An Improved System of Mnemonics/Chapter 5

THIS chapter is a continuation of the former part of the subject, in the application of figures, to characters expressive of hundreds, thousands, millions, and fractions. To accomplish this necessary part of the system, it was observed that the students ought to be well acquainted with the power and combinations of the first arrangement of numerals, ere they use them here, or they will be liable to confound the two parts, which are in themselves perfectly simple.

As all the consonants in the alphabet are engaged in the scale, page 29, the difficulty may appear insuperable: ​but notwithstanding their distinct use in that table, a certain modification of them has been effected, to produce the desired object, without interfering with the simplicity of that arrangement. The letters s and x, the students know, are applied to designate the 0, or cipher, as the words wise and vex will exhibit, making the figures 80 and 60; but if those letters were solely appropriated to the cipher, we should lose the very valuable assistance of all the words that begin with them: thus Smile, Son, Extent, &c. &c. could not be used; for the first, if changed into figures, would be 035; the second 02; the third 0121; which arrangement of figures never occurs, except in decimal fractions, to which branch it may be applied without any alteration. But for all the other parts of arithmetic, the following addition to the first plan will be found applicable.

Whenever the letters s or x, exist solely in a word, neither preceded nor followed by any other consonant, such word is to be a character for 100; thus the words Sea, So, See, As, Us, Ox, Axe, &c. &c. are each expressive of 100. If we subjoin another consonant to either of them, they each retain the character of One hundred, and the added consonant has its original value: the word Sat will be 101, the S, being one hundred, and the t a 1—Son, 102—Some, 103—Oxen, 102, &c. &c. But if we increase the number of consonants beyond two, whether three, four, five, or six, &c. in a word or sentence, the s and x so situated (beginning them) merely supply the first unit's place, and have the same power as the letters t or q, and become either hundreds, thousands, or millions, as they have consonants added to them. The word Spice is 197, the S being 1, the p and c being 97. Share is 124. If we add to the former, an s, and make it Spice, it becomes 1970, as a D ​ being added to the latter, making Shared, becomes 1246. This sentence, Spices are Eaten, make the following figures—1,970,412: the same rule applies to the letter x. The word Exact will be 171, as Exaction will be 1712, &c. &c. but when either of those letters are preceded by a consonant or consonants, they cease to be considered otherwise than orignally given, that is, they are ciphers. See would be 100, but To see would be 10.

It may appear that the example in page 43, of the word Soot, associated with Three Fingered Jack, will contravene this rule; but as that, was one of the illustrations given, to assist in recollecting a number of figures consecutively arranged, the word Soot representing the figures 01, though associated by itself, was still a part of a series of figures, in which were many consonants preceding it.

To have a character for One Thousand, and Thousand, we must combine the letters t and h; and form them into a word—thus, The will be 1000; Thee, Thou, Oath, &c. &c. will express the same number. If we add a consonant or consonants to such words, they will have their primary force, enumerating them in the order of units, tens, hundreds, &c. The word that will be 1001, the letter t being a 1—than, 1002—therefore, 1,494. Care must be taken, to mark, that th is not considered as 1 and 2, as in the table of letters and figures, for the word therefore might be mistaken, and called 12,494.

So far regards the application of th, as a character for One thousand: to use it where it is more wanting, as Thousand, is equally simple. Whenever it is preceded by a consonant, it loses its character of One thousand, and must be strictly understood to refer to Thousand solely; the preceding consonant determining its value: thus the word Faith represents 9000, the f being 9, the th being Thousand.

​If this distinction were not attended to, and th always understood to be One thousand, the word Faith might be called ninety-one thousand. Doth is 6000, Willeth 855,000, a rude oath 46,000, &c. &c. Where tн occurs in a word, preceded and terminated by a consonant or consonants, it is in the same manner to be considered as designating thousand. The word Neither will be 2004, n being 2, the th thousand, and r a 4. Mouthful is 3095, Worthless, 84,500.

It may be considered, that by this application of th, those letters can never be used as 1 and 2, but they can with perfect safety: Whenever they are found in a word or sentence not combined, as th, they have their original characters, 1 and 2, Tense being 120, Hand 226. If they even occur in the same word, not combined, they are still to be considered distinct. Phæton is 9212. The word Ought is 321: here the h is before the t; the latter must always precede it, to express 1000, or thousand.

Th being the initial letters of thousand, may be easily recollected.

