additional examples to the quicker children, and telling the result at sight.

Another rapid way of setting and testing additional exercises is the following:-See preceding exercise, lines (1) to (4). Number the children 1, 2, 3, 4. Give to the corresponding children all the lines in the sum except the last. To 1 give the last line in addition; to 2 give the half of 1's last line; and to 3 the half of 2's last line; and to 4 the half of 3's last line. Add up 1's sum, subtract the last line of 2's sum from 1's answer, which will be 2's answer; and so on.

In these compound rules the values of figures do not increase from right to left by tens, as in ordinary decimal Arithmetic; but each column (£ s. d.) has a value of its own, compared with that to the right and left of it.

As an easy exercise to accustom the class to the form required, it will be well to give sums which require no carrying, except in the £'s column, as in the accompanying example.

In Compound Subtraction, the borrowing has to be done, not by tens, but of a penny for the farthings' column, a shilling for the pence, and a pound for the shillings' column.

£

s. d. 23 2 1

3 2 3 16 11 41

£42 15 8

In all these rules copious problems should be given.

The following exercises in Mental Arithmetic will serve as types of the kinds of problems, among others, that will be found useful in Standard III :

V. I owe £67 16s. 114d. and pay 12s. 9ąd. : what remains? If I owe you £6 11s. 7d., and you owe me £3 19s. 5d., what is the balance ?

How much greater is £17 9s. 7±d. than 18s. 6‡d.?

What is the difference between £60 11s. 7d. and £51 17s. 2d. ?

After paying 11s. 11 d., what will remain out of a £5 note ?

How much is £4 17s. 6d. short of £11 19s. 81d.?

A cow is worth £17 9s. 61d., and a horse £18 11s. 6d. : what is the horse worth more than the cow?

Give me change out of a £10 note, after paying £9 7s. 6d.

I borrow £87 6s. 64d., and pay £13 11s. 24d. : what do I still owe?

My income is £11 18s. 6d., and my expenses £10 19s. 2d. : what can I save?

What sum added to £17 6s. 1d. will make £96 11s. 2‡d. ? Two men gain £45 17s. 6d. ; one draws £13 11s. 6d. : what does the other draw?

Which is greater, and by how much, £17 11s. 6‡d. or £19 11s. 3 d.?

Pay a bill of £17 16s. 11 d. out of a £20 note.

How much short of £50 is £17 19s. 11d.?

£31 10s. 6d. + £42 11s. 1d. £31 0s. 6d.

£6 11s. 7d.

£5 8s. 4d. + £3 18s. 6d.

£17 118. 34d. + £3£5 2s. 7 d.

PRACTICAL HINTS BY H.M.'s INSPECTORS ON WRITING AND ARITHMETIC (STANDARD III.).

66

'The copy-books used by the upper standards are seldom ruled for large hand, it being thought, especially by parents, that there is something degrading for the older children to be exercised in writing large hand copies, whereas it is well known that one of the chief means by which a mastery over and freedom with the pen are acquired is by constantly writing large hand copies. The ability to write a good large hand is not easily acquired, but when once it is so, writing well in any hand almost necessarily follows."

66

It would be well if the Pupil Teachers were required once or twice a week to construct sums for themselves, without having recourse to either cards or books, and to work them carefully out before giving them to the class. This, combined with the explanation of principles involved, would greatly benefit both the class and their teacher, besides adding considerably to the liveliness of the lesson."-MR. BLANDford.

"It often happens that an easy problem in compound addition, if it involves but two lines of figures, is treated as a subtraction sum, for no other reason than that subtraction sums consist of two lines.”—MR. BALMER.

"In the Third Standard it is still not uncommon for children (particularly girls) to endeavour to take a greater sum of money from a less, simply because the less amount comes first in the question given, or will have in a long division sum a remainder greater than the divisor."-MR. CAMPBELL.

"From the Third Standard upwards I always set one simple problem application of the arithmetical rules supposed to have been learned; and I do not find this

question now more fatal to our examinees than any of the other three."-MR. DU PORT.

Simple problems, such as the following, have puzzled many in the Third Standard:-Two books contain, the one 5012 lines, the other 9304; if a boy read 98 lines a day, in how many days will he be able to finish the reading of these books?"-MR. FUSSELL.