors" is the most recent remedy for the greatest ill a book- keeper's flesh is heir to, and though only a short time before the book-keeping public, has met with an enthusiastic reception wherever introduced and found hundreds of friends and advocates in all parts of the United States and Canada. It possesses none of the objectionable features of other systems, and can be adopted at any time, and in all branches of business. The idea of obtaining a check-number for every entry, by utilizing a wonderful property of the decimal system in reducing the amounts to single figures, not only considering the figure but also the place value of each figure, forms the corner- stone of this system, without whicli the claims presented are complete impossibilities. Com- pared with the method founded on the property of the number 9, it offers not only a more perfect safe-guard, but at the same time is less laborious, avoiding the process of repeated addition, the prin- ciple of subtraction being in itself a powerful fac- tor in reducing the amounts to single figures. The process is so simple that with little practice the check-number will report itself automatically, while placing the entry in the ledger. In em- ploying the 9 principle the changing of a figure does —13— not necessarily change the check-figure, while in my * 'Advanced System," founded on the property of 11, at least two figures must be changed in a counter-balancing manner to result in the same check-number, the number 1 1 embracing the whole range of decimals. The method based upon the property of the number 9 has also proved a practical failure, on ac- count of its insufficiency in discovering even the most ordinary transpositions, as well as any error amounting to 9 or a multiple of 9, as, for instance, mistaking 9 for 0, a very common error in pencil footings. Considering the difficulties generally experi- enced with the trial balance, the days of work and worry frequently spent, without accomplishing anything, and, on the other hand, the almost in- credible advantages derived from the adoption of this system, the small effort required to familiar- ize one's self with it, will appear insignificant. ♦ ' Advanced System for Locating Errors WITHOUT RE-CHECKiNG OR COPYmC ENTRIES. iii Though in the arrangement of this system a mercantile business has been supposed, the prac- tical book-keeper will, without any difficulty, be able to apply it to any special line.* As there is only one system of double entry book-keeping, no matter how widely the branches of business may differ in which it is employed, a system which simplifies the detection of errors in one set of books will necessarily facilitate it in all, the devi- ations being simply of a minor or secondary na- ture, not interfering with the general principles of double entry. But also in single entry book- keeping the knowledge of my " Advanced System'^ will be found advantageous, the proof of postings, footings and balances being entirely independent of the principle of double entry. The process of ascertaining the proof-number checks forms an im- portant part in the application of the system, therefore a complete explanation of the method by which the check-numbers are obtained, and of the many simplifications which can be employed ta facilitate the operation, may appropriately be pre- sented in the first chapter of this work. —15— PROOF NUMBER-CHECKS. The proof-number check, corresponding to any n'lven amount, can be readily found by adding every other figure, commencing witli tlie right liand figure, and deducting from tlie sum obtained, tlie sum of the figures which have first been omitted. For instance: 14.28 can be reduced to the check- number 4, by adding the alternate figures 3 and 4, which make 7, and deducting 3, the sum of the figures 2 and 1, which have first been omitted. In amounts composed of only two figures simply deduct the left hand from the right hand figure. 14 gives reduced ^, 27 . .,5, etc., as any number of ciphers can be imagined to the left of the amount without changing its value. If the difference between the sums of the left hand and riglit hand figures should be more than 10, subtract again the left hand from the right hand figure. For example: 126.19, 10—3 = 13 2 In case the sum of the figures in the right hand places is smaller add 11, or if necessary a multiple of 11 (22 oy 33), before subtracting' 54 gives re- duced 10, 11 added to 4 making 15, and 5 deducted leaving 10. Further illustrations: 81.13,4 + 11 = 15— 9 = 6 192.80, 3+22 = 25 — 17 = 8 16— t||l| It may be preferred to add the left hand or middle figures first, and to deduct their sum from the sum of the right hand or outside figures, whicli does not alter the process materially. Notes —The proceas of reduction which consists in deducting the left hand from the adjoining ri^ht hand figure, and continuing the 0|>eration by deducting their difference in the same manner, increas- ing the right hand figure by 11 whenever requirrd, is too cumbersome and therefore f.atirely impracticable. To illustrate: Ui 36, 4—2-2, 3-2= , 6—1 =5 191.29, 9-1=8, l-|-ll-8=4, ;i-f 11-4=9, 9— 9=0 The Principle of ''Addition by Subtraction" could be utilized in this connection, by complementing the figures in the even places to 10, adding these imaginary figures and the figures in the odd places together, and dropping the lO's from the sum. Whenever the sum of the figures in the odd places should be smaller, increase the check- number obtained by 1, 2, etc , according to the number of lis, which would have to be added t>efore subtracting the sum of the figures in the even places. If the difference between the sums of the figures in the left hand and right hand places should be larger than 10, decrease the check-number by 1. :M)21 3-f6-[-6-|-«+l H 4 297.83 2+i-f7+2+a U) 6 128.18 l-|-8_|_8-|-9-f8 H 3 Those who are a:)t at figures may give this method preference. The reduction of numbers can also be accomplished by forming couples, and deducting in each the left from the right hand figure. The reduced sum of these differences represents the reduced number. For instance: — 3547 5 ; 5—3=2, 7—4=3, 2+3=5. To increase the sum of the figures in the odd places may be counted as 11, For instance: 80 3. 1.50 12—5 = 7; 4.60 15— 6 = 9. Equal figures in the even and odd places can be omitted. 8.00 gives reduced 8; 577.00 reduced 5* 8.87 reduced 7- If 11 is to be deducted from a number smaller than 11, that number is invariably the check. For example: 23.94, 7 + 11—11 = 7. Whenever the sum of the figures in the right i hand or mm from es, whicli lednctlng the ntinuing the ner, increaB- cumbersome O )e utilized in ven places to he odd places er the sum of ise the check- of lis, whicli the figures in the figures in tn 10, decrease ..6 ..3 efereiice. d by forming X hand figure, need number. =5. 11 the odd ance: 5— 6=:9. ces can bo educed 5 ; ed from a nvariably 1-11 = 7. the right —17— liaiid places is by 1 smaller than tlie sum of the figures in the left liand places the check-number is always 10, the addition of 11 and subtraction of 1 leaving that difference. 19G.89, 16 + 11—17=10. 11, 22, 33, etc., all multiples of 11, give re- duced 0. Figures making together 11, as 2 and 9, ■] and 8, 4 and 7, 5 and 0, etc., if in the corresponding places of a number, no matter in what succession they follow, can be omitted. For instance, 23.9 4 ... 7, 16351 ... 5. The reduced nuinbeu is equal to the the remainder left after dividing by 11. Any possible doubt regarding the. correctness of a check-number can be speedily removed b\' dividing the given amt>».nt by 11, and acc<'pting the re- i.iainder as check for the amount. Although requiring a lengthy explanation the loperation itself is very simple, and will cause no I loss of time, the mental piocess of arriving at the check number being performed simultaneously with the marual process of making the entry. The addition of 11 to the sum of the right hand mgares will only be occasional!} required, as the number of right hand figures, and consequently their sum, is generally larger than the number and sum of the left hand figures, 7'hiph fact facili- tates the subtraction considerably. Besides 99^ of the amounts occurring in ordinary book-keeping |are smaller than $999.99. NoTB. Amounts composed of an even number of figures have aa lany right hand as left hand figures, while amounts having an odd Inumoer of figures contain more right Hand than left hand figures. 18- SELF-CHECKING POSTING. We enter now upon the most interesting, origi- nal and useful chapter of this work, containing an information which on account of its intrinsic su- periority is bound to substitute the methods em- ployed at present for proving tlie accuracy of all ledger entries. It can be easily understood and readily applied, requiring no extra work of any kind, no special preparation or change in the sys- tem of book-keeping. Far in advance of those laborious and tedious schemes of reverse posting or slip copying, which promise much but accom- plish little, it is an extremely practical method for the detection and location of errors in posting, immediately or shortly after they occurred, which will be hailed with enthusiasm by all progressive book-keepers. But before proceeding to the explanation of this method, the author invites a brief considera- tion of the initial step to posting, which consists in ascertaining the ledger folios, by either refer- ring to the index, recalling the same from mem- ory, or following a certain arrangement of the ac- counts in alphabetical order, according to lo- calities, routes, etc. Paging* first offers various advantages. It is the most convenient safeguard * The word "Paging" is used here not in its original meaning, but denotes the writing of the folio numbers in the book of original entry. nil — 19 — various against posting to the wrong account, as it insures the close comparison of names and folios. It avoids interruptions caused by fre(]uent reference to tha index, and permits the use of red ink with- out entailing the awkward practice of constantly changing pens. It also enables the book-keeper to take advantage of the location of the accounts by commencing with