

ono part i over or umW :un>tli.T. \V.- bare dr:n\n 

 in tli.-i.l'. itration how the varioua iliri:<:ti<ms in which 



tin- 1" u. -.1 might !> !'! I l>-tw.--n tlio oyo and tho objoot, and tho 

 .; how tin! |.:n-i ; uroploood in connootion 



with c;icli ..tluT. 



LESSONS IN AIMTHMKTIO. XXXIX. 



AVI:I:A(;I:S. MIXHI;I:S IN CERTAIN 



I'LoroK'l i 



' piii-tinT-; li.tM- iiivr>lrd ililfi'tvnt sums in ;ui under- 



taking, it is niiiuiiV-'t that tho profits or losses munt lie divided 



: linii in iirojHirtiim to tin: capital each has invested in 



. if tho capital of each has been in OHO for tho same 



time. 



Tim method by which tho share of each is determined in thin 



case is called l':ilowship. It w manifestly tho Homo as 



that given in Lessons in Arithmetic, XX., on Ratio and Propor- 



\rts. 7, 8 (Vol. I., page 343), whore a given number is 



divided in proportion to certain others. 



EXAMPLE. A, B, and C put into a business .300, J3500, 

 and .800 respectively. At the end of a year they have gained 

 JC I"". What is tho share of each ? 



Wo have to divide 400 in the proportion of 300, 500, 800, or, what 

 is the same thing, iu tho proportion 3, 5, 8. 



According to Lessons in Arithmetic XX, Art. 7, since 3 + 5 -t- 8 = 

 16, we divide 400 into 16 equal parts, each of which is 25. 



Tha respective shares of A, B, and C will be 75, 125, and 200. 



2. If tho sum invested by each partner is not used for the 

 eamo period of tirno, so that wo have to take into account not 

 only each sum, but tho time during which it is employed, tho 

 case is called one of Double or Compound Fellowship. 



EXAMPLE. A, B, and C contribute to a business as follows : 

 A puts in .1,200 for three months, B .1,000 for six months, 

 and C .800 for twelve months. How must they divide a profit 

 of .800 ? 



A's 1,200 for 3 months is the same as 3 x 1,200, or 3,600 for 1 

 month. 



B's 1,000 for C mouths is tho same as 6 x 1,000, or 6,000 for 1 

 mouth. 



C's 800 for 12 mouths is tho same as 12 x 800, or 9,600 for 1 

 mouth. 



Hence the shares must be in the proportion of 3,600, 6,000, 9,600 ; 

 {.., of 3, 5, 8. 



Henco, proceeding as in Simple Fellowship, the shares will be 

 respectively 



ft800, T*r800, , s 800 ; that is, 150, 250, 400. 



This example sufficiently explains the following 



Rule for Compound Fellowship. 



Multiply each capital by the number of units of time for 

 which it is employed ; the shares will be in the proportions of 

 these products, and will be determined as in a case of Simple 

 Fellowship. 



EXERCISE 60. 



1. A traveller divided 80s. among 4 beggars in such a mam.jr that 

 as often us tho first received 10s., the second received 9s., tho third 8s., 

 and tho fourth 7s. What did each receive ? 



2. A, B, and C engage in business, putting in respectively 3,500, 

 5,000, and 6,000. What would be the share of each out of a profit 

 of 1,000? 



3. A, B, and C contribute respectively to a speculation 160, 240, 

 and 4#0, and they gain 264. What will be the share of each ? 



4. A, B, C, and D embark in a business, and put in respectively 

 2,000 for 6 months, 1,500 for 9 months, 1,000 for 12 months, and 

 750 for 15 months. If at the end of 15 months the profits are found 

 to be 1,000, how must they bo divided ? 



5. A and B form a partnership for a year. A contributes 5,000, 

 to which at the end of 6 months ho adds 1,000 more ; B contributes 

 6,000, and at the end of 9 months withdraws 2,000 from the busi- 

 ness. How must they divide a profit of 1,500 at the end of the year? 