As in the great variety of arrangements with figures, th already given, though extremely useful, may not be very easily applied in some instances, we make another character, which is to represent Thousand only, not One thousand. The letters sh, when joined together, have this power = thus the word Rash is 4000, Clash, 75,000, Flash, 95,000; but in the beginning of a word followed by a consonant or consonants, it does not differ from its former classification. The word Shun, is one hundred and twenty-two; Sheriff is 12,499.

To express one million, and million, we use the vowel y, which has nearly the same powers applied to millions, that th has to thousands. The word you is one million, as are ​ the words ye, eye, aye, &c. If we add consonants, they are to be enumerated as units, tens, &c. from the right hand to the left. The word Yet is one million and—one Yon, one million and two—Younker, one million, two hundred and seventy-four, &c.; but its principal use, is to express million. Thus 3,000,000 is represented by either the words May or Gay, the M or G being 3, the y million. Day is 6 millions, Clay is 75 millions, Pulley 955 millions, &c.

Not to lose for general purposes, the services of the y; which would be be the case if always considered as a million, it may be used as a vowel in all the situations where it would be impossible that it should be mistaken for millions; thus the word Play in Geography, might be properly called 95 degrees of Longitude, as we could not say millions of degrees. In Chronology, the word Dismay, cannot be termed 603 millions of years. It only requires to be kept apart, for all those purposes where mistakes might occur, as in Revenue, Astronomy, &c. &c.

When the students are practised in the system of figures, they can make any modification of the consonants for particular purposes, that they may find requisite, but if introduced in the early part of their study, may confuse.

Thus the combination of the letters nt could be used to represent One hundred thousand. The words Ant or Aunt expressing them. When preceded by consonants, the rule applied to th and y will guide: Haunt will be Two hundred thousand—Lent 500,000—Bent, 800,000, &c—Where there are more consonants than one, before nt, their value will be understood by the common rules of enumeration: the word Flint will represent nine millions five hundred thousand:—for the letter l united to nt, being a character for 500,000, the next higher number must be millions.—Burnt is Eight millions four hundred thousand: ​reprint is Forty-nine million, four hundred thousand:—Reprinted is the same sum, with the addition of the unit 6,—49,400,006. Reprint grammar, will make the figures 49,434,334;—here the word Grammar has the proper number of consonants that follow the four hundred thousand (marked by the rnt), without any intervening cyphers.

Learners must impress upon their minds, the properties they attach to such combinations, not to translate the letters nt as 21.—But it would, perhaps, be better, only to use them where a number of ciphers occur after a figure 'or figures; as 600,000 is very conveniently represented by the word Vent, or Dont; indeed, without some such arrangement, it could not be expressed, as their would be a very great difficulty in procuring the letters s or x, to follow the letter representing 6, in any kind of grammatical order. But in such a series of figures as the one already instanced, 49,434,334, the use of the nt may be avoided, by a sentence of this nature, repair a grammar, or Repay, rigour, megara.

The students need not hesitate to use nt as 21, in all the situations, where they know that hundred thousands cannot be applied.

It is sometimes necessary in figures to recollect fractions, whether attached to pounds, shillings, and pence, or to weights and measures; to have a character for this purpose, we must make free with our first scale, as in the recent instance of thousands, &c.

We select the letter g to be the seperatrix between the numerator and the denominator, to have no value in itself, but merely to be the sign of the fraction; the numerator being the consonant or consonants that immediately precede it, and the denominator that follow it.—Thus is ${\displaystyle \scriptstyle {\frac {2}{4}}}$ represented by the words Negro or Anger; n being 2 ​the g equivalent to the dividing line; and r the character for 4—Meagre or Maugre, will represent ⁠3/4⁠;—⁠5/7⁠ by Elegiac; by Bigpie;—⁠4/1000⁠ by Argueth, &c.

Where the numerator is 1, it need not be expressed, the letter g equally representing the fraction, and such unit only—thus ⁠1/2⁠ may be known by the words gun, gone, gain, &c.—⁠1/3⁠ by game—⁠1/4⁠ by geer or gore—⁠1/5⁠ by gale, ⁠1/10⁠ To by gates—⁠1/11⁠ by go quiet—⁠1/1000⁠ by gоth, &c. &c. I Here there will be no difficulty in recognizing the fractions; for as they are always the last figures in any sum, whenever we find a word, terminating our technical phrase, that has the letter & in it, followed by another letter, expressing the denominator; we know at once that Fractions are included, as in this sentence: Times are quite Meagre—there can be no difficulty in converting it into

Although we use g as the sign of fractions where they are wanting, we may still apply it in all cases, where there is no risk of confounding it; even in the same word or sentence, in which fractions are; for knowing that they can be expressed only once in a sentence, and that the word representing them must be the last, if a g be in that word, no danger of erring can arise—as in this example, 236..13..3½ may be written, In good = Time = I go = again.