the last and proceeding towards the first pages of the ledger, at the same time relieving him of the mental strain of carry- ing the ledger folios, which frequently causes mis- takes, besides preventing the error of placing the ledger folio as an entry in the ledger, and the amount to be posted as a ledger folio in the book of original entry. If the accounts in the ledger can be easily found without the aid of the index, the ledger folio should be placed in the book of original entry before posting the amount to the ledger, or can be entirely left out, if only intended as check against omissions, an object completely covered by the proof-number method, which pre- sents the most satisfactory evidence that an entry has been made, indicating at the same time which item has last been carried to the ledger. The ledger folio, standing in no direct connection with the amount to be posted, is after all a very im- perfect safeguard against omissions, as which it was principally intended, and the indexing of new -20 accounts can be conveniently done; after being opened in the ledger. The proof of posting is accomplished in the following simple manner: Reduce each amount as soon as entered in the ledger, according to the process explained in the preceding chapter, and place the i)roof-number check thus obtained on the side of the folio in the ledger account, and a copy of the check to the corresponding folio in the book of first entry, in such position that the addition of the check-numbers can be readily per- formed. The principal reason for placing the check in the ledger first, is to prevent taking the check from the original entry. To fulfill its mis- sion the clieck-number must always be taken from the ledger, never from the original entry, and, considering the fact that the check is ascertained while making the entry in the ledger, this condi- tion is easily complied with. The checks in the ledger are rarely written in the amount columns, not to conflict w^th the entries, but are best placed in the explanation columns, close to the folios, where as a rule sufficient space can be spared. The best way of posting consists in entering the amount first, then the folio, date, explanation and finally the check, which order enables the book- keeper to arrive at the check-number while mak- ing the entry, offering an additional chance to fflance at the amount. In most instances and —21 — with little experience the proof-iiuniber will be known before the entry is completed. The Check-Numbers in the Books of Original Entry take the place of the ordinary Check Marks, and are more convenient than the Folio CMiecks, as one figure can be more rapidly placed than two or three tigures. Indexing previous to Posting also relieves tire book-keeper of taking care of three books at one time, as the Index, first used in connection with the Book of Original Entry, makes room for the Ledger. ORIGINAL ENTRY CHECKS. The reduced totals of the entries, which hav been posted to the ledger, must correspond with the reduced sum of the proof-number checks, pro- vided no error has been made. This proof can be applied daily, weekly, or whenever the posting of a p:.ge has been completed, which is most advisa- ble. In case the reduced total of a page does not correspond with the reduced total of the check- numbers, the error can be readily traced to the very" account without referring to the ledger, by comparing the amounts with the checks in the book of first entry, folio and check-number being on the same line. The omission of an entrv in the ledger is discovered by the omission of the proof-number check in the book of original entry, —22— as every folio iiiniiber must liave a elu'ck-ninnher on its side, and tlie disagreement at tlie bottom of the page. The contrast between tlie red folio and the black clieck-number is an additional aid in this connection. Still the usefulness of the sys- tcm is not exhausted, errors in footing being also discovered bv the disacrreement between the re- duced total of the original entries and the proof- number checks. As soon as a total is brought forward, the ])roof-number is also carried over and included in the sum-of the check-numbers of the following page. Whenever a wrong amount has been carried over, the following page will be thrown out of balance l)y the correct check- number, and the error immediately discovered, the wrong amount being at the head of the i)age. The irreat advantaixe of this system consists in practically returning tlie error from the ledger to the book of first entry, in producing distinct im- pressions by reducing large amounts to single fig- ures, and in closely adapting itself to the natural subdivisions of the books. The addition of the original entries can be left to the end of the month, as long as the check-numbers are put down while making the entries, or may be entirely dis- pensed with, if the separate comparison of amounts and proof-numbers is preferred. A wrong check-number, though obtained from an amount which has been accurately entered in — ba- ilie ledger, disturbs the equilibrium of the page in the book of first entry, and can be quickly traced and corrected in the above described manner, the check serving as check on the amount, and the amount as check on the check. In reality it is not the check, but the agreement between the check and the amount, which proves the work. >>'0TK. — It should be remembered that has the same importance as other check-numbers, its absence indicating]; the omission of an entry. In adding a column of check-numbers all elevens or multiples of eleven can be omitted, and the sum of the remaining flgnres may be conveniently reduced, whenever the right hand flgure is larger than the left hand figure. B^or instance, in place of 24 carry 2; instead of 47 carry 3, etc. ; while all multiples of 11, as 21, 38, 44, etc. can be en- tirely left out. Proof-footings and reductions are i)erformed men- tally, and only the reduced totals of the check-numbers are placed in the book of original entry. The reduced total of each side of the cash book sheuld agree with the reduced total of the proof- number checks, provided the balance is also repre- sented by a check-number. If a number of items have not been posted, the remaining entries can still be proved by inserting check-numbers for the amounts not brought into the ledger, or by separ- ate comparison of the original entries and check- numbers. In column cash books this proof-system applies principally to those columns the entries of which are constantly posted to the ledger, and to the totals postod at the end of the month, which can be verified separately. If the check numbers embrace the entries of two or more columns, it is not necessary to perform the addition of the totals, but simply of their reduced equivalents. The ■24— C A S // B O OK. January^ 1890. 1 s 234 P. K Wig/it, 2 50 s 5 237 Wm. M. Ayers, 225 00 4 S 129 S. W. Ilooleii. 3 00 8 6 413 Galdentood d- Wrong. 2 15 u* (i) 322 W. Pare, 1000 00 it 4 7&G E. W. Latson, 15 00 xs 9 130 S. P. Sackard, 3 50 1251 15 so 5 Balance, 243 04 6 1494 19 * This mark represents the check namber 10. COLUMN CASH BOOK. Ani'tsf'rw'rd 5 213 56 126 10 314 25 110 26 817 42 10 11 Postage, etc., M. Jarrihan, i ^413 '^ 00 ■ '> 50 12 Freight, 0. & A. U. R. 21 36 12 J. Woodgin % i 1212 56 76 13 Discount, CdlV^'BiU 1 24 14 M. Wedgsick% ( i 124 141 19 15 M. Lackemie % / y 516 2S 12 16 Expressage, S. F., 9 10 1 ! ArrCts Over, I 444 63 137 70 335 61\111 50 817 42 * NoTR. — The footinps of the columns which aro only posted once a month may be proved separately by applying the same principle. -25— 15 04 19 A2 .. work of separately comparing the araoiiuts and checks can be materially reduced by dividing the page in two or more parts, and locating the error iirst to one of the subdivisions, by means of pen- cil footings. The error of writinuj an amount in the wroni; column of the book of original entry is discovered by tb ^ omission of the check-number, if the entry has been entirely overlooked, or by the misplace- ment of the check-number, producing a disagree- ment at the foot of the page. In case an item has been erroneously placed into a column the amounts of which are posted separately, instead of appearing in a column the total of which is posted at the end of the month, or vice-versa^ the error will be discovered by a disagreement at the bottom of the page, on account of the omission or insertion of the check-number. The proof-number corresponding to the amount carried over is copied from the i)receding page and serves as a safeguard against forwarding a wrong total. Errors in footing or forwarding are immediately discovered, while errors of posting or omission can be readilv located to the account of the ledger by simi)ly comparing the amounts and checks of a single sales-book page. If sales are posted directly from impression books^ order blanks or sales sheets, place the proof-number checks with blue pencil or ink near —26— SALES BOOK. January, 1891. 5 12U 4^3 Am't forw\l. 8 Huntiinfton Ilopkins Co., 8. F.. Cal. 1 No. U Sdf-('lierkin2Ji 6 O) 173 e4G c? 1 " 1 '' f} '' 1 " u " 1 ''10 " (( a 11 Montana Commercial Co.. Miftsouhf, Mont. 2 Ooldm((nh Automatic Binder, 12 U 00 00 10 00 300 ioo d\oo 10 00 13:?9 01 Bloominf/ton Bedford Stone Co., Chicat/o. 1 Complete net of Self-Checkinfj Blank liookfi, 14 Spencer, Clawfiond- Co., Salt Lake Citi/. 1 Tnatantaneou.s Combination Index, 15 liaphael Tuck rf- Co., New York City. 1 Complete In i^t met ions in Advanced Sys- tem, etc. Ain't orer to 00 4^ 3 00 50 or. 00 00 10 ?? 143. 