which is wrapped about the seed much more closely. On Barley is grown to almost as great an extent as wheat; more one side of the grain a groove particularly in the East, as in Egypt and Syria, where it forms Wheat is very widely dif- other grain. In the mountainous parts of Scotland, and the Fig. 7. in any region of the earth, Germination of plants. attests the civilisation of thán. In the sepulchres of the Egyptian kings, for example, the common wheat was found in vessels so perfectly closed, that the grains retained their form and colour ; and as the cornplants do not grow wild in any part of the earth, and appear Fig. 6. the branches arrange themselves round the centre of the steni; but as they advance towards maturity, and acquire weight, they generally bend over on one side. Thus, a beautiful provision is made for the health of the plant. For now the air and light can visit it freely, and the rain may wash every individual grain, and preserve it from the seeds of any destructive plants. And then, as the grains are pendent and have the open extremities of the chaff towards the earth, they are effectually defended from the lodgment of rain within-an advantage which neither wheat nor barley possesses, and hence are liable to diseases from which oats are exempted. Such, then, is a brief description of some of the cultivated grasses, which have become so familiar, and so valuable as corn; and we may conclude the present lesson with an interesting and instructive anecdote related by Pliny. Cresinus, á Roman, was cited before an assembly of his people, on a charge B of sorcery, from his reaping much larger crops than others A from a small piece of ground. In answer to the charge, Cresinus produced his implements of husbandry, his well-fed Barles oxen, and a hale young woman, his daughter, and pointing to as they do under culture, they show as clearly the civilisa- them, he exclaimed, « These, Romans, are my instruments of tion of that country, as its temples which are now in ruins. witchcraft; but I cannot here show you my labours, sweats, and anxious cares." And so it is in many other instances. We see the result, it may be with pleasure or astonishment, but the skill-the toil that secured it, is hidden from our view. Let us remember, however, that nothing valuable is gained without effort, and that labour, wisely directed and perseveringly employed, will achieve what many would regard as absolutely impossible. LESSONS IN ARITHMETIC.-No. VII. RULE OF SIMPLE MULTIPLICATION-Continued. WHEN the multiplier and multiplicand consist of several significant figures, then proceed according to the following rule. Rule 4.-Place the figures of the multiplier under those of the multiplicand, as in addition or subtraction, so that units shall be under units, tens under tens, &c., and draw a line under it as before. Then, multiply all the figures of the multiplicand by the units' figure of the multiplier, and place the product under the line, as directed in Rule 1; next, multiply all the figures of the multiplicand by the tens' figure of the multiplier according to Rule 1, and place their product under the former, taking care to observe that as it is the product of tens, a cipher either expressed or understood should stand under the units of the preceding product, then the tens under the tens, the hundreds under the hundreds, &c. Again, multiply all the figures of the multiplicand by the hundreds' figure of the multiplier according to Rule 1, and place this product under the preceding one, observing that ciphers, either expressed or understood, should stand under the units and tens of that product, then the hundreds under the hundreds, the thousands under the thousands, &c., as before. Proceed in the same manner, multiplying all the figures of the multiplicand by the successive figures of the multiplier, and placing the successive products under each other, preserving them in their proper places, by ciphers, either expressed or understood, until the last product is obtained. Then, draw a line under the last product, and add together all the products thus obtained, when the sum will be the complete product of the multiplicand by the multiplier. The general principle of this rule is that the product of two numbers is equal to the sum of the products of the one number by the several parts of the other number. EXAMPLE 1.-Multiply 234567 by 376. Factors Multiplicand 231567 2. Find the products of the number 98998, by all the numbers from 11 to 49 inclusive, and the answers will be found in the table given in Exercise 6, page 58, No. IV. 3. 70508 x 70508; 1010101 × 20202; 14:857142857×7777. 99999×999; and When the factors have insignificant figures in both; or, in other words when the multiplicand and multiplier both terminate in any number of ciphers, proceed according to the following rule: Rule 5.-Multiply the significant figures of the factors as directed in Rule 4. Then, to the product annex as many ciphers as are annexed, both to the multiplier and the multiplicand; that is, to both factors. Should one of the factors have no ciphers annexed to it, then annex only as many as are found annexed to the other factor. The principle of this annexation of ciphers has alread been explained under Rule 3. EXAMPLE 1.-Multiply 4076800 by 307000. Factors Multiplicand 4076800 307000 Product 1251577600000 Here the product of the significant figures is 40768×30712515776; to this five ciphers must be annexed, because 100X 1000=100000, and 12515776×10000=1231577600000. EXERCISES. 