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"ENTERED according to Act of Congress in the year 1831,

by THOMAS W. CONKLING, in the Clerk's office of the District Court of the Southern District of New-York.

Fr the Rev. Wm. Belden, a classical teacher in the city of New-York. New-York, January 17th, 1831.

1 AR SIR,-I have examined the manuscript copy of your new Arithmetic, with as much attention as my numerous engagements would admit; and have no hesitation in saying, that it appears to me decidedly superior to every other system with which I am acquainted, in rendering the science both pleasant and easy to learners, especially those of an early age. The method which you have pursued in developing the principle and the general process under each rule, is such, that with due attention, the learner will be able to pursue this important science understandingly, with little, or no assistance from his teacher. In this respect, the work will be found a valuable acquisition, not only to learners, but to teachers also; by relieving them of much labour in the way of explanation, and enabling them to devote more of their time and attention to other duties of the school. That you will meet with merited success in this publication, is the ardent wish of,

Mr. Thomas W. Conkling.

Sir, your obedient servant,
WILLIAM BELDEN.

From Mr. S. Hammond, teacher of Public School, No. 4. and from Mr. George Everitt, teacher of Public School, No. 12.

Mr. Conkling, New-York, 2d Feb. 1831. DEAR SIR,-Agreeably to your request, we have given the manuscript copy of your Arithmetic, as attentive a perusal as the hurry of business and occasional interruptions would permit; and do not hesitate to express a favorable opinion of the performance, especially for beginners, and those who may be under the necessity of resorting to self-instruction, in that useful branch. We wish you much success in its publication. GEORGE EVERITT, S. HAMMOND.

From Aaron M. Merchant, Esq. late principal of Union Hall Academy, author of the "American School Grammar," &c.

Mr. T. W. Conkling,

New-York, Feb. 15, 1831. SIR,-I have examined your new Arithmetic in manuscript, with as much care as the limits of my leisure would allow. Your plan of arrangement is certainly good, the illustrations simple, and well calculated to arrest the attention, and facilitate the progress of learners; and the tables, to say the least, are ingenious. I think your arrangement an improvement upon every other that has fallen under my observation. There is ano

ther merit which your Arithmetic has, which is certainly a
desideratum. It is not a patchwork of those numerous publica-
tions, which have been turned out of the hands of compositors
upon the world, since the days of Dilworth: so far as I have
seen, its questions to exercise the mind of the student, are origi-
nal. We
ere I, as I have been, engaged in the instruction of
youth, I should feel it my duty to introduce your Arithmetic,
not to the exclusion of others, but in connexion with them, for in
so doing, I am confident it would save me much labour in writing
new exercises. I sincerely hope that you may receive ample
reward for your labour, in preparing it for the press.

Respectfully, I have the honour to be yours, &c.
A. M. MERCHANT.

From Mr. Jared B. Peck, teacher of a select English School.
Mr. Thomas W. Conkling,

SIR, I have partially perused the MS. of your "Young Arithmetician's Guide," &c. and was much pleased to see each compound rule immediately preceded by its appropriate table, which I consider important. Your examples for illustration are also well calculated to impress the principles of the rules upon the scholar's mind, and cause him to think for himself, without which," the young arithmetician" will never become a practical one. Wishing you success in your attempt to benefit the young student in a very important branch of education, I shall introduce your Arithmetic into my school as soon as published. Respectfully, your friend,

New-York, April 2, 1831.

J. B. PECK.

From Mr. Joseph McKeen and Mr. T. Whitlock, principals in Union Hall Academy.

Mr. T. W. Conkling,

SIR,-We have examined the Arithmetic which you propose to publish, and are of opinion that it is in some respects preferable to any in use. Without pretending to have made any new discoveries in the science of numbers, you appear to have followed the models that have the sanction of public approbation. The blanks, which you have left in your directions for an operation, requiring the learner to determine, from the nature of the question, what elementary rule must be applied, are calculated to develope the reasoning faculties; and it appears to have been your aim, to elicit thought. Many very able scientific writers. on this subject, have been less successful in this particular. We have no doubt but your book will come into honourable rivalry swith the best in use. JOSEPH McKEEN, T. WHITLOCK.

on Hall Academy,}

From the Rev. Thomas McAuley, D.D. L.L.D. late professor of Mathematics in Union College.

