IN BO'l 





mult 



14018 



:< liu 



.irry niak<- 1 1 I 



numl" -ni", by iiiriiiis of the follow 



:; 6. 



Multiply 83 by 7 ; 549 by 5 ; 6879 by 9 ; 7S91011 by 8 ; 

 567K i 7 1 .y 1 1 , and tlio result b . 



-ocluct of 1, L'. ::. ;, 9. 



i ind ill.- pmdurts of tho number 1 ' 

 I ind the products of the number 98998, the .--mall.--! num- 

 :iin.'d iii ihr : -i-. ,u Kx. 4, page '2-> 



digit-*. and \n;i will ihi<l these product- in the same table. 



(5.) Multipl, >:,71-iL' by 9; 7;s7i;s ( .!S l.v:'; lulu !nm;.iO by 7 ; 

 7980" .-m.l !ni'.)i)!i!i:t!^;t:):t i, y 5. 



(6.) Multiply tho following numbers first by 2 ami then by 3: 



vii Ihu M 



1046. 



. i-a.-ii', the I. (nested 



ba process of multiplying any 









in. L' 



11. .!_- 



following numbers first by 4 and then by 5 : 







8. 4039007 





(8.) Multiply the following numbers first by 6 and then by 7: 



:nt:;7 i 



11. 12 

 23 '.'. 



(9.) Multiply the following numbers first by 8 and then by 9 : 





4. 995323 



5. 201567 



7. 6778899 

 9. 9315925 



10. 7: 



11. (i:: 



12. 8'.' 1 



(10.) I have a box divided into two parts ; in each part there 

 are thr in each parcel there are four bags; in each bag 



>v live marbles. How many marbles are them in the box:- 

 (11.) Then- :nv MX farmers, each of whom has a grazing farm 

 .'h field has eight corners, and in each corner 

 there arc nine sheep. How many sheep do the farmers own, 

 and how many aiv fYrdhr.; on their farms ? 

 ' Case 2. To multiply i!7r, by :i37 : 



a ;;t0 + 30 + 7" if we multiply G75 by 7, by 30, 

 and by 800 t rely, we shall obtain the required product. 



Arrange the work as in operation (1) : 



(1.) C2.) 675 



337 



1785 - 875 



= ,75 

 675 



7 

 30 

 300 



Hence 227175 = 675 x 337 



472S 



2025 

 2025 



L"-7 175 



In working by this method it is unnecessary to write down 

 the one nought at tho end of the second line, and the two 

 noughts at tho end of tho third line, etc., as in operation (1), if 

 we only place each lino ono figure to tho left of tho one pre- 

 ceding, so that the work appears as in operation (2) : 



The above examples will be snflV plain the truth of 



the following 



Rule for M" ''{plication. 



(1.) When tho multiplier consists of one figure, write it down 

 under tho unit's place of the jnult'plieand. Begin at the right 

 hand, and multiply each figure of tho multiplicand by tho multi- 

 plier, setting down the result and carrying as in addition. 



Wli< n tho multiplier r.on-Ut-; of more than ono figure, 

 write down tho multiplier under tho multiplicand, units under 

 unit*. : ;<. Multiply each figure of tho multipli- 



cand by each figure of the multipn 

 tho units, and writ'- tin- r,idu"t- <0 obtained i:i separate lines, 



bo con 

 remark 



ftn fignx* of each lino directly under the figure bjr 

 .g tbfiM linen together, tbtir 



i uunilx-r. 



.Multiply th 



. and if tl ;iiM obtoined 



.1 > thu othi-i j.o work majr bo prwooMd to 



reverting Hut 



uon may be 



It m*y b 



ifl, tho <; uid figure) of UM 



<>f with tb*1 icmac, 



. T, as will be teen from an ei - 

 ou>:)i line ono figure to the right oi 



. 08 in op 



"f th(; mil 

 wo might, to 



mast c-t down 



which v. ,- on 



2740714 



, , 



2740714 



:ro added in the last operation, to 



explain tlio truth of tl o process. 



EXEJICIK 

 (1.) Find the products of the following nmnben: 



18. 15346B3 x 4702 



19. 142857 x 70000 



20. 7050680 x 70308 



>(8050 x 97280 

 23. 53COOOOO x 75300 



21. 09999999 x 90000 



25. 6785C3 J090 x 1000000 



26. 39599256S3 x 7060001 



27. 7684329009 x 100007 



28. U2S573893 x 987CSt 



29. 9698506085 x 2468103 



7 x 7065841 

 X) x 100101000 



x 45 



x 80 

 x 90 



5. 75 x 42 x 56 



6. 84 x 37 x 69 



7. 710S x 256 



8. 93186 x 445 



9. 99999 x 999 



468 



11. 7';-s5.1 x 830 

 700 



13. 3851 x 3854 x 3854 



9584 



7 71 



9999 



?2. 7070808090 x 00908070 



33. 300010003000 x 400100020000 



(2.) Multiply 2354 by 6789, and 23789 by 3G5, by reversing 

 the multiplier. 



(3.) Multiply 857142 by 19, by 23, by 48, by 97, by 103, by 

 987, and by 



(4.) Find tho products of the number 98998 by all the numbers 

 from 11 to 49 inclusive. The 1 be found in the second 



Bqnare given in Ex. 4, page 23, on Addition. 



LESSONS IN BOTAXY. II. 



SECTION II. ON THE : ATIOK OF 



VEGETABLES. 



THE observer who takes a survey of the various members of 

 the vegetable world becomes cognisant of at least one promi- 

 nent distinction between them. Ho soon perceives, that whilst 

 certain vegetables have flowers others have not ; or perhaps, 

 more correctly speaking, if the second division really posaeM 

 flowers, they are imperceptible. 



This distinction was first laid hold of as a basis of classi- 

 fication by the celebrated Linnaeus, and to thi extent the 

 classification adopted by that groat philosopher was strictly 

 natural : beyond this, however, it was altogether artificial, aft 

 we shall find hereafter. 



Now. taking advantage of this distinction, the great Swedish 



naturalist termed the evident fit .\\vringveiret:! 



from the Greek word ' "p>w; or, 



it, tr.>;;i t:.- i;rek word .jxu-fpo'i (phan'-er-ot), 



: and ho designated the non-floworinp, or more, correctly 



speaking, the non-evidont flowering plant-", by tho word crypto- 



from the Greek word rpvirr<$j (tr -.Yikd. The 



further 'ion of Linnseus was artificial, as we have 



1. Tho nature of this classification wo cannot 



study with advantage ; 'iercafterwo shall proceed to 



explain the principles on which it was based; bnt is these 