00 11 -27— 01 00 00 50 00 00 11 the folio numbers, or in the right liand corner or margin, so to be readily noticeable while turning the leaves, serving simultaneously as proof of post- ing and footing. If only a few items appear on a ])age it is doubly advisable to add the checks sep- arately to avoid omissions. In case the amounts are afterwards copied on a separate sheet or reg- ister, in order to avoid the too frequent carrying forward of totals, copy the proof-numl)er checks also, which answers the tri])le purpose, that of [>roving the correctness of the ledger entries, of the transferred amounts, and of all footings. A similar application of tlie system is to be eni- })loyed in the purchase or invoice book, or when the entries are made directly from the original in- voices, collected in stub or invoice files. In the Journal the })roof-number checks are placed on the left or right hand side of the folio numbers, in order to distinguish between debit and credit checkmarks. Every debit or credit entry in the ledger produces a debit or credit check- number in the journal. As all checks are de- rived from the ledger entry, an amount entered on the wrong side will always result in the misplace- ment of the corresponding check-number into the wrong check-column, which is bound to disturb the balance of check-numbers. The error of post- ing to tiie wrong side of an account is only likely to occur when debit and credit entries are made —28- alteriiately, ami the distinction between debit and credit check-numbers is the most practical safeguard ever devised against errors of this kind. It is highly improbable that the mistake of post- ing to the wrong side of an account will be imme- diately followed up by a second error, that of placing the check-number in the opposite column, the error not being caused by ignorance of the fact on w^hich side the entry is made, but simply by ig- noring the fact that it is wrong to enter it on that side. In case folio and amount columns are ruled side by side the credit checks can be placed in the debit amount columns without conflicting with JOURNAL. Janunry ISUl. 1^ 3 12V 'J34 17 2 112 \237 4 IS 723 Suspense, J JVotcs I tec. r W. M. Ai/ers, Chets. VdllfSM, W. Pare, S. W. Rooley 2 322\S. P. Sarkard, o323\W. S. JIndler, 31 4 U lUo 121 Profit and Loss, 613 9 Notes Paif. E. W. Mat, son. 3 1124 200 350 15 00 99 00 00 00 o 100 1000 ■'A 00 00 00 99 550 00 15 00 —20— 'g- r> 00 wo -4 00 00 99 50 00 15X)0 tlie entry. This system also removes the necessity of footing the journal pages, as it not only detects errors in posting, etc., but indirectly proves the partial footings as well as the equilibrium of the journal. In more than two-column journals the proof-number checks apj)ly principally to the sun- dries debit and credit columns, and some marginal space should be appropriated for them. The totals carried to the ledger, at the end of the month, can be proved by placing the check-numbers obtained from the ledfirer on the side or below the oricfinal total, and comparing the same. This method of verifying postings, footings, etc., is adapted to all forms and kinds of original- entry books. It can also be utilized to detect er- rors in cojiying and transferring amounts, by re- ducing the same after being copied or transferred, and comparing the proof-number with the original, which obviates entirely the liability of looking at an amount twice without noticing the mistake. Sufficient space for the check-numbers can be readily reserved in any book of first entry. My copyrighted self-checking blank book forms, how- ever, are most perfectly adapted for the reception of this system, besides containing other improve- ments which will be appreciated by book-keepers. Check columns are provided for the conveni'^nt placing of check numbers, and the most improved and advanced features of rulings, etc., are intro- duced. :J0- LEDGER CHECKS. The fhtH'ks in the ledger are placed on the left hand side of the folio in the explanation eolunnis with ink, and at the time the entry is made. In two-colnmn ledijrers, havino; only a siniTjle folio col- unin, tlie ledger check is written on the left hand side of the folio, if representing a debit entry, and on the right hand side, if representing a credit entry, there heinij no damjer of contiictinix with the ann^unt, as in the case of a credit entry the debit amonnt cohnnn is left blank. If for any special reason the |)lace near the folio is not ayail- able, the margin in the date or amouiit columns or any other suitable space may be utilized. Suf- ficient space for a small figure can be found in any ledger, no matter how crowded. If, howeyer, after careful consideration, a place for the check- number has been selected, it should be uniformly adhered to throughout the whole ledger. In order to start the system in the ledger, it is only neces- sary to extend the check-numbers of the pencil footings in pencil bet\veen the lines in the column, where afterwards the checks of the entries will be placed. At the end of the month eyery entry in the ledger will exhibit a check-number on the same line, and the totals of the entries in any account can be easily proyed by comparing it with the re- —31- duced total of the clieck-iiuiJibcrs, avoiding the danger of repeating the same mistake. The pen- cil check-numbers, representing the pencil footings of the preceding month, are included in the check- numbers following, and serve as safeguard against mistaking a pencil mark, while the new pencil checks form the basis for the next month's work. If by mistake a wrong pencil check has been placed in any account, it is bound to throw out of balance that side of the account, the amount being a check on the check and vice versa. Each ac- count of the ledger with the accompaning checks really represent a trial balance in itself. This system furnishes also the most perfect pre- ventive against omissions, the check in the book of original entry being a copy of the check in the ledger, obtained directly from the amount posted. The superiority of a check which stands in direct connection with the ledger entry over the thought- less writing of ledger folios or check marks is at once apparent. The check-numbers in the ledger not only prove the correctness of the footings of each account, they also prove every balance by deducting the check of the smaller from the check of the larger side of the account. It is essential that the checks are always deducted in the same direction as the account. Whenever the checks of the larger side are smaller, add 11 before deducting. NoTB.— The nee of the ordinary check mark (V) is recommended to indicate counterbalancing entries, which is more advisable than "rul- ing off." I -32— • LEDGER ACCOUNTS 1 The Office Menh Record Co., Chicago, III, 1891 Jan. 1 Bal. 4 113 14 23 1891 Jan. 3 C. 4 114 14 23 4 M. 3 IIG 129 01 15 I 250 100 00 25 7 147 3 15 Feb. 10 BM. 2 100 1 I 4 200 2 j 0(1 3 4 7 Feb. 30 96 15 5 8 7 163 107 315 462 213 20 19 25 21 C 5 I 34 225 5 3 9 00 2 i I S 7 27 59 I 5 214 51 726 38 82 Henry Goldman, Chicago, III. 1891 Jan. 1 C. 6 217 8 6 243 15 6 257 22 7 273 20 I 201 Feb. 5 4 7 311 12 9 321 10 I 343 1 20 4 3 359 50 00 50 00 50 00 150 00 400 00 I 40000 15000 I 1891 Jan. 1 15 25100 o o Feb.\\b 251500 o 75 00 100 00 125 GO 85000 Bal. 8 C 120 950 336 25000 00 5 00 25000 400 2600 00 Note.— The small figures denote pencil marks. —33 } 25000i0n The system offers an invaluable safeguard against "ruling off" accounts, which should be left open. Sometimes a difference of 10c. or ^100 may be en- tirely overlooked, the account ruled off, and days of labor uselessly spent in searching for the error, without thinking of going back to an account, which is apparently in perfect balance. The dis- agreement of the check- numbers exhibits this error at a glance. In ordinary ledgers it is not necessary to place the check balances in the ledger, subtractions of single figures being performed instantaneously. In bank or balance ledgers the balance checks may be placed in pencil between the line in the check column of the larger side of the account, forming the basis of the next day's work, in which case the use of check totals is entirely dispensed with. My self-checking ledger and self-checking balance ledger forms are most conveniently adapted to the use of the system, having special columns reserved for the check-numbers, besides embodying other improvements, which tend to economize labor and expense. Ledgers of retail houses contain frequently sev- eral entries on a single line, and only the exten- sions in the amount columns. By placing the check-numbers below the amounts and the reduced totals of the checks of each line on the side of the folio column of the account, a perfect proof of the iiji [f \ !:,. —34— footings performed during the month is obtained. Another way of applying the system to this class of entries consists in placing the proof-numbers in the check column under each other, and between the line to which they belong, avoiding the addi- tion of the checks before the end of the month. The best time for adopting the system in the ledger is at the end of the month, by extending the pencil checks while making the pencil footings, which immediately results in a saving of time, as all subtractions in the ledger, the drawing off of the balances on the trial balance, and the addi- tions of the trial balance are proved without going over the work. But the use of the system may be commenced at any time during the month, by ex- tending the check-numbers of the amounts pre- viously posted into the check columns. The work of extending the checks, however, need not be done at the time the use of the system is com- menced, as the check-numbers may be inserted for the new entries alone, and after sufficient experi- ence has been acquired, can be readily filled in from the beginning of the month, by devoting a few minutes every day for the purpose. DRAWING OFF BALANCES. The division of labor, which, if I am reliably informed, is most extensively carried out in the manufacture of pins, so that it requires 150 hands -35- tained. 18 class ibers in ►etween le addi- onth. I in the tending ootings, time, as ig off of he addi- iit going I mav be 1, by ex- ints pre. 