¹ The reason for the preference given to the English system of numeration of numbers exceeding hundreds of millions is as follows: If m stand for 1 million, then on this method m² = 1 billion, m³ = 1 trillion, and so on, and the significant syllables (bi(l), tri(l), &c.) correspond to the successive powers (second power, third power, &c.) of m. In the French system, according to which a billion is a thousand million, and a trillion a thousand billion, the significant syllables do not indicate a symmetrical relation of numbers. Numeration of such high numbers is not of sufficient practical value to warrant the expenditure of much time in teaching it. Long multiplication of money is postponed to the Fourth Standard because of its cumbrousness.

² The grammar for this standard is contained within a very narrow compass, and requires no text-book; but, thoroughly acquired, it, will be a solid foundation for future work. The starting-point for the teaching of grammar is the fact that, in a complete English sentence of two words, one word is a name or does duty for a name, and the other tells something about that which is named. The first step is to lead the pupil to observe the difference between the functions of these two words respectively. It is not necessary at the beginning to use the words "subject" and "predicate indeed, it is not necessary to name the two classes at all at first; but if they are to be named it would be better to call them "name" and "tale" than to employ the technical terms of logical analysis. But it is necessary for the teacher to have a very definite knowledge of the difference of function, and to guide the children to the discovery of it. When the sentence consists of more than two words it should be divided as before into subject and predicate, and then the special function of the noun as the most substantial part of the subject will come into view, and also the special function of the verb as the most essential part of the predicate. The simplest form of the completion of the predicate will show the noun in a new relation as standing for the object. After that the adjective will claim attention, as connected either with the subject or the predicate, and then the article in similar connection (unless it be thought better to postpone it until the pronouns are recognised). It only remains to complete the grammar of this standard by showing the use of the pronoun to perform the same function in a sentence as a noun or adjective.^* The technical words of this note are for the teacher and not for the pupil, who is only required, as the result of a year's study, to distinguish the verbs, nouns, adjectives, pronouns, and a: titles, in easy sentences.

^* As soon as it is perceived that the peculiarity of the pronoun is that its appropriateness varies as the speaker and the speech vary, while the noun and the adjective are names and descriptive words always applicable to the things named and described, whoever may be the speaker, it is also perceived that the adjective pronoun has equal right to recognition with the substantive pronoun, and that the rejection of the adjective pronoun by some recent grammarians is a result of hasty analysis.

³ Considering how very few of the scholars stay long enough at school to pass a standard higher than the fourth, they ought to receive some careful instruction in composition before they are presented to be examined in Standard III. The art of composition does not "come by nature." On the other hand, its acquisition may be promoted by indirect means as well as by direct teaching. Very much depends upon the power of intelligent reading—reading by sentences, as explained in the notes on Standard I. A further step will be gained by attending to the requirement for the reading of Standard III.,—reading " with due regard to the distinction of paragraphs, as well as of sentences." Just as in Standard I. the sentence is to be recognised as a unit, so in Standard III. the paragraph is to be studied in its unity, and in its relation to the unity of the composition of which it forms a part. The pupil must be led to the apprehension of a reading lesson as a whole, and helped to trace the course of thought in it, and to see how and why each group of closely related sentences is bound together in a paragraph, and separated from the groups that precede and follow. The instruction in grammar sketched in the preceding note should be interspersed with exercises in the formation of sentences, on the model of whatever sentences are discussed in the grammar lesson. When an object-lesson has been given, and while the outline of it remains on the black-board, the children should be taught how to form sentences from the words in which the outline is written. [An Otago teacher, who has been very successful in teaching composition, has a book in the press illustrative of this method.] The transcription prescribed for Standard III. will be helpful, if "due regard to punctuation and quotation marks" be paid, as the regulation requires. Oral history lessons, also, can be utilised in the same way as object-lessons. Finally, the pupils should be set to write their own account of any event that is exciting general or local interest, and of anything they have opportunity of observing or taking part in.

⁴ It is, perhaps, unnecessary to say that the geography required for this standard does not include all possible knowledge with regard to the places and objects specified. Questions as to population, commerce, and political relations, or as to the heights of mountains and length of rivers, go beyond the design of the regulation. Of the places and objects indicated the children are expected to know the names, and that one is a town, another a country, and so on; they should also know the position of each on the map. Every school should have a good map of the Road Board District, or other local division, in which it is situated.