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x is the sign of multiplication; as cx d means the product of c and d. is the sign of division; as c÷d signifies the quotient of c and d. = is the sign of equality; thus c + de means the sum of c and d equals e.

is the sign of the square root; thus

denotes the square root

of x. is the sign of the cube root, and generally any root of a quantity may be denoted by this sign, with the index of the root placed over it; thus signifies the cube root, the biquadrate root, &c.; but they may likewise be represented by the reciprocals of these indices; as x, x}, implying the square and cube roots of x.

A vinculum is a line drawn over several quantities, and means that they are taken together, as ax + b signifies the square root of a x and b.-Phillips's Compendium of Algebra. 12mo. 1824.


ALPHABET. A perfect alphabet of the English language, and, indeed, of every other language, would contain a number of letters, precisely equal to the number of simple articulate sounds belonging to the language. Every simple sound would have its distinct character; and that character be the representative of no other sound. But this is far from being the state of the English alphabet. It has more original sounds than distinct significant letters; and, consequently, some of these letters are made to represent, not one sound alone, but several sounds. This will appear by reflecting, that the sounds signified by the united letters th, sh, ng, are elementary, and have no single appropriate characters, in our alphabet; and the letters a and u represent the different sounds heard in hat, hate, hall; and but, bull, mute.

The letters of the English language, called the English Alphabet, are twenty-six in number.-Murray.

The following is a list of the Roman, Italic, and Old English Characters, being those used at the present day in England. The Roman and Italic are also used by most of the European nations.

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For the characters of the different languages, see their respective names, ARABIC, &c.

Tacquet, an able mathematician, in his Arithmeticiæ Theor., Amst. 1704, states, that the various combinations of the twenty-four letters (without any repetition) will amount to


Thus it is evident, that twenty-four letters will admit of an infinity of

combinations and arrangements, sufficient to represent not only all the conceptions of the mind, but all words in all languages whatever.

Clavius the Jesuit, who also computes these combinations, makes them to be only 5,852,616,738,497,664,000.

As there are more sounds in some languages than in others, it follows of course that the number of elementary characters, or letters, must vary in the alphabets of different languages. The Hebrew, Samaritan, and Syriac alphabets, have twenty-two letters; the Arabic, twenty-eight; the Persic, and Egyptian or Coptic, thirty-two; the present Russian, fortyone; the Shanscrit, fifty; the Cashmirian and Malabaric are still more numerous. Astle.

ALTERATION OF MARGIN. In works that are published in different sizes, this is the changing of the margin from the small paper to the large paper edition, when at press.

After the margin for the small paper copies is finally made, the additional width of the gutters, the backs, and the heads, is ascertained in the same manner, by folding a sheet of the large paper, that it was in the first instance. The additional pieces for the change should, if possible, be in one piece for each part. See MARGIN.

Folios, quartos, and octavos, are the sizes most usually printed with an alteration of margin; duodecimos are sometimes, but rarely; of smaller sizes I never knew an instance.

The alteration of margin requires care, for it occasionally happens that the sheet is imposed with the wrong furniture; and where it happens to be in one form only, and that form is first laid on, it sometimes passes undiscovered till a revise of the second form is pulled, when the error is detected, but too late to rectify it; the consequence must be, to cancel a part of the sheet, or to print the reiteration with the margin also wrong; nay, sometimes both forms are worked off with the furniture wrong, without being perceived till the compositor comes to distribute, particularly when they are printed at different presses. Such errors destroy the uniformity of the book, and spoil its appearance.

These mistakes can only be avoided by care and attention on the part of the compositor, the reader, and the pressman; but I would recommend that the furniture for the alteration should be cut of different lengths from the furniture of the small paper: in octavos the gutters and backs should be the exact length of the page, and be always imposed within the sidestick; and the head should be the width of the two pages and the gutter, and be imposed within the footstick. This method of cutting the furniture of precise lengths for the alteration, and locking it up within the side and foot sticks, will not only distinguish it from the rest of the furniture, and from the pieces that may be put in for the convenience of quoining the form, but will also preserve it from being injured by the mallet and shooting stick, in locking up, and by the indention of the quoins.

The same principle, of cutting the alteration to precise lengths, and locking it up within the side and foot sticks, will hold good in all other sizes, where it is required: in quartos, the pieces must be cut to the length and width of the page; and in folios to the length of the page only, as the margin of the head is regulated at the press.

