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By the time the learner can expeditiously run through and understand the examples I have here given, he will be competent to attempt modes of calculation adapted to his particular pursuits; he will comprehend the works of the ablest authors on arithmetic; and he will find himself more than ever capable of appreciating, as it were, at a glance, the amounts of weights, measures, moneys, &c.

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Mental arithmetic is practised with great advantage in the Edinburgh Sessional School. Mr. Wood says,"It was in arithmetic we first succeeded in kindling that ardour which has since diffused itself through every department of the institution. At the very commencement," says he, "of arithmetic, the child is taught to answer how many are I and 2, 3 and 3, 6 and 4, 10 and 5, 15 and 6, 21 and 7, &c. In preparing to enter upon subtraction, in like manner, he is asked-Take 1 from 100, how many remain? 2 from 99, 3 from 97, 4 from 94, 5 from 90, &c. So also, before entering upon multiplication, he is taught to answer twice 2, three times 3, four times 4, &c. What is this,' we

shall be asked, but the old multiplication table?'

So it undoubtedly is, and this, we beg leave to add, is the only way in which this table is now learned at our school, and it has been found a far more effectual, as well as more pleasing mode of learning it, than when we used to enjoin it as a task." Division is taught in the same manner, as are the pence tables, and other requisites for the compound rules, and places are taken and lost in the classes in the same manner as in the reading exercises. Three or four of the best arithmeticians one day calculated, mentally, and pronounced correct answers, in twenty minutes, to 147 questions, put to them out of a ready reckoner!

MNEMONICS.

Let not such of my readers as are yet ignorant of mnemonics, be deterred by the sight or the sound of a Greek word from investigating the merits of an art, which, however forbidding at first sight, will be found to improve upon acquaintance, precisely in the degree in which that acquaintance is cultivated. At least, I hope the mere sketch I propose to give of it in this place will not be deemed unworthy of attentive perusal by those who have any desire whatever to be informed of its general outline and principles.

My friend, Mr. Coglan, of Liverpool, is the author of the best publication now extant on this subject, a subject which I incidentally introduce in my lectures, and respecting which he has kindly given me permission to quote any of his observations which may assist me in my present purpose. In an early part of his very clever work, Mr. Coglan observes:

"Erroneous opinions are formed of the application of this art; it is generally called the system of artificial memory, which implies an opposition to natural memory, but a very little consideration must point out the impropriety of the term; it would be

perhaps better expressed by saying artificial helps to the natural memory, for nothing can be impressed on the mind without the exercise of memory, which this system, so far from dispensing with, calls into most active use, and only requires the assistance of those principles that have their foundation in nature. If we wished to recollect the period when the laws of Draco were promulged, and said that their venom defeated their object, as a people could not long endure them; that Moses must have tript quickly across the Red Sea to escape the hosts of Pharaoh ; that the followers of Columbus, instead of imitating their leader, seemed only anxious to trepan the unfortunate inhabitants they discovered; and that the words venom, tript, and trepan had the letters which were employed to represent the figures 623 B. C. 1491 B. C. and 1492 A. D. the proper dates when those transactions occurred,—would not the remembrance of these be truly an exercise of memory, but receiving such desirable assistance from association and arrangement ?"

Reverting to what I have advanced in the former part of this work, on the subject of tasks in education, I am happy in being able to select a passage like the following in favour of my position, from an author who principally treats on memory, and might almost be expected, therefore, to rely unduly on its exercise, especially when assisted by the means he suggests of affording aid to its powers in general. Mr. Coglan says:

"Some people seem to act as if the whole principles of knowledge consisted in being able to

repeat the sentiments or opinions of others, or the specific rules laid down, whether in the languages or sciences, and therefore deplore the badness of their memories in being unable to retain them; but if they took one-tenth of the pains in attending to general principles, which they employ in committing to memory, not only would their knowledge be more extensive, but their minds more active and efficient for all the various purposes of our nature."

In this passage there is the testimony of a philosophic mind supporting the principle I lay down in my lectures, namely, that tasks ought never to be imposed when the matter intended to be impressed on the memory can be so impressed by ordinary instruction or by reasoning on general principles. Keeping steadily in view the fact that the mind consists of three parts, or, in other words, that it possesses three distinct properties-memory, judgment, and imagination—it must appear desirable that any one of these should be assisted as much as possible by one or both of the others. To me it seems undeniable that mere tasks, learnt by rote, attach only to the memory, and that by such tasks the memory would indeed be overburdened, if it did not relieve itself by permitting its stores to escape-that is, by forgetting the unintelligible, and therefore unwelcome, lumber which oppressed it; but if, by reasoning from principles, the memory becomes stored with matter which the judgment has recognised and appreciated; or if, by the use of

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