Middle-Class Education. 33 



beyond a certain limit. But it is essential he should be taught 

 thus much, even if it be only to produce exactness of thought. 

 He should be strictly trained in the elements of geometry and 

 the laws and properties of matter. To go more into detail, he 

 should in arithmetic be quite at home in the four first rules, 

 vulgar and decimal fractions, proportion, extraction of square 

 root, logarithms, and book-keeping, so far as it can be taught in 

 schools. 



Three times a week too he should be exercised in class (a 

 practice that from the keen competition tends admirably to 

 sharpen wits) in what is called mental arithmetic (M'Lcod's 

 handbooks are excellent) an accomplishment of great value in 

 any walk of life, but especially for those to Vv^hom rapidity of 

 calculation gives so much advantage in the market. In Algebra he 

 should perfectly master simple equations, then have some little 

 practice in quadratic equations, and get on to ratio, proportion, 

 arithmetical and geometrical progression, permutations, combi- 

 nations, interest. This need occupy no long period if the teacher 

 be able and the pupil willing, but further it were needless to go, 

 for here you leave the practical, which alone concerns us, and 

 enter the realms of pure science. 



Of Euclid all gentlemen should learn most thoroughly Books 

 i. ii. iii. iv. It should be taught in class on a black-board, the 

 teacher first going through the problem himself as he expects it 

 to be said, then the next day calling upon his pupils to do the 

 same. The tutor's going through it first I know to be a mighty 

 help, that robs the volume of its horrors. After practice on the 

 black-board the class should go down, and in the presence of 

 the teacher carefully write out the proposition they have just 

 taken up in class, the MSS. to be carefully supervised by the 

 teacher and rewritten by the pupil. Then the next day when 

 they take up their new lesson they should be called upon briefly 

 and rapidly to indicate the key-point of each of these same 

 propositions, not going, as on the first day, religiously through 

 each ABC, D C F and G C H as they might by rote, but in 

 just a dozen words pointing out the kernel of the problem. This 

 is the best way to teach Euclid, rendering it thoroughly 

 available for future practical purposes. 



The elements of meclianics, the laws of matter and motion, 

 hydraulics, c^c, eminently useful as they are to every farmer, 

 experience leads me to think can seldom be taught, even from 

 Messrs. Chambers' nice handbooks, with profit to a lad under 

 sixteen years of age, which I have fixed for the limit of the 

 young farmer's school-days. 



Writing is of course a sine qua non ; and our late distingushed 

 Premier did much good by laying such emphatic stress on the 



VOL. II. — S. S. D 



