60 



THE POPULAR EDUCATOR. 



ten i- Spanish, in 1635, but that, the work having been 

 prohibited by the government, the author fled with a copy of it 

 to France, and that Le Sage, obtaining possession of this copy, 

 translated or adapted his own novel from what he found. The 

 alleged original, however, has never been produced, and it 

 seems doubtful whether it ever existed. Le Sage was un- 

 questionably a good Spanish scholar, for he has avowedly 

 translated several dramas from the language of Cervantes. 

 But it is not likely that a man of his original genius would 

 condescend to the contemptible fraud of publishing as his own 

 what he had in truth derived from another author and another 

 tongue. It will, perhaps, always excite surprise that one who 

 does not appear to have travelled in Spain should have painted 

 the manners of that country with so much liveliness and accu- 

 racy. Yet, until some clearer evidence of plagiary is forth- 

 coming, we should not be justified in robbing a great man of 

 the fame which seems to be his due. 



The first and second volumes of " Gil Bias " appeared in 

 1715, the third in 1724, and the fourth and last in 1735. Its 

 popularity was great, and it has ever since retained one of the 

 highest places in the literature of France. Few works have 

 been more widely read. Translations have been made into 

 nearly all the languages of Europe ; and, although there is no 

 figure in the work so universally and familiarly known as Don 

 Quixote or Robinson Crusoe, nor anything so distinctively and 

 strikingly characteristic, the literary reputation of this Franco- 

 Spanish novel is illustrious in all civilised lands, and millions 

 of readers have delighted in its caustic, yet not malignant, 

 satire upon human life and motives. The English version of 

 "Gil Bias " is by Smollett himself a man of genius, somewhat 

 akin to Le Sage's, though of a coarser fabric ; and with ad- 

 mirable spirit has he rendered his original. It is pleasant to 

 be able to record that Le Sage was an amiable and a worthy 

 man. He knew the evil that is in the world, but was not 

 depraved by it, nor driven into the practical cynicism of be- 

 lieving that because many persons are bad, all may be so. Of 

 the hero of his most celebrated work, Sir Walter Scott observes 

 that " Gil Bias is naturally disposed towards honesty, though 

 with a mind unfortunately too ductile to resist the temptations 

 of opportunity or example. Generous, good-natured, and 

 humane, he has virtues sufficient to make us love him ; and as 

 to respect, it is the last thing he asks at his reader's hands." 

 One of his most prominent characteristics is vanity, which 

 frequently leads him into awkward dilemmas. Inexperience 

 deceives him at the outset of his career ; self-love, at a later 

 date. His good education and pleasing manners introduce him 

 to a large round of acquaintances, and there is hardly any class 

 of Spanish society which is not reflected in the sparkling nar- 

 rative of his adventures. It must be admitted, however, that 

 the portraiture is not morally pleasing. Thieves, cheats, im- 

 postors, pretenders, hypocrites, profligates, and dupes, all 

 engaged in intrigues of a more or less questionable order, are 

 the dramatis personal of " Gil Bias." The author's conception 

 of life is not actually base, for the distinctions of right and 

 wrong are not confused by sophisms or by sentimentality ; but 

 it is ignoble, because it places out of view all the better elements 

 of human nature all the devotion, the sacrifice, and the suffer- 

 ing, that this mortal scene discloses. The most objectionable 

 thing in the school of writers to which Le Sage belonged is the 

 absence of any sufficient sense of the high tragedies of life, 

 wherein there is always something deep and sacred. But, as a 

 gallery of society-pictures, full of animation and character, 

 " Gil Bias " will interest and attract successive generations of 

 readers to the remotest time ; and the romantic aspects of 

 the old Spanish nationality lend an additional charm to the 

 relation. 



