IN BOTANY. 



IliT 



, of \\lii<-li 1'ilTo i- < ouipoaed are . 



i X 5 X 7 X 7X 11. 



. 19. 

 1 the greatest common measure of tho following 



.5 and 465. 5. 1*79 and 8425. 



un.l l.'7l. iidOO. 



7. 1*3, 3996, and 106. 



5471. 8. G7ii, 1440, and 3472. 



solve all tho composite numbers from 9 to 108 into their 

 prime factors. 



..solve into their prime factors 180, 420, 714, 836, 2898, 

 1 1 I'.'-J. 17i!8, 1492, 8032, 71640, 92352, 81660. 



.;! tho greatest common measure of the following 

 mnnl'i T.-i by resolving them into factors : 



. <W, and 108. | 2. 56, 84, 140, and 168. 



3. 5355, 6545, 17017, 36405, 91385. 



5. Find tho greatest common measure of tho following 

 numbers : 



1. 105 and 165. I 3. 110, 210, and 315. 



2. 108, 126, aud 162. | 4. 24, -Hi, 54, and 60. 



C. Find all the divisors common to tho following numbers: 



-, 21, and 36. 

 J. 1 1, js, u, uud 35. 

 3. 10, 35, 50, 75, and 60. 



4. 82, 118, and 146. 



5. -ki and 6C. 



7. Besolvo the following numbers into their primo factors : 



1. 120 and 14-1. 



J. i*0 aud 420. 



3. 714 and 836. 



4. 574 and 2898. 



5. 11492 and 980. 



6. 650 and 1728. 



7. 1192 and 8032. 



8. 4604 and 16806. 

 0. 71640 and 20780. 



10. 84570 and 65480. 



11. 92352 and 1660. 



That our readers may have sufficient practice in multiplication 

 and division, we give in this lesson upwards of one hundred 

 examples in these rules. The operations should be contracted 

 when practicable, and the correctness of every result should be 

 tested by the methods given in our Lessons on Multiplication 

 and Division. 



EXERCISE 20. 



1. Find the product 678954 X 72, by multiplying by succes- 

 sive factors. 



2. Find in the same way the product 78530700 X 1250. 



3. Find the product of the following by dividing by succes- 

 sive factors : 



1. 16128 



2. 25760 



24. 

 56. 



3. 91080 * 72. 



4. 123456 + 168. 



5. 142857 * 112. 



4. Divide 9643 by 30, by 300, and by 3000. 



5. Divide 3360000 by 17000. 



6. Divide 123456789 by 290000. 



7. Multiply and also divide : 



9. Divide one thousand billions by 81 and 729. 



10. Divide a thousand thousand millions by 111. 



11. Divide a thousand millions of millions by 1111. 



12. Divide 908070605040302010 by 654321. 



13. Divide 4678179387300 by the following divisors, sepa- 

 rately, 2100, 36500, 8760, 957000, 87700, 1360000, and 87000. 



14. If the annual revenue of a nobleman be ^637960, how 

 mnch is that per day, the year being supposed to be exactly 

 365 days. 



15. What is the nearest number to one thousand billions that 

 can be divided by 11111 without a remainder? 



1-:. II .w often could 43046721 be rabtnwUd from 



17. How many timM doe* 



A hat number U that which divided by 123456 would 

 given ;:>!, and a remainder ' 



I 1 .'. U .!:. tho following example* in multiplication: 



LESSONS IN BOTANY. IV. 



SECTION VI.-LEAVES CONSIDEEED AS TO THEIB 

 FUNCTIONS. 



ALTHOUGH leaves have a great variety of uses, yet the principal 

 is that of respiration or breathing. In this manner they become 

 the representatives of lungs in animal beings. But though 

 plants breathe, tho vegetable function of respiration in them is 

 not to be considered as similar to that function in animals. On 

 the contrary, it is directly the reverse : the very gas which 

 animals expel from their lungs as useless or injurious, plants 

 receive through the medium of their leaves, take out of it that 

 which is suitable to their wants, then exhale the portion which 

 is refuse to them, but which is necessary to the existence of 

 animals. What a train of reflections does the contemplation of 

 this beautiful provision call forth! Not only are vegetables 

 useful in supplying us with food and timber, not only do they 

 beautify the landscape with their waving branches and pic- 

 turesque forms, but they are absolutely necessary to the exist- 

 ence of animal life as a means of purifying tho atmosphere ! 



The breathing function of leaves is far too important to 

 admit of being lightly passed over with these few remarks, yet 

 a difficulty occurs in pursuing it further, inasmuch as to under- 

 stand the precise theory of vegetable respiration the reader 

 must be acquainted with certain facts in chemistry. Some 

 readers, doubtless, are acquainted with these chemical facts, 

 others are not ; consequently, the best plan will be to present a 

 slight outline of these facts at onoe. 



To begin, then : did the reader ever set fire to a bit of stick 

 or a little charcoal ? No doubt he has. What does the reader 

 think becomes of this stick or charcoal ? Is it lost, destroyed ? 

 Oh no, there is no such thing as destruction in all nature ; 

 substances, even when they appear to be destroyed, onlj change 

 their form. What, then, becomes of a piece of stick or a piece 

 of charcoal when we burn either in the fire ? Now, whenever 

 philosophers desire to study the conditions of an experiment, 

 and the choice of more than one set of conditions stands before 

 them, they very properly take the simplest. We have here two 

 sets of conditions ; the burning of a stick is one, the burning of 

 a piece of charcoal is the other. The latter being the simpler of 

 the two, we will take it, and use it for our purposes ; moreover, wo 



