LESSONS IN FRENCH. 



Six in 56 (in the took of 8) is six in 5 x o T 3, or 46, that U, 7 and 4 over. 

 .-., HI m,m tho settle of 8) is six in 4 x 8 + 4, or 30, that ii, 6 and over. 



Six in 3 I* and 3 over. 

 Biz in 35 (in the scale of 8) U six in 3 x 8 + 5, or 20, that U, i and 5 over. 



A ud similarly for tho other lines. 

 This operation, in fact, proven that 



+3x8 + 5 



3x6* 



6. One application of the duodecimal scale ia very useful in 

 ordinary practice. 



In finding areaa and cubical content*, as we showed (Lesson 

 XVIII, Arts. 7 and 8, Vol. I., page 292), we have to multiply tho 

 numbers indicating the dimensions together. Now, since 1 foot is 

 12 inches, any dimension given in feet and inches can bo at once 

 written down in the duodecimal scale. Thus, 5 feet 9 inches 

 would bo written 5'9, putting a point after tho 5 to express that 

 tho 9 is fa of the unit, for tho same reason that, in the decimal 

 notation, we place a decimal point before the tenths' place. 



Now suppose we have to find the dimensions of a board, tho 

 length of which is 5 feet 9 inches, and breadth 4 feet 5 inches, 

 we should have to multiply 5'9 by 4-5 in the duodecimal scale. 



This would be done as follows : 



5-9 

 4-5 



24-9 

 1)0 



21-49 



We say 5 times 9 are 45 ; that is, 3 X 12 + 9. Write down 

 the 9, and carry 3. 5 times 5 are 25, and 3 are 28, which is 

 2 X 12 + 4, and we therefore write down 24. 



Again, 4 times 9 are 36 ; that is, 3x12, or in the duo- 

 decimal scale, 30. Write down the cipher, and carry the 3. 

 4 times 5 are 20, and 3 are 23, which is 1 X 12 + 11 , or, in 

 the duodecimal scale, le, which we write down. 



Adding, we get 9 ; 4 ; e and 2 are 13 ; that is, 1 X 12 + 1. 

 Write down 1 and carry 1 ; 1 and 1 make 2. 



The result, therefore, is 21 - 49 in the duodecimal scale. 

 Now, 21 is 2 X 12 + 1, or 25 in the decimal scale ; and 49 is 

 4 X 12 + 9, or 57 in the decimal scale. 



Hence, the answer is 25 sq. feet 57 sq. inches. 

 7. We can verify the process by fractions : 

 5 ft. 9 in. = 5J ft. 

 4 ft. 5 in. = 4& ft. 



Hence the area of the board = 5J x 4/jsq. ft. = ^JJ* sq. ft. 

 48 ) 1219 ( 25 sq. ft. 57 sq. in. 

 96 



N.B. It will assist the learner, 

 in multiplying, adding, etc., in 

 the duodecimal scale, to re- 

 collect that it is exactly the 

 same process as multiplying 1 and 

 adding pence, and reducing 

 them to shillings. Thus, in the 

 above example, we might say : 



__ 5 nines are 45, that is, 3 and 



336 9 pence; 



336 



48 ) 2736 

 240 



fives are 25 and 3 are 



that is, 2 and 4 pence. 



And so on. 



28, 



8. EXAMPLE 2. Find the cubical contents of a room which 

 is 25ft. 9 in. long, 14ft. 4 in. broad, and 16 ft. 4 in. high. 



25 ft. 9 in. = 21-9 in the duodecimal scale. 

 14 ft. 4 in. = 12-4 



16ft. 4 in. = J4-4 



21'9 



12-4 



870 

 436 

 219 



269-10 

 14*4 



35U-440 = 6028 (Tib. ft. 684 cub. m. 



The tame Example worked by fraction*. 

 The contents in oubio feet is 

 25{ x ui x IGJ = ij x Y * V " *41*. 



36 ) 217021 ( 6028 cub. ft. 

 216 



102 

 72 



801 



3 ) 2*404 ( 624 oub In. 



tie 



n 



144 



144 



13 * 1728 = 22164 



Ant. 6028 cub. ft., 624 cub. In. 