'he work I not be 1 is com- erted for X experi- filled in evoting a a reliably )ut in the 150 hands to finish a single one of these tiny objects, can also be profitably applied in book-keeping. The adoption of this principle, however, need not carry with it the doubling or tripling of the office force, which would be a serious objection, but merely implies dividing the work, dissecting complex pro- cesses into their component parts; in short, doing one thing at a time. An instance, which has been repeatedly suggested, is the placing of the ledger folios in the books of original entry before posting, and check marking the folio numbers afterward. The labor of taking off the balances from the ledger on the trial balance can also be consider- ably reduced by dividing the process into two dis- tinct operations; first computing the balances, and then drawing off the balances on the trial balance. The loss of time entailed by going twice through the ledger, is amply counter-balanced by the saving of time resulting from the increased speed with which the operations are separately performed. The balances in the ledger are best placed between the lines in the debit or credit date columns, which are most conveniently ruled for the purpose, having the same dimensions as dollar and cent columns. The horizontal diagonal or vertical writing of pencil balances in the ex- planation columns is not recommended; this prac- tice giving the ledger accounts an untidy appear- ance, besides conflicting with other uses to which —36— these columns are put. The advantage of having a financial history of the account, which can be easily obtained by glancing over the date columns, would also be sacrificed. The copying of the balances from the ledger on the trial balance can be quickly done, no time being wasted with changing pen and pencil, or handling separate sheets of paper on which the calculations are performed. In computing the balance of an account reverse the process of subtraction into that of addition, which is speedier, and requires less mental effort. To illustrate: Debit total, 513.49; Credit total, 417.62 Credit total, 417.62; Balance, 95.87 Balance, 95.87; Debit total, 513.49 Instead of deducting the smaller from the lar- ger amount, add to the smaller amount sufliiciently to produce the larger. The result is really the same, while the process is radically different. In- stead of saying 2 from 9 leares 7, say 2 and 7 are 9; instead of deducting 6 from 14, add 6 and 8, etc. The operations of adding and subtracting, on the smaller side of the account, can be simul- taneously performed, the total, including the bal- ance, being known. It is only necessary to add the columns of the given items, increasing each partial sum by the figure required to produce the —37— corresponding figure of the total, always carrying the tens. For example: 122.61 41.23 426.91 238,97 Balance, 829.71 Note.— The awkward copying of debit and credit footings on sep- arate slips in order to ascertain the balance of an account, is entirely avoided by this method, which in connection with the Proof furnished by my "Advanced System/' is perfectly safe and reliable. There are some book-keepers who desire to have as few pencil marks as possible in the ledger, and therefore place only the balance under the last item of the larger side of the account. This bal- ance is then included with the new entries of the following month, and care must be taken to ex- clude items of the preceding month on the smaller side, which may be accomplished by drawing a short line. The practice of taking a trial balance of ledger footings recommends itself on account of saving the computation of balances, thereby decreasing the liability of making mistakes, but is objectionable, as it requires the drawing off of two large amounts for every small one, more than doubling the w^ork of footing the trial balance. The best way of laying out a trial balance book is to leave no vacant lines at the beginning of the vear. Write out the accounts in condensed form —38— and open pages in the trial brJance book for the reception of all new accounts of folios 1 to 100, 101 to 201, 201 to 300, etc., taking care that suf- ficient space is left for every 100 pages of the led- ger, some sections receiving more new accounts than others. These directions are contrary to the ad- vice given by trial balance book manufacturers, most interested in increasing their sales, but en- able the book-keeper to avoid the common incon- venience of blank and crowded pages, the needless scattering of balances throughout the trial balance book, and will prove instrumental in dispelling the wrong idea that books requiring a single writ- ing of names each year are only adapted to ledgers, which receive a limited number of new accounts. My '* Improved Self -Checking Trial Balance Book " has been arranged with a view of accom- modating book-keepers in the use of my * 'Advanced System," but will be found equally convenient by others, as it embodies every valuable improvement which a thorough acquaintance with practical re- quirements could suggest. It has two short leaves, which bring name and amount columns closely to- gether every four months, and its special copy- righted features consist in check columns on the side of the amount columns, guide numbers on each side of the book which facilitate the following of names across the page, and the words. Folios . . . to .... , printed at the head of every page, indicat- I' i —39— iiig the ledger folios represented thereon. A mar- ginal space may be utilized to denote the transfer of an accoimt from one folio to another. Each page contains 50 lines, ruled alternately in red and blue, to aid the eyes in going across the page, and a "monthly summary '' 3tals" is appended. A suggestion worth heedii^^: Blurred pencil marks are a fruitful cause of errors, therefore employ a hard pencil with a fine point, while computing the balances in the ledger. TRIAL BALANCE CHECKS. Each page of the trial balance can be proved separately, by placing the balance of the checks on the side of the balance of each account, and comparing the reduced total of the checks with the reduced total of the balances. In case of a disagreement ascertain first if the additions have been made correctly, and proceed to the compari- son of checks and amounts until the wrong bal- ance is reached. It is recommended to draw out the checks independently of the balances, by first taking off the balances of each opening (two opposite folios) of the ledger, or one page of the trial balance, and then returning to the same accounts of the ledger and withdrawing the checks. This apparently increases the work, but in reality tlie two processes require less time, if performed >eparately, besides furnishing an invaluable safe- guard against the omission of a balance, as it is n —40— R i TRIAL BALANCE. January^ 1891. February, 1891. 3 347 96 4 187 59 ' 9 25100 00 4 25150 00 r X 375 00 o 275 00 5 452 37 (I) 413 26 y t 2 268 75 I 168 75 2 596 00 (I) 5 6 (I) 43S 54 75 450 12 06 08 00 2 596 00 (I) 6 9 438 75 350 12 08 00 . 7 1272 00 5 852 00 5 767 85 5 426 85 9 643 92 9 463 92 6 2 48 7 5 46 7 5 46 3 24 12 5 92 12 6 112 37 3 435 63 16 28 I 3 09 r 6 28 I 3 00 6 5 23 04 10 4 25 23 34 5 4621 (I) 26389 o 3959 9 26185 04 Note: Names of accounts and folio numbers have been omitted in this illustration as they are not essential in exhibiting the workings of my system. The check balances may be put down in pencil, and erased as soon as they have served their purpose. This is especially recommended in ordinary Trial Balance Books with crowded columns, and can be conveniently done as the Account Balances are first drawn off in ink, and are not disturbed by afterward removing the pencil checks. Always deduct the check of the smaller from the check of the larger amount, and in case the latter is smaller add ii before deducting; which also acts as safeguard against placing a balance on the wioug side of the Trial Balance, as in withdrawing the Check Bal- ances, the condition of the accounts must be considered, the trans- placing of a Balance having the same effect on the Check as transposing figures. —41— 91. 150 00 168 75 438 12 75 08 350 00 5185 09 04 1 omitted in iie workings pencil, and s especially ed columns, es are first smoving the m the check dd II before \ balance on ; Check Bal- i, the trans- i transposing next to impossible that check and balance of the same account will be repeatedly overlooked, the account assuming an entirely different appearance when the check balances are examined. The checks in the trial balance, if drawn off separately, can be written in pencil, and erased as soon as the work is completed, the trial balance checks being merely intended as an aid in copying the balances correctly from the Ledger and prov- ing the pages of the trial balance. This system applies equally well, if the trial balance is composed of totals instead of balances, by placing the check totals of each account on the side of the corresponding totals in the trial bal- ance. In case the footings of the trial balance are forwarded from page to page, forward also the corresponding checks, which serve as safe- guards against carrying wrong amounts. If the footings of each page are recapitulated at the end of the trial balance, the checks of these footings are recapitulated in the same manner, preventing errors in copying and proving the totals of the summary. The addition of the checks in the trial balance can be considerably simplified, by reducing the sums whenever convenient, according to the prin- ciple of the system, and carrying the reduced num- bers, a mere pastime compared with the awkward carrying of hundreds in ordinary footing. "1 —42— In this system every difference is dissected into its component parts, each trial balance page exhibiting its own mistakes, which are easily located and removed, while the difference of a trial balance may be entirely misleading, indicat- ing, for instance, a transposition of figures, though being caused by three or four mistakes. The common dread of making the final footing gives way to a feeling of safety, which can hardly be overestimated. If work is pressing during office hours the book-keeper is enabled to take the trial balance home in the evening, trace every error to the very account, and return the next morning, ready to make the corrections in the ledger. The drudgery of hunting for mistakes, according to the old and primitive methods, is avoided, and correct trial balances at the first footing become the rule and not a rare and almost alarming exception. Detecting Errors of Previous Months. Frequently my ''Advanced System" is adopted as a last resort in order to remove an error which occurred in the past, instead