This romantic element is more particularly observable in the 

 early chapters of the story, where the hero then a youth of 

 seventeen is captured by a band of robbers who dwell in a 

 series of caverns situated in the depths of a wild forest. Here 

 Captain Rolando and his fellow-brigands lead a jovial sort of 

 life, attended by an old negro and an equally ancient serving- 

 woman. The caverns are duly apportioned as distinct sets of 

 apartments, comprising kitchen, dining-room, bed-rooms, and 

 stables, with divers connecting passages, fortified against 

 intrusion by iron grates. It is a little difficult to believe in 

 such a subterranean world, and Le Sage has thought fit to put 

 into the month of Captain Rolando an explanation as to how it 



came to exist. " This is not a work of our hands," says he, 

 " but was made many years ago ; for, after the Moors had got 

 possession of Grenada, Arragon, and almost the whole of Spain, 

 the Christians, rather than submit to the yoke of infidels, fled, 

 and concealed themselves in this country, in Biscay, and in the 

 Asturias. Fugitives, and dispersed in small numbers, they 

 lived in mountains and woods ; some lurked in caves, and 

 others contrived many subterranean abodes, of which number 

 this is one." Gil Bias is compelled for a time to serve with the 

 robbers, but he watches for an opportunity, and ultimately es- 

 capes, in company with a lady whom the brigands have taken 

 prisoner. It is after this that he figures as a man of the world, 

 according to the Spanish type of two centuries ago. 



LESSONS IN ALGEBRA. II. 



DEFINITIONS (<xmtinid). 



27. When four quantities are proportional, the proportion is 

 expressed by points, in the same manner as in the Rule of Pro- 

 portion in arithmetic. Thus a : b s : c : d signifies that a has to 

 b, the same ratio which c has to d. And ab : cd -. : a + m -. b + n, 

 means that ab is to cd, as the sum of a and in, to the sum of 

 b and n. 



28. Algebraic quantities are said to be like, when they are 

 expressed by the same letters, and are of the same power ; and 

 unlike, when the letters are different, or when the same letter is 

 raised to different powers. Thus ab, Sab, ab, and 6ab, are 

 like quantities, because the letters are the same in each, although 

 the signs and co-efficients are different. But 3ci, 3y, 3bx, are 

 unlike quantities, because the letters are unlike, although there 

 is no difference in the signs and co-efficients. So x, xx, and xxx, 

 are unlike quantities, because they are different powers of the 

 same quantity. (They are usually written x, x s , and X s .) And 

 universally if aiy quantity is repeated as a factor a number of 

 times in one instance, and a different number of times in another, 

 the products will be tinlike quantities; thus, cc, cccc, and c, are 

 unlike quantities. But if the same quantity is repeated as a 

 factor the same number of times in each instance, the products 

 are like quantities. Thus, aaa, aaa, aaa, and aaa are like 



29. One quantity is said to be a multiple of another, when the 

 former contains the latter a certain number of times without a 

 remainder. Thus 10a is a multiple of 2a ; and 24 is a multiple 

 of 6. 



30. One quantity is said to be a measure of another, when the 

 former is contained in the latter any number of times, without 

 a remainder. Thus 36 is a measure of 15?) ; and 7 is a measure 

 of 35. 



31. The value of an expression, is the number or quantity for 

 which the expression stands. Thus the value of 3 + 4 is 7 ; that 



of 3X4 is 12; and that of ^ i* -2. 



32. The RECIPROCAL of a quantity, is the quotient arising from 

 dividing A UNIT by that quantity. The reciprocal of a is -; the 



reciprocal of a +b is -TTL; * e reciprocal of 4 is 4 - 



33. In commencing arithmetic the learner has to study the 

 method of expressing words by figures, and, vice : .v;v* ". figures by 

 words ; so in algebra he must first accustom himself to convert 

 statements made in words into algebraical expressions, and also 

 to write out algebraical expressions in words. We give two 

 examples, first of all, of the method of converting statements in 

 words into algebraical expressions, and follow them by an exercise 

 to the same. The answers to the examples in this exercise will 

 be found at tke end of our next lesson. 



EXAMPLES. What is the algebraic expression for the follow- 

 ing statements, in which the letters a, 6, c, etc., may be supposed 

 to represent any given quantities ? 



STATEMENT IN WORDS (1). The product of a, b, and c, 

 divided by the difference of c and d, is equal to the sum of 6 and 

 e added to 15 times h. a j e 



ALGEBRAICAL EXPRESSION (1). -^-j = b + c + I5h. 



STATEMENT IN WORDS (2). The sum of a, 2b, and 3c is 

 equal to the difference of d and e divided by 10 times the pro- 

 duct of / and g. ^ 



ALGEBRAICAL EXPRESSION (2). a + 2b + 3c = ^-^-f-. 



Ivjg 