1. Multiply 10101001000 by 100101000. 2. Multiply 707080800 by 909090000. 3. 300010003000×400100020000. PROOF OF MULTIPLICATION. Generally speaking, the best proof of multiplication is to reverse the position of the factors; that is, to make the multiplier the multiplicand, and the multiplicand the multiplier. As this process, however, would be both awkward and tedious in some cases, especially in its application to Rules 1, 2, and 3, a proof founded on the principle of Rule 4,-viz., that the product of two numbers is equal to the sum of the products of the one number by the several parts of the other number, is to be preferred. We proceed to show the application of this principle to rules 1, 2, and 3. 285376 122304 Taking the first example in Rule 1, we find that the multiplier 8 is composed of two parts, say 5 and 3; then, multiplying the multiplicand separately by each of these parts, and adding the partial products, we shall have the same result as if we multiplied by 8. Thus : 1st partial product 163840 2nd partial product 98304 Now taking these partial products and adding them together as follows, we have the complete product; thus: 1st partial product 163840 400 Complete product 262144 As this product agrees with the former (page 94, No. VI.), the proof must be considered complete. Again, taking the first example in rule 3, we find that the multiplier 900 is composed of 400 and 500; then, multiplying the multiplicand separately by each of these parts and adding them as before, we shall have the same result as if we multiplied by 903 Thus :Multiplicand 78912345600 1st multiplier 78912345600 32768 Multiplican 1 2nd multiplier 1st product 31564338240000 2nd product 8915617280000V Adding these partial products together, we have the complete product, as follows: 500 1407402 units' product 16419690 tens' product 70370100 hundreds' product 88197192 Partial products Complete product NOTE.-If ciphers occur as significant figures in the multiplier, it is not necessary to put down a line of ciphers as the product of the figures of the multiplicand by the cipher of the multiplier; but merely to place the part al products in their own proper places, without regard to the cipher or ciphers which may occur in the multiplier. EXAMPLE 2.-Multiply 3070809 by 20306. Multiplicand 3070809 20306 18424854 units' product 6141618 tens of thousands' product Partial products { Complete product 62355847554 EXERCISES. 1. Multiply 857142 by 19; by 23; by 48; by 97; by 103; by 987; and by 4567. 1st product 2nd product 31561938240000 Complete product 71021111040000 This product being the same as before (page 95, No, VI.), the proof is complete. Lastly, taking the first example in rule 4, and inverting the multiplier and multiplicand, we find the product as follows: 1 2 4 5 376 Multio .er = Product 88197192 The product or result here also, being the same as that formerly obtained under Rule 4, the proof is complete. The same principle as that adopted in the two preceding examples of proof may be followed in this example also; thus, separating 376 into any two parts, as 244 and 132, the partial products of the multiplicand by these numbers, will stand as follows: 3 3 6 2 20 1 2 3 4 + 2632 2256 co 1880 1504 1128 752 8 12 16 10 15 20 12 7 14 2 3 4 6 8 6 7 8 9 9 18 27 36 10 11 11 22 33 33 44 12 12 24 36 48 13 14 15 16 16 17 18 19 5 6 7 10 12 15 18 20 21 25 30 24 30 36 28 35 42 49 567 8 16 24 32 40 48 56 45 54 63 10 20 30 40 50 60 70 44 55 66 77 Besides various other uses to which this table may be applied, we shall point out four of considerable importance to the trading community. The vertical (upright) or horizontal (from side to side) column containing the products of 12 by all the numbers from 1 to 20, will be an excellent substitute for a pence table. If we take the vertical column of the products of 12, then the number of shillings, answering to any number of pence in this column, will be found in the first vertical column, on the left hand. Thus, if you wish to know how many shillings are in 204 pence, look down the column having 12 at the top, for the number 204, and in the same horizontal line with it, on the left, in the first vertical column, stands 27, the number of shillings. The column containing the products of 20, by all the numbers from 1 to 30, will be a substitute for a shillings' table. If we take the vertical column of the products of 20, then the number of pounds, answering to any number of shillings in this column, will 8 9 10 11 12 13 14 15 16 17 18 19 20 12 14 16 18 20 22 24 26 28 ვე 32 21 28 32 36 40 44 48 52 56 95 100 85 90 84 90 56 63 70 77 84 91 98105 112 119 126 133 140 64 72 80 88 96 88 96 10 104 112 120 128 136 144 152 160 90 99 108 117 126 135 144 153 162 171 180 2nd product 30962814 8 9 10 11 12 13 14 15 16 17 18 19 20 Complete product 88197192 The complete product here being the same as the preceding, the proof is again complete. To obtain the parts of a multiplier for this process, take any number less than the multiplier, for the 1st part; and subtract the 1st part from the multiplier, and you will obtain the 2nd part; then proceed as above. 72 81 80 90 100 110 120 130 140 150 160 170 180 190 200 83 99 110 99 110 121 132 143 154 165 176 187 198 209 220 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 | 247 | 260 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280| 15 30 45 60 105 120 135 150 165 180 195 210 225 240 255 270 285 300 75 90 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380 76 95 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 | 400 As it may be of considerable use to many of our arithmetica. readers, and may save a great many small calculations, we add here an extended multiplication table. 