of being embraced as an important addition to the science of accounts, and with a desire of removing the difficulties with the trial balance in the future. The system em- bodied in this work, though only fully accomplish- —43— ing what is claimed for it, if the knowledge is possessed by the book-keeper while the work is being done, can also advantageously be applied to back work, and will result in a great saving of time and labor over the ordinary (lack of) ** method," which consists in hunting aimlessly in all directions^ repeatedly overlooking the same error. The footings of the trial balance, as well as the drawing off of balances from the ledger, can be proved by placing the check of the pencil totals of each account in the ledger, between the line in the corresponding debit or credit check column, and writing the balance of these checks on the side of the balance of each account in the trial balance. Every page of the trial balance can be proved separately and an error readily traced to the very account, by simply comparing checks and balances. To verify the additions in the ledger, the checks of every entry must be extended in the check col- umn, and the total of the debit and credit check- numbers of each account including the checks of the pencil footing of the preceding month, com- pared with the checks of the pencil footings. An error in extending any of the check-numbers is readily discovered in the amount in which it occurred. To locate errors of posting or omission as well as to prove the accuracy of footings and transfers —44— in the books of original entry, the checks in the ledger must be copied on the side of the ledger folio numbers in the books of original entry, and the total of the checks compared and forwarded with the footings of each page. The work can be conveniently done by two persons, the book-keeper handling the ledger and calling the check to the assistant, who places it in the book of first entry. In many instances it will be possible to locate an error to the general or individual accounts, and to the debit or credit side, which reduces the labor of applying this system materially. The applica- tion of my "Advanced System," however, will in- variably detect the error with the least possible effort, the most laborious task of verifying the ledger entries being only performed, if absolutely necessary. Errors which baffled the skill of expert book-keepers have been located and detected in less than three hours with the aid of my *' Ad- vanced System," thereby amply demonstrating its applicability for discovering errors in '^back work." li! PREVENTION OF MISTAKES. 1. Do not divide your attention while posting by repeatedly looking back to the original entry. The proof-number check is an ample safeguard against errors in posting. —46- 2. Prevent translocating dollars to the cent culumns by writing ciphers in the vacant places (24.00 not 24. — ) in the books of original entry as well as in the ledger. , 3. Never post debit and credit entries alter- nately. This effectively prevents posting to the wrong side of an account. 4. Be careful in placing the correct folio num- bers in the books of original entry. Most errors of posting to the wrong account can be traced to negligence in paging. 5. The entries of the ledger should not be **ruled off" during the month. A check-mark (V) will accomplish the object more effectually, and give less occasion to make mistakes. 6. Apply a special proof to all footings which are not directly verified by the operation of the system. v. Errors in copying can be prevented by re- ducing the copied amounts and comparing the check-numbers with the original. 8. Take care in placing the amounts in the proper columns in the books of original entry. The books of first entry form the foundation of all ledger work, and must be assumed to be cor- i*ect. •,. ■ .■ ■ , ,; ._ -■■■_■„.. ^- ',•,.'. ■ , ^ .. 9, Figures cannot be made too distinctly. Be particularly careful not to mistake 1 for 7, 4 for i » • 46 ^, or (1) for 0. Make all pencil marks with a hard pencil to prevent blurring. 10. Avoid crowding two fig ures into the same column, as one ; of the figures is likely to be over- looked. • • SCIENTIFIC PRINCIPLES. Though the practical application of my *' Ad- vanced System " requires only a superficial knowl- edge of its scientific foundation, it will no doubt prove interesting to many to understand the laws and principles governing its operation. The agreement between the check-number of a total or balance and the reduced sum or difference of the check-numbers cannot be reasonably attributed to accident or chance, or be the result of an arbi- trary scheme of interlinking figures, but must necessarily have a permanent and substantial basis, an explanation of which is here presented. It is a peculiar fact, which can be readily veri- fied, that whenever we deduct the left hand from the right hand figure in any number, we not only arrive at the difference between the two figures, but the difference represents also the remainder after dividing the number by 11. For instance: 59 4 38 5 19 8 In case a number is composed of more than two figures, the remainder, after dividing by 11, can be easily obtained by separating the number from the right to the left in groups of two figures, and deducting the sum of the left hand from the sum of the right hand figures of each group, or, to ex- press it in a simpler form, by adding every other figure, commencing with the right hand figure, and deducting from the sum obtained the sum of the figures which have first been omitted. For in- stance: 3.48 11— 4=7; 12.46 8—5=3 The check-numbers employed in this system are nothing else but the remainders obtained after di- viding by 11, and the universal laws on which the system is based are that the sum of the remainders must be equal to the remainder of the sum, and the difference of the remainders equal to the re- mainder of the difference, provided the same di- visor is employed. To illustrate: 26 .... 4, remainder after dividing by 11, 4 .... 26 12 1, '' ** « " 1 12 38 ... .5, remainder after dividing by 11, 3 .... 14 The reason why this system discovers mistakes, is that the sum or difference of incorrect remain- ders will not correspond with the remainder of the correct sum or difference, and the remainder of an incorrect sum or difference will not agree wiih. the sum or difference of the correct remain- -48— ders. The fact that wo can arrive at the remain- ders after dividing by eleven withont dividing at all, by taking advantage of a wonderfnl property of the decimal system, makes it a practical system, as one would soon get tired of dividing every entry by eleven, in order to ascertain the remainder. But to arrive at the Remainder after dividing by eleven, it is essential that we always deduct the left hand from the right hand figures. Then the question arises, what is to be done in case the right hand figure or the sura of the right hand figures is smaller. A simple consideration of the funda- mental principle of the system removes the diffi- culty. Whenever the right hand figure or the sum of the right hand figures is smaller add eleven (or, if necessary, a multiple of eleven) before de- ducting. Take, for instance, the numbers, 59, 5 from 9 leaves 4; 38, 3 from 8 leaves 5 95, 9 " 16 " 7; 83, 8 <' 14 " 6 "•11 11 Peculiar as it is, whenever two figures have been transposed the sum of the right and wrong check- numbers will always make eleven, showing an in- teresting relation of the number eleven to the transposition of figures. Still the fact in inself is of little practical consequence, the system locating an error to the very account, which renders it im- material what the nature of the error may be. -49— In some cases the addition of eleven to the sum of the right hand figures will not be sufficient, necessitating the addition of a multiple of eleven, while in other cases the subtraction of the sum of the left hand figures will leave a difference larger than ten, requiring a further reduction, by deduct- ing the left hand from the right hand figure, which results in the omission of eleven contained therein. For example: 91.91 18 from 2+22 = 24 leaves 6. 19.19. .. .2 from 18 leaves 16, 1 from 6 leaves 5r The check-numbers employed in this system vary between and 10. They are never larger than 10. 11 gives reduced 12 (( 1 13 t( 2 14 a 3 15 a 4 16 a 5 17 a 6 18 a 7 19 li 8 20 a 9 21 n 10 22 gives reduced 23 '' 1 24 ** 2 25 *' 3- 26 a 4 27 '* 5- 28 '* G 29 ** 7 30 <* B- 31 <* 9) 32 • << 10 All multiples of 1 1 are reduced to — 1 1 . . 0, 22..0, 33..0, 44..0, 55 . .0, 66 . .0, 77 . .0, 88.. 0, 99.. 0. 'i 1 — 50— .' The total of the 11 check numV)ers equals 55 — 0+1+2+3 + 4 + 5+0 + 7+8+9 + 10 = 55, a multi- ple of 11. In order to avoid the writing of two figures as a check-mark, the check-number 10 may be repre- sented by a single sign, by writing O around the 1. This mark can be produced by a single stroke, similar to the formation of a 1 in parenthesis. The Roman X is not recommended on account of its similarity to the figure 4 when rapidly written, but any arbitrary sign will answer, as long as it is understood that it represents the number 10 and adds as 10, the addition of 10 offering no difticulty, being even more readily performed than that of 9, 8 or 7. REVIEW. Anyone who h? lowed with attention the chapters of thi*" .w must have been impressed with the fact ^at the information presented therein is not an aggregate of disconnected rules, but a complete system, based on a simple and original idea, which furnishes a chain of proof from the first entry, posted to the ledger, to the last footing, made in the trial balance. Every amount posted to the ledger produces a check in the ledger, and a copy of the check in the book of original entry, on the side of the —51— folio, taking the place of the ordinary check mark. The agreement between the reduced total of the checks and the check of the total of each page of original entry proves the correctness of posting and footing, and the forwarding of the reduced total of the check-numbers from page to page is a valuable safeguard against carrying wrong totals. As the checks in the books