side express parts in tenths; the figure on the left side ascending in value according to its distance from the dot, and those on the right side diminishing in value according to their distance. Thus in the expressions just repeated, 5,5 means 5 things and five-tenths, as 5 pounds and five-tenth parts of a pound; and the other 53,75, means 53 pounds, and 75 hundredth parts of a pound. The 5 in one remove being five-tenths, and the 5 in two removes being but five hundredths. So that in reading if you come to such a passage as 7,2 pounds, instead of saying 7 and I know not what, it should be read seven pounds and two tenths; or 291,36 it should be read two hundred and ninety one pounds, and thirty-six hundredths; or if it be 270,036, it should be read two hundred and seventy, and thirty-six thousandths. This is called DECIMAL NOTATION, and it may be easily practised, for most of its operations are exactly like those in whole numbers, and hence its convenience and universal use. There is another mode of fractional expression, thus, as or or thus, beginning at the top, called the numerator, and ending with the bottom, called the denominator, we read two-thirds, threefourths, or twenty-three seventy-fourths; but as most fractions of this kind are convertible into decimals, and then more easily worked, so these expressions are called VULGAR FRACTIONS, the decimal form being at once more refined and convenient.

23

74

I am not however intending to give you a formal treatise on arithmetic, but I am relating what you ought to know, and what masters too often omit to explain, because they think our sex unable to understand those things which they teach so fully to boys. We ought at least to be acquainted with the nature of expressions which we meet with in every sensible book, and to be able to read them aloud, without blushing for our ignorance.

*

LETTER XXIX.

Practice of Arithmetic.

MY DEAR CHILDREN,

I hope you will be reconciled to my observations about Arithmetic, by my assurances of its utility, and even pleasantness, when duly pursued. I am not prepared to supercede your master, or your Joyce or Walkingame, though I will indulge in a few other observations before I dismiss the subject. Arithmeticians make a great display of rules and business; but in truth, it is a very simple art, the whole of it being limited to four operarations, ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION; all the rest being an application of these, in concert with a moderate degree of industry and

COMMON SENSE.

The first point is to become perfect, dodgingly perfect, in the multiplication table; and after being mistress, up to 12 times 12, then to proceed as high as 20 times 20; and be as ready as in striking the keys of your piano-forte. This being accomplished, and thoroughly accomplished, you will be able to compute any thing, simply by the aid of your own attention to the question. Some tables of weights, measures, and monies, should also be learnt completely; and you should be ready at compound multiplication, because it is the ready means of checking your tradesmen's bills, and keeping your domestic

accounts.

The rule of three, or proportion, is a pleasing me thod of exercising the faculties in little problems, but it is absurd when either of the terms are 1, because in that case, it is in truth but a sum in multiplication or division. Interest at 5 per cent is rea dily computed, because 100s. per 1007. is a shilling or 12 pence per pound per annum, and of course, an even penny per pound per month.

For young ladies, the rules for permutations, com

binations, and chances, are always worth pursuing, and they are easy and highly diverting, while they are often applicable in real life, and in card parties may enable you to save your money.

Allow me, while on this subject, to direct your attention to certain marks used in arithmetic for brevity. You ought to write them out, and be mistress of them, as they constantly occur in books. They are as follow: + for more, or add ;- for less or subtract; x for multiply; + for divide; and = for equal to. There are but five; they may be learnt in five minutes, and yet how often have I seen them confuse well-educated persons.

You ought, however, to know that the genius of man has not limited these pursuits to figures; for there is an abstract arithmetic, called ALGEBRA, in which letters are used for any numbers at pleasure, known or unknown; and then by uniting them with the above characters, and reasoning upon their additions, subtractions, multiplications, divisions, transpositions, &c. we arrive at rapid results on the most difficult problems. Many ladies have arrived at great excellence in this art; but it is very seductive, and employs more time than is compatible with domestic duties. I have known some elegant women, who have declared, that they could better amuse themselves over an algebraic problem, than at a play, a concert, or a ball, and who say, that they prefer their Ladies' Diary, or their volume of Nicholson, even to a novel or a volume of poetry.

Akin to Algebra is GEOMETRY and without any immediate connexion, the one is commonly a step to the other. I am no geometrician, but I confess, I did once read the first six books of Euclid, and a delightful study it is for long winter evenings. At the same time, as I drew all the diagrams, I learnt the use of a set of mathematical instruments, and I can assure you, I never derived more profit from any exercise whatever. It improved my drawing generally, and gave a precision to my ideas on many sub

jects, which I never could otherwise have possessed. If you would be mistress of perspective, or draw in architecture, then the use of a case of instruments, and an acquaintance with practical geometry, are indispensable preliminaries.

LETTER XXX.

Writing and Letter-writing.

MY DEAR CHILDren,

In connexion with arithmetic I may mention writing, chiefly because the same master usually teaches both; at least writing in its operative sense, an art which, as depending on a good pen, I advise you to learn to mend and make. I have sometimes thought that those gentlemen endeavour to add to their own importance by neglecting to teach pen-making, and thereby create in us a dependence on them. For my part, I set up for myself early in life, and in mending my own pen I have never been the humble servant of our writing master. Every woman who can thread her needle ought to be able to make and mend her own pen, that she may write with clearness and pleasure, and with that easy flow which is lady-like, and not in the stiff characters used by young women educated in charity schools.

The art of writing extends, however, much higher in its objects than the form of the character. It is the means of expressing our thoughts, and this is its true end. It connects us with our absent and distant friends, and in many cases enables us to converse even with remote posterity. To effect these objects, however, several arts, and some degree of perfection in them, are essential. We must spell well, or write words in their usual letters. We must understand the accidence and syntax of our language, and prove it by avoiding errors. We must

reason with our pen in our hand just as we reason in our ordinary intercourse, and illustrate our arguments by experience and knowledge.

Blair's simple models supplied a deficiency in this branch of education, for since this book appeared, it has enabled myself and others to make all our pupils ready letter-writers. In teaching this art it is infallible, and for several years we have, by using it systematically, never had a bad letter-writer. Of the various branches of composition, women excel specially in letter-writing, and perhaps the best specimens in existence are those of Madame de Sevigné, Lady Mary Wortley Montagu, and Miss Seward. All the published letters of men, even those of Cowper and Hayley, are inferior in ease and grace to the letters of those ladies, and many other women who could be named.

In studying composition, if you proceed beyond Blair's or Murray's grammars, the shortest course is Irving's, and it ought to be read. If more is desired, then the elegant lectures of Hugh Blair furnish sufficient knowledge to make a finished critic. I have often lamented that no convenient abridgement of this superior work has been adapted to the use of schools, and for want of one I long ago felt the necessity of making one myself, and the M. S. has, as you know, been twice worn out by my senior pupils. Such a volume, or even a couple, carefully abridged, from Blair, with a view to practical instruction, and enriched by a chapter or two from Rollin, two or three from La Harpe, and two or three from Johnson, Knox, Aikin, and Barbauld, would be an invaluable treasure in British schools of both sexes.

Speaking practically on composition, its beauty depends on the mind and knowledge of the writer. If you think soundly and possess much information, either from reading or from intercourse with the world, you can scarcely fail to write with interest. If the pen fail to express what the mind thinks, the