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waterford. John Binns, o Wallace, Richard Allen, master John Graham, . A John James Sargent, % Friends' School, Benjamin Goouch, Alderman Watson, ewtown, 24 copies. Richard Davis, Thomas Taverner, Richard Farrell, 12 do. Nugent O'Reiley, Thomas Newsom. .. Samuel White, 3 do. William & Rich. Jacob G. N. Russel,

William Goouch, 3 do. Peter White, James Seyward,
James D. Morris, 2 do. George Ridgeway, Thomas Mark,
Henry Ridgeway, 2 do. Alexander Boyd, James Kelly
John’Grenam.” Mo William Sherman, George W. Todd. . .
Nicholas Walsh, S.M. William Hellier, Doctor Wm. Campion
Peter D Bourke, RCS. Terry Clarke, Rev. M. Keating,
John Griffith, William Cherry, Matthew J. Moore,
Michael O'Connel, Philip Barron, Esq. William Piercey,
Henry Penrose, Robert Hull, out, Samuel Phelps
Nicholas Power, Shannon Peet, H. B. Fitzgerald
Samuel Woods, Edward Joshua Peet, John Rochford,
William Ridgeway, Rachel Barnes, William Gill,
Anthony Jackson, Matthew Jones, James Morgan,
Thomas Doyle. John Smith, Lecturer, William Erson,

William Edwards, J. Foley, Lecturer, &c. Mary Unthank,
Isaac T. Jacob, 2 do. J. O'Neal, 12 copies. John_&_W. Hill,
William Palmer. Matthew Murphy. H. M. Robinson,
Joseph & Thos. Waring - John A. Doughlas,
Josiah Pope LIMERICK. John W. Owens.
Benjamin Moore, jun, Luke Bernard, 12copies Thomas Tracy,
Thomas M*Chene, Edward Bernard, fido. Doctor Hargrove,
Thomas Hutchinson, Joseph M *}”. J. J. Jones,

Thomas Goouch, - and Sons, Charles O'Hara,
Micheal Laffan George M*Kern, 2do. Thomas Devitt,
Benjamin Moore, sen. Thomas Abbott, Lt. Charles Still,
John Bull, • George Unthank, M. Fitt,
Joseph Pike, jun. • Joshua Mark, John Piercy,
Joseph Denny, James Fisher, jun. Philip M.Ardell,
Catharine Walsh, -John Glinden, Capt. J. H. Fitzgerald,
John Morrison, Joseph O'Sullivan, Alderm, R. Westropp, ,
John Barden, Thomas P Vokes, Henry Ormsby, o
o Myers, Henry Longworth, William Giddis,
James E. White, Mrs. Sargent, William Evans,
John Strangman, Sir C Marrat, Joseph Fisher,
Matthew Hanrick, D. F. G. Mahony. Heury Watson, Mayer
Joshua Jacob, William Taylor, Sheriff Piercy Young,
Abraham Henderson, B. C. Fisher, Doctor Raleigh,
John Watson, Samuel Alexander, Doctor Geary,
Robert Watson, William Magrath, Darby O'Grady,
Thomas White, Robert Reeves. Thomas O'Brien,
Joseph Strangman, jun William B. Kelly, John Unthank, M. D.
Joseph Straugman, sen G. T. Hill, Robinson Unthank,
Francis Moore, Henrietta Fitzgerald, Thomas Ormsby.

James Shaw, Jonas Morris, Joshua Hill,

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James Hill
James Han #
Rev. Wm. H. Fitzgerald
William Worrals,
Michael Walsh, Atty.
William Small, N. P.
William Shannen,
Joseph Seymour,
T. Vereker,
F. J. O’Neale,
James. O'Neale
Jamnes-Fisher, Joseph.
#. Shannon,
ames F. Carroll,
William Roe,
R. G. Maunsell,
Samuel Bindon,
Edward Parker
Samuel Evans.
John Morgan,
William D. Hoare,
John Shine
James T. Fogarty,
John M*Donnel.
John Tuthill, Esq.
Paul Erson,
John T. Baylee,
Rev. James Martin,
Bolton Waller Col. . .
H. I. Poe
i; M.Mahon
Thomas K. Kidd,
Timothy Buntin,
Robert "Currie,
Patrick Cussen,
John Abell,
Thomas Walker,
George Vincent,
W. S. Martin,
Joseph Delany,
Andrew James Watson,
Captain Hickie,
John. Mullock,
William Waller, P.C.,
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William Martin,
James Dodd,
John Dodd,
John Russé,
William M*Intosh,
John Armstrong,
Richard Mera,
William Finney,
Charles Beale,
James O’Duggan,
Joshua Carroll,
Paul Abbott,
William Abbott,
Samuel Barrett,
Frederick Miller,
G. R. Penrose,
John Newsom,
Penis Newsom,
Thomas Martiu
Jacob Mark,
Elizabeth Pike,
John Fennell,
Eben Pike,
Nicholas. Howell,
William Lecky,
Thomas Lecky,
Thomas Bennett,
Reuben Harvey,
Reuben Deaves,