of original entry are copied from the checks which have been pre- viously placed into the accounts of the ledger, the omission of an entry in the ledger must necessarily result in the omission of the check in the book of of original entry, which would be immediately noticed, besides producing a disagreement at the bottom of the page. At the end of the month the checks, accumu- lated in the ledger during the month, prove every footing in the ledger, by adding the checks, verifv the balance of each account, bv ascertain- ing the difference of the check-numbers, prevent the drawing off of a wrong balance from the ledger, by placing the balance of the checks on the side of the balance of the account in the trial balance, and prove the footings of the trial balance, locating an error to the page of the trial balance, and enabling the book-keeper to trace it to the very account, without referring to the ledger, by simply comparing the balances with the checks. —52— With the adoption of this System, every page of original entry is transformed into a trial balance, every account of the ledger represents a trial balance, and every page of the trial balance a trial balance, exhibiting ti'3 mistakes contained therein and facilitating their detection. In conclusion I am justified in claiming that my " Advanced System " is the only system known, which locates an error to the very page of the trial balance, no matter how many accounts have been transferred from one section of the ledger to another, and which enables the book- keeper to trace an error to the very account with- out referring to the ledger, re-checking or copy- ing entries. Ill ADVANTAGES OF THE SYSTEM. The preceding pages of this work contain a practical exposition of the system, together with a complete explanation of the scientific principles and laws, which govern its application. The al- most incredible claims made for this system have all been substantiated in turn, without deviating for a moment from the general plan of the work, which has been so arranged as to communicate a thorough understanding of the information offered, and to impress the learner with the logical and systematic order of its sub-divisions. The present —53— chapter, while partly recapitulating the knowledge presented, is principally intended to demonstrate in numerical order the broad assertions made re- garding my " Advanced System for Locating Er- rors," at the same time fixing upon the mind the essential points required in its application. WHAT IT DOES! 1. It locates an error in posting; to the very account -without referring to the ledger, re-checking or copy- ing: entries, and almost instantaneously. Whenever the reduced total of the proof-number checks of any page does not correspond with the check of the total, the error can be quickly traced to the account of the ledger by simply comparing the amounts with the checks in the book of orig- inal entry. As the check-numbers range only be- tween and 10, while the number of items to be posted has no limitation, it may be argued that the possibility of a wrong entry producing a cor- rect check-number is not entirely excluded, that this ''proof of posting" is not infallible, and therefore useless! Indeed, such a conclusion would not be consistent with common sense, since there are no infallible methods within human reach. It is the experience of almost every book- keeper that a wrong entry may liave been re- checked repeatedly without being discovered. 54 Those employing the cumbersome copying of en- tries have found that the ^^system" may be in balance, while the ledger is not, etc. What is claimed for the system offered in this work, is that for the least expenditure of time and labor the greatest number of advantages are gained; that, if used judiciously, it is bound to reduce the trouble resulting from errors in trial balances to a mini- mum, and that, discovering all errors which are likely to occur in posting, it will prove an invalu- able addition to the knowledge of every office man. The danger of a wrong amount producing a correct check-number, or of two counter-balanc- ing errors on a single page, is very small, as errors in book-keeping do not occur regularly at intervals of 15 minutes, and only when the difference of the trial balance is divisible by 11, or gives reduced 0, the remote possibility of an error in posting is to be considered; otherwise the accuracy of the ledger entries can be relied upon and the presence of a difference is not attributable to a failure of this system. The posting of an amount, which gives reduced 0, into the wrong column, a very far-fetched pos- sibility, results in a difference, which, divided by 9, produces the transplaced amount. This error is readily located by merely glancing over the pages of original entry. -oo- Examples: 20.90 2.00 .'337. TO 33.77 9)18.81(2.09 9)303.93(33.77 The error of posting dollars as cents, which ])roduces the same check-number, can be easily traced, the division of the difference by 99 (9X 11) producing the exact amount of the error. Examples: 24.00 7.00 325.00 24 07 3.25 99)23. 76(. 24 99)673(7 99)321.75(25 NoTK.— Tranelocations of dollars into the cent columns result in differences which give reduced 0, the number of dollars, increased by 1. added to the number of cents, invariably producing 100, for in- stance: 23.76, 23+1-1-76=100. The error of posting dollars as cents or vice iiersa can be readily discovered by affixing or pre- fixing a dash ( — ) to the check-number, whenever an amount of dollars without cents has been transferred to the ledger, and by casually compar- ing these amounts with the corresponding check- numbers on the page of original entry. These checks may be written in the follow^ing manner: — 1,- 2,-3, — 4,— 5,— 6, — 7,— 8,— 9,-0, or with a single stroke, by connecting the dash with the figure, if convenient. This safeguard could also be extended to prevent the posting of hundreds of dollars as dollars, by annexing or prefixing a —56— plus (-|-) mark to the checks of the former amounts. But as these are errors of gross negli' gence, and this system can hardly be expected to transform frail book-keepers into infallible beings, the suggestion already transcends the scope and purpose of this work. I frankly admit that it will not do to make all kinds of blunders, depend- ing upon the system to remove them by magic. Ordinary carefulness, such as every book-keeper ought to observe, will still be required, but in connection with this the many preventives and correctives furnished by my " Advanced System," will make the taking of a trial balance a compara- tively easy task, and remove the anxieties gener- ally connected with it. To exhibit by way of contrast the superior value of my *' Advanced System," it may be well to allude here to the old transposition rule, which merely assisted in as- certaining the difference between the transposed figures by dividing the difference of the trial balance by 9. Example: ' 91 76 * 19 67 9)72(8 9—1=8 9)9(1 7—6=1 It is obvious that the smaller the difference between the transposed figures, the larger the number of possible combinations. While in the J? ■ ■ ■ — 57— first example only four, in the second, eighteen combinations are possible, though only h.?lf that number had to be considered, as it could be readily ascertained if the larger or smaller amount was the combination of the error. Transpositions with 1, 3, 5, etc., figures between the transposed figures are of very rare occurrence. Differences caused by these transpositions are di- visible by 99, 9999, 999999, etc., the results of these divisions showing the differences between the transposed figures. Examples: - I435.i2 5.62 1235.14 2.65 9999) 199.98(2 99)2.97(3 The number of nines in the middle of such dif- ferences indicate the number of figures which have not changed their position. Errors of transposition, with 1, 3, etc., figures between the transposed figures having retained their places, can be prevented by looking at, pro- nouncing or writing the figures of each amount in couples, as for instance; 3147.20 as 31-47-26, or 351.26 as 3-51-2C. The error of posting 147 as 741, 351 as 153, etc., becomes then a practical im- possibility. This would also counteract any tend- ency of posting 13.16 as 16.13, etc., and frequently facilitate arriving at the check-numbers, by de* — 58^- ducting the left-hand from the right-hand figure in each group, and adding the differences. )t. It Indicates directly the account in ^vhich an entry has been omitted, and points out the repetition of an entry. The omission of an entry in the ledger results in the omissson of the corresponding check in the cash book, sales book, etc., which would be im- mediately noticed, besides producing a disagree- ment betAveen the reduced total of the checks and the check of the total of the page. This system furnishes a double check against omissions, one which would lead to the detection of the error by casually glancing over the page, the contrast be- tween the black check-figures and the red folio- numbers being very striking, and another, result- ing in the disagreement of the page, as every check figure is needed to produce its equilibrium, which also acts as safeguard against repeating an entry. 