ods of this study cannot be arbitrary, or established by the dicta of any individuals. Grammar will not then so much express what we conceive ought to be as what is, and the proper duty of the grammarian will be not to invent, but to investigate and classify laws that are universal and immutable. Then Grammar falls into the category of inductive Science, and must be studied in the light of the facts and principles pertaining to human thought.

This leads me to observe, that there is but one true system of Grammar. The names of Authors may be "Legion, "but the system is one and invariable. Hence that specious tittle "A new system of Grammar” is always delusive. If it is a Grammar at all, it must embrace the essential elements of all Grammars. It may be new in giving simplicity to what was before complicated; in its arrangement it may be new; in its definitions it may be more comprehensive and exact, for in all these matters improvement may be made, but to make a new system is a work beyond any effort of man, however Titanic he may be.

Plato well observes that reason and discourse are one, and until we can change the principles of reason, those of discourse must remain alike unchangeable.

There is often much perplexity among teachers, with respect to the best text book on Grammar. In making some suggestions respecting the matter of a text book I would observe first that the excellence of a work is relative-relative to the intellectual development of the scholar. The same book would be unsuited to all grades of intellect. As the study of Grammar is less mechanical than that of any other branch, it requires a certain amount of intellectual development before the study can be commenced with profit. We learn in early life most by observation and hence those studies that are essentially dependent on this faculty will then be most easily acquired. For this reason teachers should not encourage scholars to begin this work too soon, and when they do begin, a book should be selected with judicious care.

The prominent qualities of a good Grammar I take to be, natural order in its arrangement; clear, concise yet comprehensive definitions and rules; the avoiding of perplexing technicalities, and strained constructions; accurate diction; adaptation of rules to the idioms of the language; and examples illustrating every principle.

It is but candid to say that most of the Grammars now in use have, some one of these, in phrenological parlance, largely developed. The most deserving would be that one, which should combine all these excellencies in the highest degree.

The importance of a natural order must be apparent to every one, when he considers that there is an order in thought; that we pass with ease from the simple to the complex, from the clear to what is abstruse.

But the science of Grammar is built up by definitions, and in respect

to these no grammar may be pronounced absolutely perfect, and perhaps such perfection is unattainable. Definitions and rules are designed for constant application, and hence they should be constructed with comprehensive simplicity. This doubtless is difficult, but in this will appear the skill of an Author. It is a great annoyance to a teacher to give a definition or rule made for the case in hand, and find that it does not suit. At once he is compelled to criticise the author, and to give the impression to the beginner, that the science of Grammar is yet unsettled in its principles. It would be easy to illustrate how this obviously just requirement, with respect to rules and definitions, is violated by the most reputable grammarians, but it may be more convenient to do so when we treat of the methods of Teaching the Science.

True Science aims to simplify, hence all unintelligible and meaningless expressions will be avoided. It would be impossible to unfold with precision a science like grammar without the use of technical terms, but these should always be used in the same signification and with appropriateness. If a technical word obscures the idea rather than throws light upon it, the term should at once be discarded.

But one of the most difficult things to meet with, in a grammarian, is a simple method of construction. It is the custom af many grammarians to adapt the language to their graminars, and not the grammar to the language. Their system is made inflexible, and the language plastic; and into what fantastic shapes it is sometimes molded. And for what? Simply that it may be parsed. The idioms of the language are changed and mutilated in order that somebody's grammar may be quoted as authority. Those doing this have forgotten, or never knew, that the language as existing, is authority for the grammar, and not the grammar for the language.

Accuracy of diction is also an essential element of a good text-book. As little would we esteem the teacher of music who persistently violated the common rules of his art, as we could that author on grammar who by his diction continually blundered in application of the principles that he professes to teach.

It is not enough that the characteristics which we have mentioned should be incorporated in a treatise on grammar, but that every princi ple should be elucidated by appropriate examples. Exercises on every topic should be sufficiently copious to fix a clear and ineffaceable impression upon the mind. Thus the study will become "practical while giving the theoretical view.

Having presented some views respecting the nature of the science of Grammar, and of the characteristics of a good text-book, we reserve the method of teaching for subsequent consideration.

The anticipated cost of railroads in progress in India is $250,000,000.

Mathematical Department.

