LESSONS IN ALGEBRA. 



341 



months, its popularity had increased in a degree which must 

 bare satisfied the expectation* of tho author, had thee been far 

 more sanguine than ho ever entertained.'' The structure of 

 tho story, as tlm \N nt .-r subsequently admitted, showed signs of 

 immaturity ; Imt. tho public were attracted by its freshness, its 

 I'i.-t unique power, and tho novelty of the icenes of Scottish 

 lit, to which it introduced the reader. Within the next four 

 yean, "Wavorloy" wa followed by "Ouy Mannering," "Tho 

 Antiquary," "The Block Dwarf," "Old Mortality," "Bob 

 Boy," and "Tho Heart of Mid-Lothian : " many others came 



All these tales, like tho first of tho set, were published 

 anonymously, and tho stories were known as "Tho Waverley 

 Novels," or " The Scotch Novels." Considerable curiosity was 

 manifested to know who the author really wan, and the mystery, 

 which was well sustained, may possibly have added to the 

 success of tho works. Tho original motive for concealment 

 was that the author was doubtful of tho reception which ho 

 would meet, and did not care to bo identified with failure. 

 Afterwards, tho inank continued to be worn out of a certain 

 whimsical feeling, which found a pleasure in tho wonderment 

 of tho public. Numerous wero the guesses as to the personality 

 of the author of " Waverley ; " some plausible, others ridicu- 

 lous. In time, Scott came to be generally regarded as tho 

 creator of these interesting fictions, and ho was sometimes pat 

 to awkward straits by being asked in direct terms if such was 

 not the fact. It is rather unpleasant to learn, on his own 

 authority, that he used to meet these questions by a positive 

 denial. He considered (and, indeed, rightly so) that no one 

 was entitled to drag from him a secret which it was his plea- 

 sure to keep ; and he placed his denial on the same formal and 

 purely defensive footing apart from all questions of truth or 

 falsehood as the plea of " Not Guilty " advanced by a criminal 

 on his trial. Byron is said to have told a friend that Scott, 

 talking with him one day in the office of Mr. Murray, the 

 publisher, inadvertently admitted, by implication, that the 

 Scotch Novels were his ; and to all the author's friends and 

 associates it was an open secret. The fact, however, was not 

 specifically divulged until February, 1827, when Scott himself 

 avowed his long- veiled authorship at the anniversary dinner of 

 the Edinburgh Theatrical Fund Association. 



Scott was forty-three years old when the story of "Waverley" 

 was published. It is not often at such an ago that a man 

 who has for many years been labouring with the pen strikes 

 out a new line of imaginative creation, achieves in that line 

 the most brilliant and lasting success, and, though dying at 

 the comparatively early age of sixty-one, lives to produce an 

 immense number of works in the particular class of literature 

 to which, until middle life, he had been a stranger. The great 

 novelist expired on the 21st of September, 1832, and ho continued 

 writing up to within less than two years of his decease, alter- 

 nating fiction with historical, biographical, and other literature. 

 For a long time, however, ho had been overworking himself, 

 owing to pecuniary embarrassments, and his later novels are 

 generally allowed to have been far inferior to his earlier. But 

 the best of these works are a gain of a very high order to the 

 world of fiction. The author of "Waverley" had a deop 

 knowledge and keen appreciation of Scotch nature and Scotch 

 manners, and was especially at homo when depicting them. 

 But he was too cosmopolitan a man to confine himself to one 

 circle, and his reproduction of the England of past times is 

 vivid and sympathetic. It was in tho past that he mainly lived, 

 and this it was which made him the greatest writer of historical 

 romance that we have had. His imitators were numerous, and 

 some were distinguished ; but not one has attained his eminence, 

 with the exception of Lord Lytton. For several years after 

 tho death of Sir Walter Scott, historical fiction continued to 

 form one of the principal branches of novel-writing ; but it has 

 recently fallen into disrepute. After a while, tho style degene- 

 rated into a trick ; the art became vulgarised by inferior hands ; 

 critics discovered an element of untruthfulness in what had 

 once been so highly admired ; and even the uncritical began to 

 fear that their conceptions of actual history ran some danger 

 of being vitiated by the kaleidoscopic effects of the romance- 

 writer. The tendency of tho present day is towards realism in 

 art ; but it is possible that future times may witness a reaction 

 in favour of the kind of story-telling of which Scott set the 

 example in " The Waverley Novels." 



LESSONS IN ALGEBRA. XL 



ADDITION OP FRACTIONS. 

 To ADD fractional quantities together. 



Rule. Reduce the yiven fraction* to fraction* having a 

 common denominator if necessary / then add their numerator*, 

 it >i.l I'lace the turn over the common denominator. 



2 + 4 

 1G 16 "* " *""* """ "TflT 



oi 



EXAMPLES. (1.) Add 7a and , of a pound. 

 3 





of a pound. 



(2.) Add * and ^ together. 



Here, reducing them to a common denominator, they become 



1 **A be u *u . ad + bc 



- and - whence their sum is rj . Ans. 

 bd bd bd 



136. For many purposes, it is sufficient to add fractions in the 

 same manner as integers are added, by writing them one after 

 another with their proper signs. 



_ o 1 



EXAMPLE. Find tho sum of , -, and -_ 



by 2m 



_ o J 



Hero the sum is simply - -J . An*. 



b y 2m 



137. To odd fractions and integers together. 



Write them one after another with their signs ; or convert the 

 integers into fractions, reduce the fractions to a common denomi- 

 nator, and then add as before. 



EXERCISE 18. 



1. Find the Bum of - m and _ 2r+ d 



d 



2. Find the sum of - and - 



d 



3. Find the sum of - and 



V * 



4. Find the sum of - and 



o + b a I 



5. Add to -lA. 



d m r 



6. Add ~ 4 to L 6 . 



2 7-3 



4a 6c 



7. Add , , and together. 



b d 





8. Add,,and + together. 



2 y o a 



9. Add a + \, c + ?, zy, and a b together. 



10. Add 42 - ,a - , and a + togetLw. 



c Sx 3* 



f toother. 

 4o 



** * 



11. Add - *-Zl ,.f*y. 



2c c 2c zy 



12. Add2+,*L, M d - together. 



13. What is the sum of a and - t 



m 



14. What is the sum of 3d and - t 



' ' ,' 



15. What is the sum of 5* and a -*P 



SUBTRACTION OF FRACTIONS. 



138. Rule. Change the sign of the subtrahend, that is, oj 

 tin; fraction to be subtracted ; and then proceed a* in addition 

 of fractions. 



EXAMPLE. From ? subtract 

 o m 



Here, reducing the fractions to a common denominator, they 



_ ii_ 



become , and , Now, changing the sign of the subtrahend, 

 bm bm 



we have " m - ; then, proceeding as in addition of fractions. 

 bm bm 



we have ""* ^ 

 bm 



6* 



bm 



Ant. 