3. It oflTers a safeguard agAinst postingr to the ivrons side of an account or to a ivrongr account, as ivell as against double and counter-balancing errors. The distinction between debit and credit check- numbers is an ample safeguard against posting to the wrong side of an account. As every debit entry in the ledger produces a check-number on the left hand side of the ledger folio, in the book of first entry, and every credit entry a check on the right hand side, the error of posting to the -69- wrong side of an account not only results in a dis- agreement at the foot of the page, but will, as a rule, be discovered while placing the check to the entry in the book in which the mistake originated. The placing of the folio numbers in the books of original entry before posting insures the close comparison between folios and accounts, and is in itself a safeguard against posting to the wrong account. The mind being relieved of paying special attention to the amounts, naturally in- creases its watchfulness regarding the accounts. In copying the checks from the ledger in the book of first entry, an additional glance at the name will invariably discover this mistake. This habit can be easily acquired, the use of check-numbers relieving the mind of comparing the amounts. A more absolute check against posting to the wrong account can be obtained by omitting the check- numbers in the ledger at the time an entry is made, and placing the checks into the correspond- ing accounts, after the posting of a page has been completer?. The account in which the entry should have been made will exhibit no vacancy for the check, while the wrong account will contain an entry without a corresponding check-number. This process does not require as much time as ordinary re-checking, no attention being paid to the amounts. However, the extra labor required by this process may be saved, as the ordinary —60— application of the system acts as a preventive against this error, which, by the way, does not disturb the equilibrium of the trial balance, and is quickly discovered by the unfortunate individ- ual, who is charged too much or credited too little. The consecutive numbering of accounts would be a valuable safeguard, but necessitates a ledger which is made specially to order, besides increas- ing the account numbers to an inconvenient size. The use of the initials of the ledger accounts in connection with the check-numbers in the books of original entry, and the comparison of these initials, copied from the ledger, with the names found in the books of original entry, the applica- tion of numbers indicating the position of the account in the ledger, etc., etc., belong to a class of impracticable schemes, which are of limited value, and do not permit of general introduction. Counterbalancing errors on different pages of the trial balance, or in different accounts of the ledger, are detected individually, thereby increas- ing the reliability of the trial balance. 4. It proves the totals in the books of original entry, \«'ithout requirinis a second footing. The footings in the books of original entry are proved by the agreement of the reduced total of the checks with the check of the total. 5. It detects errors of forwarding totals or bal- ances w^ithout comparing the amounts carried. — 61— The forwarding of the checks simultaneously with the forwarding of the corresponding totals or balances detects the carrying of wrong amounts, by means of a disagreement of checks and totals on the following page. 0. It verifies the footins^s of each account in the Ledffer -without soing over the additions. The footings of each account in the ledger are proved by the comparison with the corresponding check totals, which, however, can be dispensed with, as the agreement of the checks and totals of the trial balance proves also the correctness of the additions in the ledger. 7. It proves the correctness of every Imlanoe with- out repeating; the operation, and locates an error im- mediately to the account in which it occurred. The correctness of every balance is proved by the agreement with the corresponding balance of the checks. But the separate comparison of each account and check balance is only required in case of a disagreement at the bottom of the trial bal- ance page, as there is no reason to look for an error, before one is positive that an error has been made. Never trouble trouble, etc, 8. It prevents the omission of a balance in the Trial Balance, rullns ofT accounts w^hich should be left open, and mistakine the pencil footiuKS of pre- cedinii; months. The separate drawing off of the check balances is a safeguard against the omission of a balance in the trial balance, which would be readily dis- PRi —62— covered by the appearance of a superfluous check, and the consequent disagreement of the checks and balances of the trial balance. " Ruling off" accounts, which should be left open, is prevented by the disagreement of the pencil checks on both sides of the account. While not every account is in balance when the check-numbers balance, the check-numbers must always be in balance, when the account balances, therefore whenever an account appears to be in balance the balance of check-num- bers will serve as final test. The mistaking of a pencil figure is detected by the disagreement of the pencil checks and pencil footings, and the disturbed balance of the corresponding trial bal- ance page. 9. It discovers the transfer of a wrong balance from the liedger to the Trial Balance, embracing all classes of errors, transpositions, translocations, transplacements, etc. The drawing out of the check balances on the side of the account balances in the trial balance is a perfect safeguard against transferring a wrong balance from the ledger to the trial balance, and discovers all errors which are likely to occur. This system also furnishes an effective safeguard against transplacing a balance on the wrong side of the trial balance, the withdrawing of the check balances necessitating a consideration of the nature of the account balance, as the check of the smaller amount must always be deducted from the check «g —63— of the larger amount. Any violation of this prin- ciple produces a disagreement of the checks and balances at the bottom of the particular trial bal- ance page. ' lO. It proves the foottnKM of the Trial Balance and indicates the page and account in ^vhich an error has been made, no matter if the totals are carried forvrard or recapitulated. The agreement between the reduced total of the checks and the check of the total proves the accu- racy of each page of the trial balance, while a disagreement indicates the presence of an error. The checks can be forwarded from page to page or recapitulated at the end of the trial balance, which proves the correctness of the amounts carried or recapitulated. The addition of the check columns may be called a recreation, compared with the repeated footings of amount columns, as the carrying of hundreds is entirely avoided, and the separate comparison of the checks and balances is only required in case of a disagreement at the foot of the page, it being unreasonable to look for an error before one is certain that an error has oc- cured. . • APPENDIX. ii il FOREIGN CURRENCIES. My " Advanced System " being based on a property of the decimal system, its usefulness is not limited to the United States and Canada, but extends to all foreign countries having a decimal currency. The difference of name and size of the various monetary units does not effect the princi- ple in the least. A notable exception, however, is England. The subdivisions of English money are not decimals of one pound, and require a special adaptation of the system. The method of reduc- tion for the purpose of arriving at the check-num- bers, which consists in adding the alternate figures, commencing at the right hand, and deducting from the sum obtained the sum of the figures which have first been omitted, is not materially altered, only that two places must be allowed for the shillings and pence. For example: £64, 13, 01; ('7+3+4)--(0-t-l+6) = '7 , ' 12, 05, 13; (3+5+2)— (l-[-0+l) = 8 37, 02, 09; (9+2 + 7)— (0+0+3)= 15.. 4 Note.— The noughts merely Indicate the vacant places, but are not to be written in practical work. —05— The principal difficulty consisted in the carrying of shillings from the pence and of pounds from the shillings columns, but has been overcome by a close investigation of the principles governing the application of the system to the process of di- vision. The agreement of the check-number of the total and the total of the check-numbers can be readily brought about by deducting from the latter 8 times the number of pounds carried, or adding 3 times that number to the check total. Note.— The reason for this rule lies in the relation of pounds to shillings (1:20) and shillings to pence (11:2), in the reduction of the numbers 20 and 12 to 9 andl, and in the subtraction of 1 from each of the reduced numbers, as the number of £ and s carried are already included in the total, leaving 8 and 0. The product of the number of £ carried by 8 or 8 may first be reduced to a single figure, which sim- plifles the operation considerably. Example: H T % t ■ % 30 3X8 = 24 £114, 123, 91, 16, 26, . ■% 26, 6, 13, 2, V, 19, 9 11 5 8 4 7 30 9 i:2V9, 16, 8..25— S^l^-.e 6 39. .6 Note.— To deduct 8 times the number of £ carried, is equivalent to adding 3 times that number. The check for the balance of an account is ob- tained by adding 8 to or deducting 3 from the — G6- pi I! III difference of the check numbers, whenever £1 has been *' borrowed," and reducing the sum, if larger than 11. Example: £15, 5, 9. .7 £126, 13, 2. .9 12, 19, 8..() 48, 7, 8. .8 1 1..78, 6 1 9. .2, 6, 1.. 1 + 8 = 9 1 + 11— 3 :=9 In all other particulars the application of this system to English currency is the same as ex- plained and illustrated in this work. MIXED NUMBERS. The applicability of this system is not confined to money values, but can be easily extended for proving the accuracy of Ledgers, etc., the entries of which represent bushels and pounds, etc. Es- pecially when the number of units which make up the higher denomination gives reduced 1, as for instance 56, the standard for rye, corn, etc., the use of my advanced system is as convenient as with dollars and cents, as the number carried need not be considered, being already included in the answer. The check of 4,123 bu., 14 lbs. ... 