THE HISTORY OF ART. 



I 



If, instead of dividing by 100010, we divide by 100000 (which is 

 done at ouoo by cutting off 5 decimal places to the right), wo 

 hall obtain a revolt which will bo very nearly correct, being, in 

 fact, too great only by nog&nD * tho 8um divided; 



for lanaa = ICHIB "*" ISOBKIBBM* 

 Now. 10 - 0400 farthings, and nujflgoro - roMMfarv - TiraVn. 



tuarly, 



Hence, to get our result correct to the nearest farthing, we must 

 from it OTjJgjo of a farthing for every 10 which occurs in 

 the original dividend. But since this dividend is 100000 times 

 the result, it will bo the same thing if wo rojoct 1 farthing, for 

 every JB10 in the result. 



Performing, then, this operation upon the above example 



s. d. 



i) 787132 12 



262377 10 8 



A) 26237 15 0| 



2623 15 6,* T 



10-78371 13 2JandiJf. 

 20 ' 



15-67433 

 12 



8-09198 



4 



36795 



The operation gives 10 15s. 8d., and therefore, rejecting one 

 farthing, since the result only contains .10 once, we find the 

 result correctly to a farthing to be 



10 15s. 7jd. 



06s. It does not necessarily follow that this method will be 

 really the most convenient when the interest is to be found for 

 a number of days. For instance, if the days reduce to a simple 

 fraction of a year, it will be best to proceed by the ordinary 

 method. The artifice is explained here as being a useful exer- 

 cise for the student, and as an ingenious method which it may 

 bo sometimes useful to employ. 



EXERCISE 55. 

 Find the interest upon : 



1. 1456 10s. Od. for 131 days at 5 per cent. 



2. 1000 for 201 days at 6 per cent. 



3. 1698 14 8 for 189 days at 5 per cent. 



4. 1476 8 6 for 20 days at 2J per cent. 



5. 847 12 6 from July 8 to Bee. 26, at 5 per cent. 



6. 987 18 9 from April 21 to Sept. 24, at 5 per cent. 



7. 7597 10 8 from May 6 to Aug. 21, at 5 per cent. 



COMPOUND INTEEEST. 



10. Where compound interest is reckoned, at the end of one 

 year the interest is added to the principal. This amount be- 

 comes the principal for the second year, and the interest upon it 

 for the second year must be calculated and then added to its 

 principal, and so on. The difference between the final amount 

 at tho end of a number of years, and the original principal, is 

 the compound interest. 



EXAMPLE. To find the compound interest for 3 years on 

 1 00 at 5 per cent. 



At tho end of the 1st year the amount is ... 105 

 Tho interest of this for the 2nd year is ... 550 



At the end of the 2nd year the amount is 

 The interest on this for the 3rd year is. 



. 110 5 

 5 10 



At the end of the 3rd year tho amount is ... 115 15 3 

 Hence tho compound interest gained in 3 years is 15 15s. 3d. 



"In finding the compound interest upon any sum, this is the 

 process which must be followed. It will therefore readily bo seen 

 that, when the number of years is large, and the principal and 

 rate per cent, complicated, the operation will bo very laborious. 

 All questions of compound interest are very much facilitated by 

 the use of Logarithms, of which, however, we cannot treat here. 



Tables of the compound interest upon jl, at different rates 

 per cent., and for different numbers of years, are constructed 

 for practical use. 



EXERCISE 56. 

 EXAMPLES IN COMPOUND INTEREST. 



1. Find the compound interest upon 350 for 3 years at 5 per 



2. Find the compound interest npon 555 10t. for 2 yean at 4J per 



i-i-lj! . 



1 tho different* between the simple and the compound iaterect 

 upon 250 for 4 yean at 6 per cent. 



4. Find tbti difference between the limpU and the compound i^MWt 

 upon 365 4*. Sid. for 3 yean at 4 per cent. 



1 the compound intenet upon 250 for 3 jean at S| per 



<!. t. 



6. Find tho compound interest upon 1040 for 3 jean at 4 per 

 cent. 



7. Find the compound interest npon 625 for 2 jean at 4 per oast. 



8. The difference between the compound and simple interact of a 

 sum for 3 yean at 4 per cent. is 19i. ; find the mm. 



[N.B. Find this difference for 100, and compare it with 19c.] 



9. I buy a field for 1000, for which I receire 30 a jear not, 

 which I invest as Boon as received at 4 per cent, compound interest. 

 At the cud of 3 yean I sell it again for 1030. What have I lost 01 

 gained by buying the field instead of investing the purchase-money on 

 the same terms as I did the rent ? 



THE HISTORY OF ART. 



XH. TITIAN AND THE ECLECTICS. 



FROM the days of Eaffael and Michel Angelo onward, the 

 history of art becomes mainly the history of the different 

 national or sectional schools into which painting was divided. 

 The general progress of all the fine arts grows too wide to 

 follow in detail, and it is therefore necessary to confine our- 

 selves to the great central art alone. Perfect technical mastery 

 of tho principles of painting had now been generally acquired. 

 After Raffael and Michel Angelo, the mere handicraft of the 

 artist could be taught almost mechanically, so that the veriest 

 tyro could draw with a wooden accuracy and a fidelity to life 

 which would have astonished the careful but undeveloped 

 mediaeval painters. The varieties that could now arise were 

 mainly those of a more delicate, intimate, and personal sort, 

 dependent not so much npon differences of technical mastery as 

 upon differences of taste or fancy. Every one could now learn 

 the principles of perspective, of anatomy, and of chiaroscuro 

 (or light and shade), but everybody had not the fancy, the 

 feeling, and the power of touching our higher and finer chords 

 which mark the really great painter ; for the artist works with 

 his brains and his heart as well as with his fingers. It was in 

 these matters of feeling and taste that the greatest differences 

 were henceforth to be noticed. Moreover, art now began to 

 split itself up into many classes or kinds. Hitherto we have 

 heard nothing of landscape, nothing of any kind of art not 

 religious ; and we have dealt with Italy almost exclusively, 

 leaving out of consideration Germany, France, the Low Conn- 

 tries, and England. Henceforth, however, we get, not a con- 

 tinuous stream of development in one country, but a divergence 

 of art into many separate linos. During the Middle Ages, 

 painting was all devotional in subject, and all given over to the 

 delineation of the human figure. From the days of the Renais- 

 sance onward it has gone on multiplying its subjects and its 

 aims in every direction. It has divided itself into historical, 

 domestic, landscape, still life, and innumerable other branches, 

 and each of these has been variously cultivated in various 

 countries and by various schools. It is obvious that we can 

 only glance very briefly here at the most important and most 

 characteristic of these. 



Even during the lifetime of Michel Angelo and Raffael, a 

 second great school of art, distinct from the Roman and the 

 Florentine, was growing up in Italy itself at Venice. This 

 school dated back into the Middle Ages, but it attained ripeness 

 at the same time as that of Florence. Tiziano Vecellio, whom 

 we in England ordinarily call Titian, was two years the junior 

 of Michel Angelo, being born in 1477 ; but, as he attained the 

 great age of ninety-nine years, he considerably outlived even 