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ANCIENT CUSTOMS. The following Customs used in Printing Offices in former times are extracted from Moxon's Mechanick Exercises, published in 1683, the first practical work that appeared on the Art of Printing. I insert them because I think it interesting to trace the old Customs, that were established by printers to preserve Order among

themselves; and to show the changes that have taken place since that period. The insertion of them in this place will also tend to preserve them, as the original work is now very scarce, and this department of it has been superseded by subsequent publications, which however, with the exception of Mr. Hansard's work, have not copied these Customs.

"Ancient Customs used in a Printing-house.

"Every Printing-house is by the Custom of Time out of mind, called a Chappel; and all the Workmen that belong to it are Members of the Chappel: and the Oldest Freeman is Father of the Chappel. I suppose the stile was originally conferred upon it by the courtesie of some great Churchman, or men, (doubtless when Chappels were in more veneration than of late years they have been here in England) who for the Books of Divinity that proceeded from a Printing-house, gave it the Reverend Title of Chappel.

"There have been formerly Customs and By-Laws made and intended for the well and good Government of the Chappel, and for the more Civil and orderly deportment of all its Members while in the Chappel; and the Penalty for the breach of any of these Laws and Customs is in Printers Language called a Solace.

"And the Judges of these Solaces, and other Controversies relating to the Chappel or any of its Members, was plurality of Votes in the Chappel. It being asserted as a Maxim, That the Chappel cannot Err. But when any Controversie is thus decided, it always ends in the Good of the Chappel.

"1. Swearing in the Chappel, a Solace.

"2. Fighting in the Chappel, a Solace.

"3. Abusive Language, or giving the Ly in the Chappel, a Solace.

"4. To be Drunk in the Chappel, a Solace.

"5. For any of the Workmen to leave his Candle burning at Night, a Solace. "6. If the Compositer let fall his Composing-stick, and another take it up, a Solace. "7. Three Letters and a Space to lye under the Compositers Case, a Solace. "8. If a Press-man let fall his Ball or Balls, and another take it up, a Solace. "9. If a Press-man leave his Blankets in the Tympan at Noon or Night, a Solace. "These Solaces were to be bought off, for the good of the Chappel: Nor were the price of these Solaces alike: For some were 12d. 6d. 4d. 2d. Id. ob. according to the nature and quality of the Solace.

"But if the Delinquent prov'd Obstinate or Refractory, and would not pay his Solace at the Price of the Chappel, they Solac'd him.

"The manner of Solacing, thus.

"The Workmen take him by force, and lay him on his Belly athwart the Correctingstone, and held him there while another of the Work-men with a Paper-board, gave him 101. and a Purse, viz. Eleven blows on his Buttocks; which he laid on according to his own mercy. For Tradition tells us, that about 50 years ago one was Solaced with so much violence, that he presently Pd Blood; and shortly after dyed of it. "These nine Solaces were all the Solaces usually and generally accepted: yet in some particular Chappels the Work-men did by consent make other Solaces, viz.

"That it should be a Solace for any of the Workmen to mention Joyning their Penny or more apiece to send for Drink.

"To mention spending Chappel-money till Saturday night, or any other before agreed


"To Play at Quadrats, or excite any of the Chappel to Play at Quadrats; either for Money or Drink.

"This Solace is generally purchas'd by the Master-Printer; as well because it hinders the Workmens work, as because it Batters and spoils the Quadrats: For the manner how they Play with them is Thus: They take five or seven more m Quadrats (generally of the English Body) and holding their Hand below the Surface of the Correcting Stone, shake them in their Hand, and toss them upon the Stone, and then count how many Nicks upwards each man throws in three times, or any other number of times agreed on: And he that throws most Wins the Bett of all the rest, and stands out free, till the rest have try'd who throws fewest Nicks upwards in so many throws; for all the rest are free: and he pays the Bett.

"For any to Take up a Sheet, if he receiv'd Copy-money; Or if he receiv'd no Copymoney, and did Take up a Sheet, and carryed that Sheet or Sheets off the PrintingHouse till the whole Book was Printed off and Publisht.

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Any of the Workmen may purchase a Solace for any trivial matter, if the rest of the Chappel consent to it. As if any of the Workmen Sing in the Chappel; he that is

offended at it may, with the Chappels Consent purchase a penny or two penny Solace for any Workmans singing after the Solace is made; Or if a Workman or a Stranger salute a Woman in the Chappel, after the making of the Solace, it is a Solace of such a Value as is agreed on.