1, is just the same as for $4123.14, though the number of pounds are not decimals of bushels, and the ad- —67- 1 dition or subtraction of the clieck-numbers will in- variably prove the addition or subtraction of the corresponding quantities. To illustrate: 8 2 8 V 9 1234 bu. 17 lbs. 5621 '' 46 4263 '' 19 649 '' 51 1262 " 12 " (( n n 6 8 26421 bu. 18 lbs. 21539 " 51 a 9 4881 bu. 23 lbs.. 9 7 13031 bu. 33 lbs.. 7 With the above discovery a wide and almost unlimited area of usefulness is opened for my " Advanced System," which is bound to find its way into erery office, where a saving of time and labor is of any consequence. The ease with which it can be adapted to special requirements, and the facility with which it may be acquired, justify the prophecy. OTHER CHCEK SYSTEMS. A knowledge of the wonderful property of the number 1 1, on which this system of proof is based, leads to the investigation of uie properties of var- ious numbers, which may be utilized in a similar manner. That there is no other number of equal practical importance for the purpose of proving the accuracy of a book-keeper's work, will be { ! I t —68— readily gleaned from tue following exposition of the subject. The different numbers and their cor- responding properties are arranged in numerical order. The Number 7. — In order to arrive at the re- mainder after dividing by 7, without employing the tedious process of division, the amount must be separated from the right to the left in groups of 3 figures, the sum of the .'ft hand groups de- ducted from the sum of the right hand groups, and the difference divided by 1, 14239, 239—14 = 225 7)225(32. The impracticability of the idea is apparent without further comment. The Number 9. — The remainder after divid- ing by 9 is easily obtained by simply adding the digits of the amount, and repeating the operation, if the sum is composed of two figures. All nines or figures making together nine can be omitted. J^o5*«**12.«..o, 147J9., ..o The system of proof based on the property of the number 9 is not sufticient, as it does not dis- cover the transposition of figures, an error not likely to happen while adding, but commonly oc- curring in posting and copying. The error of mistaking a for a 9 is also overlooked. The process of addition, though simpler than addition and subtraction combined, as employed in my a -69— Position of their cor- numerical at the re- employing )unt must in groups groups de- li groups, 2. apparent ter divid- Ming the »peration, All nines tnitted. ►perty of not dis- rror not lonly 00- error of L The addition in my " Advanced System," lacks the counterbalancing principle, which materially reduces the mental effort in the latter. The Number 13. — The property of the num- ber 13 is similar to the property of the number 7, and equally useless from a practical standpoint. The Number 99. — By separating an amount from the right to the left in groups of two figures, adding these groups together and repeating the process, if the sum should be composed of more than two figures, the remainder after dividing by 99 is ascertained. 145361, 14 + 53+61 = 128, 1 + 28 = 29 A proof-system, founded on this property, would be too cumbersome, besides furnishing no greater assurance of the correctness of the work than the *' Advanced System." The Number 101. — The remainder after di- viding by 101 can be found by separating the amount from the right to the left in groups of two figures, and deducting the sum of the left hand from the sum of the right hand groups. In case the sum of the right hand groups should be smaller, add 101 before deducting. 14,215.61, (61+42)— (15 + 1 ) = 8V The property of the number 101 offers a valu- able safeguard against the translocation of amounts from the dollar into the cent column^. The —70- Hi todiouaness of the process of arriving at the re- mainder, and tlie awkwardness of writing a num- ber, generally composed of two figures, as check- mark, reduce its practical usefulness to a minimum. Note.— The number 100, which is the largest check-number em- ployed in this System, could be indicated by 00, thereby avoiding the additional inconvenience of writing three figures as check-marks. Still, those who are inclined to doubt the use- fulness of my " Advanced System," on account of its limitations in not directly discovering the errors amounting to 01) oi* a multiple thereof, which are exceptionally rare, may avail themselves of the System, based on this property, and additional in- formation regarding its application will be cheer- fully given by the author. The sum and difference systems, based on the properties of the numbers 990, 9099, etc., and 1001, 10001, etc., by forming groups of 8, 4, etc., figures, possessing only theoretical value, are entirely be- yond practical consideration. CONDENSED TRIAL BALANCES. As my *' Advanced System" furnishes a satis- factory proof of the correctness of the ledger, it may be desirable, under certain circumstances, to dispense with the monthly taking of the trial bal- ance, provided a general idea of the condition of the ledger, regarding the total amount of out- standings or liabilities, etc., could be obtained. Also in case of a peculiar combination of counter- —71- balancing errors, the ability of readily locating the mistakes to a snbdivision of the ledger, and to the debit or credit side, will be appreciated by book-kee])ers. These results are easily accomplished by divid- iiig the accounts of tlie ledger in the following four classes: 1. Stock, Proprietor's or Partners' accounts, 2. General accounts, 3. Debtors' accounts, 4. C^reditors' accounts, and by the introduction of four accounts, repre- senting the above classes, and containing in con- densed form all entries of these accounts. These accounts are opened with the totals of the corres- ponding balances at the beginning of the year or at the end of the i)receding month, and the entries are made, in bulk, after posting, or at the end of the month, directly from the books of original entry. They are debited for the totals of the debit entries, credited with the totals of the credit entries, which have been placed from any of the books of first entry into the four classes of ac- counts. ' The totals of Cash Paid Out, M'd'se Sold or Ret\l, Bills Pay. Issued, etc., etc. 1 J to Individual Accounts appear therefore on the Debit side, —72— while the totals of Cash Received, "^ M'd'se Bought or Ret'd, Bills Rec. Received, etc., etc. J L from Individual Accounts are en- tered on the Credit side of the condensed Drs.' or Crs.' account, and there- fore on the opposite side of the condensed General account. The balances with which to open these new ac- counts during the year are readily obtained by the following process. Take first the balance of the Stock or Proprietor's account or find the total of the balances of the Partners' accounts, as exhibited in the trial balance of the preceding month, which is supposed to be in balance. Ascertain then the totals of the general Debit and Credit balances of the same trial balance and place the same on the corresponding side of the General account. De- duct then from the total of the trial balance the sum of the General Debit balances, the difference being the net balance for the Drs.' account, and obtain the balance of the Crs.' account, bv sub- tracting from the total of the Trial balance the sum of the General Credit balances and Proprietor's or Partners' balances. The re-addition of a great number of Drs.' and Crs.' balances is therefore avoided. Note.— Whenever a Debtors account should produce a Credit bal- ance or a Creditor's account, a Debit balance, these balances must be deducted from the total of the Debtor's or Creditor's balances, to ar- rive at the net balance of all Drs.' or Crs.' accounts. 13- ILLUSTRATION. TRIAL BALANCE. • Stock ) ^y . Proprietor's or I T^ . , ( ances. Partners ) ■/ General Debit Balances. 50,000.00 General Crebit Balances. - 40,000.00 Debtors' Balances. 20,000.00 60,000.00 • Creditors' Balances. 30,000,000 100,000,000 100,000,000 Corresponding with the subdivision of accounts, the entries to the ledger can also be classified in entries between: Stock, ) Proprietor's or > accounts and General accounts, Partners' ) General accounts and General accounts. General accounts and Debtors' accounts, and General accounts and Creditors' accounts, NoTB : Entries between Stock, Proprietor's or Partners' accounts and Debtors' and Creditors' accounts, and between Debtors" and Cred- itors' accounts are of rare occurrence. —'74— CONDENSED LEDGER, composed of Stock, Proprietor's or Partners' Account, General A(jcount, Debtors' Account and Creditors' Account. STOCK, FlWPlilETOirS OH FAHTNEMS' ACCOUNT. Cash Drawn, Etc. Balance, Etc. GENERAL ACCOUNT. Dr. Balance. Cash Rec'd. M'd'se Bought. M^cCse Befd from. Notes Bee. Bec^d. Miscellaneous Entries. Etc. Cr. Balance. Cash Paid. . M'd'se Sold. M'd'se Befd to. Notes Pay. Iss^d. Miscellaneous Entries. Etc. DEBT OB S' ACCOUNT. Balance. Cash Bec'd. ' M'd'se Sold. MWse Befd from. Etc. Notes Bee. Bec'd. Etc. CBEDITOBS' ACCOUNT. Cash Paid. M'd'se Bet'd to. Notes Pay. Iss'd. Etc. Balance. M'd'se Bought. Etc. Note: In more extensive sets of Books or to salt special require- ments, the General account can again be subdivided in Resources, Liabilities, etc., the Debtors' account in City, County, etc., and the Creditors' account into Eastern, Western, etc., accounts. In order to directly arrive at the total outstandings and liabilities, some book- keepers prefer to include Notes Receivable in the Debtors' Account, and Notes Payable with the Creditors' Account. ;OUNT, OUNT. trie ft. require- jonrces, and the Drder to e book- ccount, Tlie advantages derived from the adoption of these condensed acconnts are indeed too nnmerous to mention. It will be sufficient to state a few, and while the progressive book-keeper will allot to them a special book, the conservative may at least have a sheet of ledger-ruled paper to spare for this purpose. In favor of the introduction of these new ac- counts, the author claims that: They give the totals of the Debit and Credit entries into any of the four classes of accounts. They exhibit the balances of the Stock, Propri- etor's or Partners' accounts, Debtors' and Cred- itors' accounts. They prove the correctness of the entries into any of the four classes of accounts. They enable the book-keeper to locate an error to the different classes of accounts and also to ascertain if the difference results from an error on the Debit or Credit side. They show^ the progress of a business better than all other accounts combined. A condensed balance of the ledger can be taken in a few minutes, no matter how complicated the accounts may be; which, in connection with the proof supplied by my *< Advanced System," obvi- ates the absolute necessity of taking an itemized Trial Balance every month. m