6. A, B, and C form a partnership ; A contributing 1,000, B 2,000, 

 and C 3,000. After 9 months C withdraws, and after 3 months more 

 D is admitted to the partnership, contributing 1,500. At the end 

 of 18 months, the partnership being dissolved, the profits aro found 

 to be 900. How must they be equitably divided ? 



KEY TO EXERCISES IN ARITHMETIC. XXXVIII. 



EXERCISE 58. 



1. 0) 3jJ years. () 3} years. I 3. 68*'' days. 

 S. ( l ) UAWrt m. () HJSfm. | 4. 5 years. 



GREAT BOO Is 



XIII. THOMSON'S SEASONS." 



IT is customary to speak of Thomson as a Scotch poet ; bnt 

 it would bo difficult to give a more inexact description of hiic. 

 The poet of " Tho Seasons " was born in the neighbourhood of 

 Kelso, in Roxburghshire, a few miles beyond the English border. 

 His mother was tho daughter of a Mr. Trotter, of Foggo, 

 in Berwickshire ; so that he appears to have belonged entirely 

 to that south-eastern part of Scotland which is English in 

 population, and at ono time formed a portion of the kingdom 

 of Northumberland. Thomson wrote all his poems in pure, 

 classical English either tho scholarly English of Milton, aa 

 in " Tho Seasons " and most of his other works, or the some- 

 what archaic English of Spenser, as in "The Castle of 

 Indolence." His mind does not seem to have had any Scottish 

 leanings, such as were powerfully developed in Allan Ramsay 

 (a contemporary of Thomson), Burns, Sir Walter Scott, and 

 several others. His patriotism, as evinced in such poems as 

 " Britannia " and " Liberty," was distinctly British and 

 Imperial, without any reference to the particular quarter of 

 tho realm within which he had himself been born ; and it may 

 bo doubted whether Thomson would not have regarded " an 

 auld Scots song," or a new one either, as anything better than 

 a piece of provincial barbarism. He came to London at 

 twenty-five years of age, and it does not appear that he ever 

 returned to Scotland. Thomson must therefore be reckoned 

 among the English poets, even though " Scotia," in the lan- 

 guage of Burns, may, " with exulting tear," proclaim that he 

 was her son. 



When tho young genius arrived at London, in 1725, ho 

 brought with him some fragments of the poem on " Winter," 

 afterwards forming part of " The Seasons." He was advised 

 to combine these into one connected piece, and to get it printed 

 forthwith. On the poem being completed, it encountered the 

 usual difficulties which beset the productions of unknown 

 authors. For awhile, it could find no publisher ; but at length 

 it was sold at a low price, and issued in 1726, with commen- 

 datory verses by Hill, Mallet, and a lady who wrote under the 

 fictitious name of "Mira." In the first instance, it fell still-born 

 from tho press ; but, chancing to please an influential gentleman 

 of taste in those days, named Whateley, he literally brought it 

 into fashion by praising it wherever ho went. Repeated editions 

 were called for, and Thomson suddenly found himself the 

 happiest and proudest of men, a successful poet. That was the 

 ago of patrons ; for, although there was a book-baying public, 

 it was not considered safe to rely on the general body of readers 

 without the protection of some great man, whose favour was 

 usually procured by a fulsome dedication. Thomson inscribed 

 his "Winter" to Sir Spencer Compton, who, however, took no 

 notice of tho author until his friend Hill published in a news- 

 paper some verses to Thomson, in which ho rebuked the great 

 for their neglect of genius. The conscience-stricken Sir 

 Spencer immediately sent the poet twenty guineas. 



The poem on '"Summer" followed in 1727 ; "Spring" was 

 published in 1728, and " Autumn " in 1730. The four divisions 

 make up the work which we know as "The Seasons," but 

 which in fact arose in the fragmentary way we have just related. 

 If we had had regard simply to intrinsic qualities, we should 

 not have included Thomson's " Seasons " in our list of " Great 

 Books." Pleasing and attractive as the poem is in many 

 respects, it is not great in any true sense of the word. A poem 

 which consists almost entirely of description, which contains 

 neither story nor exposition of character, which is concerned in 

 nono of the grand passions of human nature, and which results 

 from the power to observe, rather than from the power to 