"The price of all Solaces to be purchased is wholly Arbitrary in the Chappel. And a Penny Solace may perhaps cost the Purchaser Six Pence, Twelve Pence, or more for the Good of the Chappel.

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"Yet sometimes Solaces may cost double the Purchase or more. As if some Compositer have (to affront a Press-man) put a Wisp of Hay in the Press-man's Ball-Racks If the Press-man cannot well brook this affront, he will lay six Pence down on the Correcting Stone to purchase a Solace of twelve pence upon him that did it; and the Chappel cannot in Justice refuse to grant it: because it tends to the Good of the Chappel: And being granted, it becomes every Members duty to make what discovery he can because it tends to the farther Good of the Chappel: And by this means it seldom happens but the Agressor is found out.

"Nor did Solaces reach only the Members of the Chappel, but also Strangers that came into the Chappel, and offered affronts or indignities to the Chappel, or any of its Members; the Chappel would determine it a Solace. Example,

"It was a Solace for any to come to the King's Printing-house and ask for a Ballad. "For any to come and enquire of a Compositer, whether he had News of such a Galley at Sea.

"For any to bring a Wisp of Hay, directed to any of the Press-men.

"And such Strangers were commonly sent by some who knew the Customs of the Chappel, and had a mind to put a Trick upon the Stranger.

"Other Customs were used in the Chappel, which were not Solaces, viz. Every new Workman to pay half a Crown; which is called his Benvenue: This Benvenue being so constant a Custome is still lookt upon by all Workmen as the undoubted Right of the Chappel, and therefore never disputed; yet he who has not paid his Benvenue is no Member of the Chappel nor enjoys any benefit of Chappel-Money.

"If a Journey-man Wrought formerly upon the same Printing House, and comes again to Work on it, pays but half a Benvenue.

"If a Journey-man Smout more or less on another Printing-House and any of the Chappel can prove it, he pays half a Benvenue.

"I told you before that abusive Language or giving the Lye was a Solace: But if in discourse, when any of the Workmen affirm any thing that is not believed, the Compositer knocks with the back corner of his Composing-stick against the lower Ledge of his Lower Case, and the Press-man knocks the handles of his Ball-stocks together: Thereby signifying the discredit they give to his Story.

"It is now customary that Journey-men are paid for all Church Holy days that fall not on a Sunday, Whether they Work or no: And they are by Contract with the Master Printer paid proportionably for what they undertake to Earn every Working day, be it half a Crown, two Shillings, three Shillings, four Shillings, &c.


It is also customary for all the Journey-men to make every Year new Paper Windows, whether the old will serve again or no; Because that day they make them, the Master Printer gives them a Way-goose; that is, he makes them a good Feast, and not only entertains them at his own House, but besides, gives them Money to spend at the Ale-house or Tavern at Night; And to this Feast they invite the Correcter, Founder, Smith, Joyner, and Inck-maker, who all of them severally (except the Correcter in his own Civility) open their Purse-strings and add their Benevolence (which Workmen account their duty, because they generally chuse these Workmen) to the Master Printers: But from the Correcter they expect nothing, because the Master Printer chusing him, the Workmen can do him no kindness.

"These Way-gooses, are always kept about Bartholemew-tide.

And till the Master

Printer have given this Way-goose, the journey-men do not use to work by Candle Light.

"If a Journey-man marry, he pays half a Crown to the Chappel.

"When his Wife comes to the Chappel, she pays six Pence: and then all the Journeymen joyn their two Pence apiece to Welcome her.

"If a Journeyman have a Son born, he pays one Shilling.

"If a Daughter born, six Pence.

"The Father of the Chappel drinks first of Chapel Drink, except some other Journeyman have a Token; viz. Some agreed piece of Coin or Mettle markt by consent of the Chappel for then producing that Tohen, he Drinks first. This Token is always given to him who in the Round should have Drank, had the last Chappel-drink held out. Therefore when Chuppel-drink comes in, they generally say, Who has the Token?


"Though these Customs are no Solaces; yet the Chappel Excommunicates the Delinquent; and he shall have no benefit of Chappel-money till he have paid. "It is also customary in some Printing-houses that if the Compositer or Press-man make either the other stand still through the neglect of their contracted Task, that then he who neglected, shall pay him that stands still as much as if he had Wrought.