In these various modifications to produce useful characters for hundreds, thousands, millions, and fractions, there may be a few objections started, in applying some words that are not reducible to the rules laid down; although the instances are very few that can be cited, it may be necessary to mention them.

We shall begin with the doubts that may arise with ​the letter S, in its double capacity; for although the writer conceives, that the application is sufficiently perfect in all its bearings; yet as objections have been made by some friends, who were satisfied with his explanations; he thinks it proper to notice them here, lest others should entertain similar opinions. How can the words, as, ass, and asses, be reconciled to represent 100? (their application is not doubted, where a consonant precedes them, for then they would be all ciphers). If the readers refer to page 53, they will find it clearly expressed, that the first word As, is 100; and if they read a little further, they will find that if another consonant be subjoined to a preceding s, that such word will still be for 100, and the second consonant will have its original value, as in the word Sat, being 101. If this be easily understood, there can be no difficulty in determining that the word Ass is 100, for the second S being a cipher, when preceded by a consonant, can neither add to nor diminish the former. If it were allowed that as the first word As, was a hundred, and that another cipher added to it, would make it a thousand, then the second s would have a superior value to the t in the word Sat, or n in the word Son, &c. which words are plainly enough understood to be 101 and 102.

The subsequent explanation, page 53, will shew that Asses, can express no more than 100; as the word Spice shews; which is 197.—Three consonants for three figures; and so far from its being a defect in the system, to have several words, to represent the same figure or figures, Mnemonicians will find, that however copious the English language may be, that the words are, if any thing, too few for the purposes, to which they may wish to apply them.

If the letter S had only two powers; to be used as a cypher, when preceded by a consonant; and when begin​ ning a word, to be a character for 1 in all situations, whether for tens, hundreds, thousands, or millions, it would be certainly more simple, but much less useful than the pre-sent arrangement, as a little practice will prove.

The junction of th, for one thousand is not so perfect; for there are a few words that do not come under the given rules; for it is observed in page 54, that th commencing a word, is one thousand and if followed by other consonants; They are to be enumerated in the regular mode, from the right hand to the left, in units and hundreds, as the word Thorough Exhibits, making 1432—Here it is evident that if more than three consonants follow th, the rule will not apply, as in the word Thoroughfare, which makes the figures 1,432,94, being two figures more than can come under the head of thousands, if th be allowed to hold the same rank throughout. But here the students are desired to recollect, that in their application of this system, they have always the choice of their own words; and when one occurs that cannot be employed easily, they may reject it and take another, of which they have no doubt; that as figures are not intended to represent words, but words to represent figures; they have themselves the selection, and of course, would not use one that might confuse them.—Further, that although th was intended to be applied as a character for 1000, Yet it was principally devised for thousand, to which no objection can be found; for its value cannot be injured by any number of consonants preceding it, as it may be extended to millions or billions, and yet retain its proper character, as this word will shew, Dreadful Oath, which is in figures, 64,695,000, sixty-four million, six hundred and ninety-five thousand.

But that their may be no words in the language, unapplied, if desired; this arrangement will be found effec​tual. When th is followed by more than three consonants, it shall lose its character of One thousand and be considered a 1;—thus Thoroughfare will represent 143,294, one hundred and forty-three thousand, two hundred and ninety-four this rule will be found easy and effectual. One doubt more may arise in the word Thither, in which th occurs twice; this can be remedied by making the second, hold its character of thousand, but the former th to be a 1 and 2—it will become by this mode, 12,004: Thrash, by the same rule, 124,000. But these exceptions may be left aside without any inconvenience; nor can they be urged as a cause for abandoning th, which is found to be so generally useful.

The objections to Y may be in those words, which begin and end with it; but they can be overcome, by considering in all such cases, the final Y as a vowel. As Yearly may be viewed as if the y were an i, Yearli, which would therefore be one million and forty-five: Yeomanry, one million, three hundred and twenty-four.