DANIEL KIRKWOOD, EDITOR.;

PROBLEM NO. 236.-FROM THE MATHEMATICAL MISCELLANY. In a given semicircle, it is required to inscribe the greatest isosceles triangle, having its vertex in the extremity of the diameter, and one of its equal sides coinciding with the diameter.

PROBLEM No. 237.-By Q.

In a given hemisphere it is required to inscribe the greatest right cone, having its vertex in the circumference of the base of the hemisphere.

PROBLEM NO. 238.—Bx Q.

37 lbs. of tin lose 5 lbs. in water, and 23 lbs. of lead lose 2 lbs. in water; a composition of tin and lead weighing 120 lbs. loses 14 lbs. in water. How much does this composition contain of each metal?

PROBLEM NO. 239.-By Q.

A cylindric vessel 10 inches in diameter, and partly filled with wine, is inclined till the horizontal surface of the fluid leaves 8 eight inches of the bottom dry, and meets the side of the vessel 24 inches from the bottom; required the number of cubic inches of wine in the vessel.

PROBLEM No. 235.

Find the diameter of the sphere, which placed in a given conical glass full of water, shall cause the greatest quantity of water to overflow.

then rcxcx the distance from the center of the sphere to the

r

vertex of the cone, a

ex

=

the hight of the segment immersed in water. Now

and a +x

r

=

the solidity of the spherical segment is found by the following rule:"From three times the diameter of the sphere, subtract twice the hight of the segment; multiply the remainder by the square of the hight, and that product by .5236."

2ca

CX 2

Hence .5236(4z — 2a +24) (a + x − = ? } 2

}

segment = a maximum. Differentiating and reducing, we find

x

arc

cr+c3-2r2

Remark. When a = 6 inches, and r = 21⁄2 inches, this problem becomes the 27th in Robinson's Calculus, Art. 29.

Resident Editor's Department.

Rev. Charles White, D. D., President of Wabash College, died on the 5th ult. He was about fifty years of age, an able and highly esteemed teacher.

Mr. G. H. Stowits, one of New York's best teachers, an able and eloquent lecturer, will visit our Association, deliver and address, and participate in the discussions. Mr. Stowits was recently presented with an elegantly framed picture of the class of graduates, at the closing exerci ses of his school in Buffalo, N. Y. His address to the class is spoken of by the Buffalo papers as a masterly effort, able and eloquent.

We have not thought it necessary to call attention to the Department of Practical Teachings, conducted by Pres. Benton, as it commends itself to all who see it. To us, having again engaged in the practical duties of the profession, it has been of great interest and benefit,-emphatically the word in time fitly spoken. Why has Prof. B. had no assistance? Are there no other teachers in Indiana who can write articles for the school room?

We are under obligations to Mr. C. II. Moore, of Terre Haute, for the names of several new subscribers to the SCHOOL JOURNAL. Mr. M writes that he obtained them at the office of the County Examiner, Col Edwards, who generously relinquished his fee for examination on this condition. Would that many other examiners had some of his professional zeal and generosity. The examiner of Marion county also remembers the JOURNAL when he examines teachers.

We had the promise of an illustrated article on School Gymnastics from Dr. Lewis, of the Normal Institute, for this No., but from some cause he has failed to send it. Possibly we may get it for the Jan. No. We hope so.

An article by Mr. T. J. Vater, on the "Cramming versus the Drawing out System," is in type, but deferred to next No. for want of space. The JOURNAL was almost made up when it was received.

FALL APPORTIONMENT OF SCHOOL REVENUE.

We have before us the Second Semi-Annual Apportionment of School Revenue, by the Superintendent of Public Instruction, for the year 1861. It embraces the delinquent tax, the liquor license, the unclaimed fees, and the interest on school fund collected since the spring reports. The $25,000 alluded to in the 118th section of the school law will not be added until the coming year, as the revenue from which it is to be dǝrived is yet to be collected.

This apportionment is made upon the same basis of enumeration as the spring apportionment. The total amount collected from school tax is $50,088 59: from interest of common school funds, $27,855 84; from liquor license, $23,245 00; from unclaimed fees, $761 15; total for apportionment, $ 105,768 69.

The distributive share apportioned to each county, in dollars and cents, is as follows:

-Owing to the same causes of "war and trouble," which induced the