"The Compositers are Jocosely called Galley Slaves: Because allusively they are as it were bound to their Gallies.

"And the Press-men are Jocosely called Horses: Because of the hard Labour they go through all day long.

"An Apprentice when he is Bound pays half a Crown to the Chappel, and when he is made Free, another half Crown to the Chappel; but is yet no Member of the Chappel; And if he continue to Work Journey-work in the same House, he pays another half Crown, and is then a Member of the Chappel.

"The Printers of London, Masters and Journey-men, have every Year a general This Feast, which since the re-building of Stationers Hall is commonly kept there. Feast is made by four Stewards, viz. two Masters and two Journey-men; which Stewards, with the Collection of half a Crown apiece of every Guest, defray the Charges of the whole Feast; And as they collect the Half-Crowns, they deliver every Guest a Ticket, wherein is specified the Time and Place they are to meet at, and the Church they are to go to: To which Ticket is affixed the Names and Seals of each Steward.

"It is commonly kept on or about May-day: When, about ten a Clock in the Morning they meet at Stationers Hall, and from thence go to some Church thereabouts; Four Whifflers (as Servitures) by two and two walking before with White Staves in their Hands, and Red and Blew Ribbons hung Belt-wise upon their left Shoulders. Those go before to make way for the Company. Then walks the Beadle of the Company of Stationers, with the Company's Staff in his Hand, and Ribbons as the Whifflers, and after him the Divine (whom the Stewards before ingag'd to Preach them a Sermon) and his' Reader. Then the Stewards walk by two and two, with long White Wands in their Hands, and all the rest of the Company follows, till they enter the Church.

"Then Divine Service begins, Anthems are Sung, and a Sermon Preached to suit the Solemnity: Which ended, they in the same order walk back again to Stationers Hall; where they are immediately entertain'd with the City Weights and other Musick: And as every Guest enters, he delivers his Ticket (which gives him Admittance) to a Person appointed by the Stewards to receive it.

"The Master, Wardens and other Grandees of the Company (although perhaps no Printers) are yet commonly invited, and take their Seats at the upper Table, and the The Tables being furnish'd with rest of the Company where it pleases them best. variety of Dishes of the best Cheer: And to make the entertainment more splendid is usher'd in with Loud Musick. And after Grace is said (commonly by the Minister that Preach'd the Sermon) every one Feasts himself with what he likes Best; whiles the Whifflers and other Officers Wait with Napkins, Plates, Beer, Ale, and Wine, of all And to make their Cheer sorts, to accommodate each Guest according to his desire.

go cheerfuller down, are entertained with Musick and Songs all Dinner time. "Dinner being near ended, the Kings and the Dukes Healths is begun, by the several Stewards at the several Tables, and goes orderly round to all the Guests.

"And whiles these Healths are Drinking, each Steward sets a Plate on each Table, beginning at the upper end, and conveying it downwards, to Collect the Benevolence And at the same of Charitable minds towards the relief of Printers Poor Widows. time each Steward distributes a Catalogue of such Printers as have held Stewards ever since the Feast was first kept, viz. from the Year of Christ 1621.

"After Dinner, and Grace said, the Ceremony of Electing new Stewards for the next Year begins: Therefore the present Stewards withdraw into another Room: And put Garlands of Green Lawrel, or of Box on their Heads, and White-wands in their Hands, and are again Usher'd out of the withdrawing Room by the Beadle of the Company, with the Companys Staff in his Hand, and with Musick sounding before them: Then follows one of the Whifflers with a great Bowl of White-wine and Sugar in his Right Hand, and his Whifflers Staff in his Left: Then follows the Eldest Steward, and then another Whiffler, as the first, with a Bowl of White-wine and Sugar before the second Steward, and in like manner another Whiffler before the Third, and another before the Fourth. And thus they walk with Musick sounding before them three times round the Hall: And in a fourth round the first Steward takes the Bowl of his Whiffler and Drinks to one (whom before he resolved on) by the Title of Mr. Steward Elect: And At taking the Garland off his own Head puts it upon the Steward Elects Head. which Ceremony the Spectators clap their Hands, and such as stand on the Tables or Benches, so Drum with their Feet that the whole Hall is filled with Noise, as applauding the Choice. Then the present Steward takes out the Steward Elect, giving

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