KEY TO EXEBCISE8 IN LESSONS IN ARITHMETIC. XLU. 

 EXEECISK 62. 



19. 8l! grains. 



20. 281-973. 



21. 3s. 2d. 



22. 46 taels 1 mace 2 



cands. 5 cash. 



23. 391 Ibs. 11 oz. 7-296 



drams. 



24. 25 it. 50 cento., 

 nearly. 



25. 78 18s. 9jVd. 



26. 146 thalers 

 groschen. 



27. 13423 francs 

 centimes. 



28. 939 florins 87! 



kreutzers (100 



kreutzers being 



equivalent to 1 

 florin) . 



1. 9 12i. 2f,d. 



2. 5306 farthings. 



3. 4 19s. 



4. 9 days. 



5. 68} Ibs. 



6. 2926. 



7. 36 19s. 2|d., or 

 4Js. per yard. 



8. 76 10s. Id. 



9. French metre is 

 3-2204 Rhenish 

 feet. 



10. 1800 Ibs. 



11. 31JJ? chaldrons. 



12. 29061S. 



13. 836jV,yds. 



14. 285 cwt. 2 qrs. 

 24 Ibs. 



15. 388 dishes 53} Ibs. 



16. 14. 



17. 818 T V. 



18. 149 14s. 9>d. 



9ft 

 41 



29. 1127 florins 85 '12 



30. 



kreutzers. 



shillings. 



31. 15463 grrs. approxi. 

 mately. 



32. H 



33. llll 



34. 126-295 sovereigns. 



35. 6 thalers 20 gros., 

 nearly. 



36. 9 florins 52 kreutz. 

 nearly. 



87. llfWr florins. 



38. 24| francs. 



39. 16marks3schUls., 

 nearly. 



40. The fixed number 

 for (36) (37) (38) 

 (40) is HH. and 

 for (39) W. 



41. 25 fr. 63 cents., 

 nearly. 



42. 4 reis 50 mil-reis., 

 nearly. 



43. 4-29 mil-reis. 



44. The number of pence received for a dollar in each of the five 



Hence th 3 4th way is the most advantageous. 

 45. About 11 francs 82 cents, per oz. dearer in Paris. 



LESSONS IN FRENCH. XLVL 



SECTION CII EXAMPLES ILLUSTRATING THE VABIOUS 

 USES OP THE PRINCIPAL CONJUNCTIONS. 



A MOINS QUK. 



It n'en fera rien, a moins que vous 



ne lui parliez. 

 A moins que vous ne preniez bien 



votre temps, vous n'en viendrez 



pas a bout. 

 Quel indigne plaisir peut avoir 



1'avarico ? 

 Et que sert d'air.asser, a moins 



qu'on en jouisse ? 



BOURSAULT. 



Aussi ils n'ont aucune force pour 

 le possoder surement 



PASCAL. 



Ma douleur serait trop miSdiocre, 

 si je pouvais la ddpeindre ; aussi 

 je ne 1'entreprendrai pas. 



MME. DE SKVIONK. 



He will do nothing of the kind, urdeu 



you speak to him. 

 Unless you chooso your HTM veil, 



you will not accomplish it. 



What unworthy pleasure can avarice 

 of erf 



What it the use of hoarding up un- 

 to* we enjoy / 



Therefore, they have no strength to 

 potMM it safely. 



Jly grief would bt too trying if I 

 could depict it ; o that I will not 

 undertake it. 



C'est ce qu'il y a de plus sage ; au 

 reste, c'eat aussi de qu'il y a de 

 plus juste. MABMONTEL. 



AU EESTK. 



Thu it Oit wiMst way ; 6*id, tt ii 

 al*o the tnoet just. 



CAB. 



Voila les perils, voici le moyen de 

 les Writer ; car eufin, le bras de 

 Dieu n'est pas raccourci. 



MASSILLON. 



Thoce are the danger*, (Ate u tte %Mf 

 of avoiding them ; /or >naUy, tAe 

 influence of God it not U power- 



M 