469134 703701 234567 34 36 38 40 54 57 60 68 72 76 80 be found in the first vertical column, on the left hand. Thus, if you wish to know how many pounds are in 340 shillings, look down the column having 20 at the top, for the number 340, and in the same horizontal with it, on the left, in the first vertical column, stands 17, the number of pounds. The column containing the products of 16 by all the numbers from 1 to 20, will be an ounces' table. If we take the vertical column of the products of 16, then the number of pounds (weight), answering to any number of ounces (avoirdupois) in this column, will be found in the first vertical column on the left hand. Thus if you wish to know how many pounds are in 224 ounces, look down the column having 16 at the top, for the number 224, and in the same horizontal line with it, on the left, in the first vertical column, stands 14, the number of pounds (weight). Lastly, the column containing the products of 14 by all the numbers from 1 to 20, will be a pounds' table for stones. If we THE CIRCULATION OF THE BLOOD. take the vertical column of the products of 14, then the number of In a chemical point of view, the blood represents the whole stones (weight) answering to any number of pounds in this column, body in a liquid state, since the blood contains all the elements will be found in the first vertical column on the left hand. Thus, which enter into the human frame, and which are combined in if you wish to know how many stones are in 238 pounds, look the form of albumen, febrine, colouring matter, fat, and salts, down the column having 14 at the top for the number 238, and in It is owing to this composition that the blood is fitted to the same horizontal line with it, on the left, in the first vertical furnish the materials of growth and increase to every individual column stands 17, the number of stones. part. But while it furnishes the materials of nutrition to DEFINITION.-When a number is multiplied by itself, the pro- every part of the body, it sustains itself a positive loss; and this duct is called the square of the number. Thus, when we say 9 loss must be continually made up, otherwise the blood will no times 9 are 81. the number 81 is called the square of 9. The longer be fitted to minister to the nutrition of a single part. name square is borrowed from applied geometry, because in finding If every tissue in the body is taking from the blood that which the area of a square, the length of whose side is given, we multiply is adapted to support and preserve itself, then we must restore this length, given in numbers, by itself, and the product is the area. to the blood that which it has lost. This we do by the food Thus, if the side of a square was 6 feet long, the area of the square which we eat, and the air which we breathe. would be 36 square feet; because 6x6 = 36. If the loss which the blood sustains is to be made up by our The table given above contains, diagonally (that is from corner to taking food, then the food itself must undergo certain changes. corner) from the blank corner to 400, in the last square on the right, The first change takes place in the mouth. Why has the great the squares of all the numbers from 1 to 20. The square of Creator furnished the mouth with two rows of teeth? Though any number is found at the place where the vertical and horizontal essential to beauty, they were given not for ornamentonly, but for columns, that contain the number, meet. Thus, the square of 12 use. Most articles of food require to be masticated or chewed. is found by running the eye down the column having 12 at the top, And for this a beautiful provision has been made in the teeth, till it come to the horizontal column having 12 at the beginning. of which we have sixteen in each jaw. Four of these are The square of 12 is thus found in the table to be 144. placed in the front, and are called INCISORS, from their power of cutting or dividing the food; two are named CANINE or dog. like teeth; and the other ten are known as molars or grinders. LESSONS IN PHYSIOLOGY.-No. IV. MAN. Plants have no blood, but they have a circulation. In the leaf, the ascending sap undergoes such an elaboration or preparation as adapts it to the nourishment and growth of the plant; and from the leaf, there is a network of small vessels, which runs along the branches of the stem and roots, and by which the sap is thus conveyed In the act of chewing, the food becomes mixed with the SALIVA to every part, till it is all but entirely exhausted by the dif. of the mouth, which partakes of an alkaline, and so reduces ferent tissues through which it has circulated, taking up into it into a kind of pulp: Till it is so reduced, it is not in a fit themselves all its nutritive matter. The only condition neces- state to pass into the stomach. In the stomach the gastric sary for the life and increase of the lowest plants, is, that they juice should have access to every particle of matter that passes be in immediate contact with the two elements of air and into it; but this is impossible unless there be a thorough ad. water. Their whole substance is nourished by means of the mixture of the food and the saliva in the mouth. Persons who fluid which surrounds