Mr. Thomas W. Conkling, Philadelphia, July 19, 1831. DEAR SIR,-I have read with great pleasure, your interesting Elements of Arithmetic, and am fully of the opinion that it will be a very profitable book for the use of those who are beginning that interesting branch of science, a branch which every child should be made familiar with. I think there is a charming simplicity, and natural order, and harmony, maintained through the whole treatise, which could not have been obtained otherwise than from your long experience in teaching, and your good sense in observing; and which cannot fail to secure the approbation of all who are in the habit of instructing children, as soon as they become acquainted with it. I think your book will help both the teacher and the pupil, and make the labour light and pleasant. I would have been pleased to have seen more examples for practice appended.

I am very sincerely and affectionately,
Your friend and servant,

THOMAS MCAULEY.

From the Rev. William McMurray, D.D.

As far as I have been able to examine The Young Arithmetician's Guide, by Mr. Conkling, I fully accord with the preceding opinion of Dr. McAuley. Wm. MCMURRAY.

New-York, July 21, 1831.

From Mr. John Gould, principal of the Japhian School.

Mr. T. W. Conkling, New-York, July 21, 1831. SIR, I have examined your new Arithmetic, which you left me in sheets, with as much care as my other calls would admit, and have formed a very favourable opinion of its merits. The arrangement and exemplification of the various rules meet my entire approbation; and the directions for solving the questions, (which are nearly all original,) are well calculated to relieve the teacher from so frequent application, by directing the scholar to your copious and well-arranged tables. To test their utility, I gave the book to one of my pupils, ciphering in Reduction, who was unusually puzzled to know when to divide and when to multiply, and by what, and was confirmed in the opinion I had formed of their usefulness. I need not say I shall introduce it into my school immediately after vacation. Hoping you may be rewarded for your labour,

I remain yours with respect,

Mr. Conkling,

From the Rev. John M. Krebs.

JOHN GOULD.

DEAR SIR, If, after the very hasty glance, which is all that I have had time to bestow upon your book, I may be allowe

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(as you desired me,) to express an opinion of its merits, I do not hesitate to say, that that part of its plan which most attracted my attention, seems calculated to afford benefit to both teachers and scholars. By inducing the latter to think for themselves, you do them an especial service; and this you do, by furnishing them with ample materials and facilities in the numerous examples and guides which are given under every rule. The student is here excited to enquire and experiment for himself, by the very spirit of philosophy, the desire of discovering truth, and is led on from attainment to attainment just because he has light enough afforded to assist him in the search, and is rewarded for his intelligent pursuit by the knowledge which he has attained for himself. In this enquiring age he who imparts that information which either unfolds or tends to discover the "How" and the "Why?" is just so far a public benefactor. This appears to be the main object of your book, and I hope therefore that public approbation will adequately reward you for the pains which it has cost you. Yours, &c.

New-York, July, 1831.

JOHN M. KREBS.

From the Rev. Elihu W. Baldwin. Mr. Thomas W. Conkling,

DEAR SIR,-1 have examined with considerable care and much interest the "Young Arithmeticians Guide," the plan and arrangements of the work are such as will afford new and substantial aid to the learner, with some experience in the instruction of youth, I am free to say that I should prefer it to any Arithmetic with which I am acquainted.

Yours Sincerely,

Mr. Conkling,

ELIHU W. BALDWIN.

From Mr. Benjamin F. Hart.

New-York, July 23, 1831. SIR,-Your son handed me your work on Arithmetic, for examination. To test its usefulness, I placed it in the hands of two of the small boys of my school, one aged 8 and the other 10 years, requesting them to begin at reduction, corresponding with the rule they cipher in, and to read and observe the instruction contained therein, and to do as many sums as they could, without my assistance, in four hours. The result stand's as follows: they worked out 189 sums in the given time, I was astonished at the ease and alacrity with which they advanced, this was owing to the simple and well arranged notes and instructions contained, as they advanced, under each question. There was no difficulty on their part whatever, in understanding every thing connected with the subject. The tables are all admirably arranged, and completely The capacities of small children. I am of opinion, sir,

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