(a) Cleanliness of person. Hands and face should be washed frequently, teeth should be cleansed, and dirt removed from the

nails. The whole body should be washed every morning if possible, and a cold bath taken frequently both in summer and winter.

(b) Cleanliness of dress. With children this will depend much on the parents; but show how boys and girls can themselves do a great deal to keep their clothes clean. They should get into the dirt as little as possible, and by keeping their persons clean they will be helping to keep their clothes clean. Then they can brush their clothes, and clean their boots; and their parents, if they see that they are anxious to be clean themselves, will take a pleasure in doing all they can to help them. Elder girls can assist greatly in keeping their younger brothers and sisters clean.

(c) Cleanliness in dwellings. Show how important this is. A dirty house is uncomfortable, liable to disease, and injurious to the other two forms of cleanliness, viz., of person and of dress. The floors should be scrubbed, the walls and yard swept, the hearths kept tidy, and everything removed likely to create annoyance and discomfort to the inmates. When the father comes home in the evening from his work, he should see everything looking bright, clean, and comfortable. Show how children can co-operate with their mother in producing this effect; the boys can be careful not to bring any more dirt into the house than they can help; they can scrape and rub their feet on the mat when they enter; they can polish the fire-irons and other utensils, and sweep up the yard. The girls can assist their mother in almost all the household duties. Both boys and girls can set a good example to their younger brothers and sisters.

4. Means of cleanliness. These have mostly been already given, and the children should now be called upon to name the various operations connected with cleanliness; as, washing, scrubbing, bathing, combing the hair, etc. Then call for the names of materials used in these operations; as, water, soap, soda, etc. Lastly, the names of instruments, etc., used for purposes of cleanliness should be asked for; as, the comb, brushes of various descriptions, door-mat, scraper, etc.

Use a black-board throughout the lesson for writing down the heads, and recapitulate at the close.

(6) Divide ax3 − (a2 + b)x2 + b2 by ax

ax — b)ax3 — (a2 + b)x2 − b2(x2 + ax

bx2

-

ỏ (4th year, Feb. 1880.)

-b

(10) Solve the equations (Fifth year, June 1875)

x2 + y2 = 50

Under this head we propose to insert queries on subjects likely to interest our readers, and invite answers from those able and willing to oblige their fellow-teachers.

(6) What traces of the Feudal System are now existing in the tenure of land?

(7) If one angle of a triangle be a right angle, and another equal to twothirds of a right angle, prove from the First Book of Euclid that the equilateral triangle described on the hypotenuse is equal to the sum of the equilateral triangles described on the sides which contain the right angle.

(8) Parse fully: "All controversies that can never end had better perhaps never begin."

ANSWERS TO QUERIES.

(4) page 95. Let ABC be a triangle, having its side AB trisected in D,E; AC in F, G; BC in H, K. Through D,F; E,H; K,G draw LDFM, LEHN, NKGM forming the new triangle LNM, which has to be proved equal in all respects to ABC. Join DG, EF, EC, BG, EG. Then triangle DFE triangle DFA (1. 37). Also triangle GDF=triangle DFA, therefore the triangles DFE, GDF are equal; and they are on the same base DF, therefore DF is parallel to EG (1. 39), therefore triangle EDG= triangle EFG. But triangle EDG=triangle EGB, and triangle EFG = triangle GEC (1. 38), therefore triangle EGB=triangle GEC, and they are on the same base EG, therefore EG is parallel to BC (1. 39). But DF is parallel to EG, therefore BC is parallel to DF or LM. In the same way it may be proved that AB is parallel to MN, AC to LN, FH to AB, and FH to NM. Therefore LF = HC (1. 34), FM=HK or BH, and therefore the whole LM-the whole BC. Similarly LN-AC, and NM=AB. Therefore triangle LNM = triangle ABC in every respect (1. 8).

T. P. (5) page 95. We must suppose the two given lines not parallel, or the problem can only be performed under very limited conditions.

Let ABC, DBF be two straight lines, cutting each other in B. Let F,G be two other given straight lines; it is required to draw between ABC and DBE a straight line equal to F and parallel to G. From B draw BH equal to F and parallel to G. Through H draw HK parallel to BE meeting ABC in K. Through K draw KL parallel to BH meeting DBE in L. Then it will easily be seen that KL is the straight line required.

ALPHA.

THE TEACHER'S LIBRARY.

MOFFATT'S PUPIL TEACHERS' COURSE. Year I. Price 2s. 6d. London: Moffatt and Paige.

This book contains the whole course of instruction for Pupil Teachers (male and female) of the first year. It comprises Geography of Europe, with Appendix, taking up particularly the Alps, the rivers Rhine and Danube, the European Railways, the various routes to the Continent, the Telegraphs; English History, the succession of English Sovereigns from the reign of Egbert, with dates, to the present time, with genealogical tables and explanatory notes; English Grammar, the pronoun, adverb, and preposition, with their relations in a sentence, with lessons and exercises in parsing; Recitation, two selections, with very careful explanatory notesGray's Elegy, and Cowper's Lines to his Mother's Picture; Composition, directions and hints, with specimens of letter writing, and answers to questions in geography and grammar; Music, résumé of Candidates' course, the relation of treble stave to bass, places of notes on both, simple common, and simple triple time; Arithmetic, vulgar and decimal fractions, simple and compound proportion, with answers.