Samuel N. Penrose,

Richard Bradford, William Harvey,

Eugene Finnerty,

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COUNTY KILDARE.
James. White, -
James Forbes, 2 copies.
George Newsom,
Joseph Phelps Newsom,
George Hanks,
Samuel Hanks,
George Shackleton

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William Harvey, Wm. Joseph Williams,

Daniel Mahony. Paul Abbott, jun.

To adapt this work to the capacities of children, endeavours have been made to give the rules, questions and illustrations in as plain a manner as the subject would admit of, and to exhibit the initiatory rules of the science, in a form much more copious than other writers have thought necessary to adopt, while some of the rules which have engaged their attention are slightly, and others not at all noticed. This has been done with the view of supplying a sufficient number of examples in the fundamental rules of Arithmetic, which are commonly taught by questions and exercises set by the teacher; and in general it is not customary to put a regular treatise into the hands of the pupil, until he is in some degree acquainted with them, which might chiefly arise from the want of a treatise in which those rules were sufficiently diffuse, and at the same time so plaim as to be understood by children. The author of the work now submitted to the public, being himself for some years a teacher, found, in common with many others, this method of setting the questions in the first rules, to be attended with much loss of time, both to himself and his pupils, to remedy which he wrote out such rules and questions as he found adapted to his purpose, which he has altered from time to time as occasion served, and hopes such a set of rules and questions are now presented, as will eontribute to the ease of the teacher and improvement of the pupil. He has mostly confined himself to such matter as commonly occurs to merchants, traders, and others in a more humble. sphere of life; and while it has been his principal object to render this work particularly useful to them, he has also been careful to introduce such subjects and information as will be necessary to prepare the pupil for pursuing with advantage studies of a more advanced nature, at the same time avoiding whatever was foreign to pure Arithmetic. He has reduced the science to

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the rules of Numeration, Addition, Subtraction, Multiplication and Division whole, compound and fractional; Rule of Proportion, Practice, Tare and Tret, Rates per Cent, Interest, Discount, Equation of Payments, Exchange, Unlimited Quantities, Duodecimals, Positions and Square, and Cube Roots; by which all or most of the questions, hitherto proposed in books of arithmetic may be solved, and all that is necessary. for common transactions or for mercantile practice. He has omitted Logarithms, Progressions, and what are called the uses of Square and Cube Roots, which in his opinion more properly belong to higher mathematical science, than to a system of arithmetic. . Some may object that, Tare and Tret, Rates per Cent, Discount, Equation of Payments, and Exchange might have been included in the Rule of Proportion, and that they are only particular applications of that rule, or of Practice, which is only a contracted mode of performing it; in a mathematical point of view he grants they are nothing more, yet, as branches of useful learning, he found they could not be so well introduced in it, as there are particular directions to be given, and observations to be made relative to each. This objection not being applicable to Barter, Fellowship, or Loss and Gain, they are not given under separate heads, but such parts of them as are really useful are included in the Rule of Proportion. . Fractions, vulgar and decimal have been introduced immediately after Division, which obviates the necessity of two or three times repeating the Rule of Three ; to this arrangement, some may object that children in this stage of science fire generally too young to comprehend Fractions, but to those the author respectfully replies let them make trial before they hastily condemn; in every instance he has had an opportunity of noticing, both in his own practice, and upwards of eight years spent in respectable seminaries, he always found that children thus taught made a mush quicker and more certain progress than those who were instructed in the usual manner, and it must be evident to those who are masters of arithmetic, that

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