them. Take, for example, the sea- eat fast never sufficiently chew their food; being imperfectly weej-every part of its soft external surface being equally in chewed it never becomes thoroughly mixed with the saliva : contact with the water, every part of the weed takes from the and passing into the stomach in this state, it never surrounding fluid, and assimilates whatever is suited to itself. digests as it ought, and hence such persons are doomed It is only, as we ascend the scale of animal life, that we find pro- to suffer all the horrors which arise from indigestion. vision made for circulation ; and this provision may consist of The mouth into which the food is received is lined with a single vessel, with the power of contracting and sending for a beautiful thin membrane or covering, which extends back ward the fluid which it contains through all the vessels that wards, and terminates in a common tube or funnel, which is issue from it, as in the star-FISH, up to the complex and won called the PHARYNX. The pharynx is divided into prolonged derful structure and apparatus of the human heart. tubes, one of which descending from the pharynx is called the The human body is made up of an assemblage of countless ESOPHAGUs, or commencement of the digestive canal; while the cells; but the arrangement and disposition of these cells is other, which is situated in the pharynx and named the LARYXX such, that they cannot all come into immediate contact with AND TRACHEA, is the passage to the lungs or respiratory organs the influences of the external world, as in the case of a simple The digestive canal traverses the chest, developes itself in the plant. Between the external world, however, and these cells, bowels, terminates in the anus, and in its whole course reprethere comes the nutritive and vital fluid of the blood, sents a tube whose superior opening is the mouth. which goes to every individual part of the body, and which, in Although the quantity of saliva formed in the mouth during its circulation, represents two distinct currents. One current four-and-twenty hours is from fifteen to twenty ounces, yet its conveys to the cells the material of nutrition and secretion ; flow takes place only as it is wanted, or as food is taken into and the other current carries away from these cells the materials the mouth, and the work of mastication goes on. But if you of absorption. The vessels or tubes, in which these currents are hungry, and pass the kitchen during the process of cook are performed, are called the arteries and the veins. The ing, or go into a room in which a nice dinner is being served, arteries convey the blood in its pure and vital condition to every or even let your mind be directed to some favourite dish, there part of the system, and the veins take it up in a degenerated will be an instant flow of saliva, or to use the common phrase state, and carry it back to the heart and lungs, to come in con. -a watering of the mouth. tact with the air in the organs of respiration; while the The food being prepared by the mouth, this is followed by absorbents are small, delicate, transparent vessels, which take the act of swallowing. The pulp passes from the mouth into up from the surface of the body, or from any cavity, those por- the æsophagus, which descends from the pharynx into the stotions of nutritive matter which are not in a state of perfect mach. The stomach, of which the annexed engraving is but solution, and which, by passing through the thoracic duct, a simple and imperfect representation, is the grand receptacle or the passage which lies in the front of the spine, between the for the food, and in which it comes into immediate contact chest and the belly, is prepared for entering into the current with the GASTRIC JUICE. While the saliva is alkaline, this of the blood. These little vessels are called LACTEALS, from juice is acid, and is poured forth from the walls of the stomach the Latin word LAC, which signifies milk, because of the milk- on every successive introduction of food. The presence of food like appearance of the fluid ; or lymphatics, because they is necessary to excite this fluid, and hence it is never detected absorb the lymph or superfluous moisture which is found in the in the empty stomach. Its flow may be increased by taking a body. small quantity of salt, pepper, mustard, or any other stimu. . LESSONS IN PHYSIOLOGY. lating substance that can affect the mucous membrane. But | liquids—the bile and the pancreatic juice. The PANCREAS is a its appearance and chemical properties, and whose use seems It renders more soluble the fatty matter that enters into It takes from the chyme a certain portion of its acidity, if its acid be in the extreme. It gives to the chyme its colouring matter, and a resinous substance designed to prevent its decomposition, It partly excites in the in testine those movements which determine the progress of the chyme along the whole length of the intestinal canal. The action of the liver is it accumulates in the gall-blad- decomposition, and which Independently of the pan- JUICE, similar in its nature, source, and uses, to the gastric THE COURSE AND TERMINATION Bladder Spleen fluid, whose action it supple- OF THE THORACIC DUCT. ments and completes. Duodenum [A The arch of the Aorta. B The Thoracic Aorta. c The Abdominal Aorta and Branches. D The left Subclavian Vein. E E The junction of the internal Jugular and Subclavian Vein at each side. F The Re ceptaculum Chyli. & The Thoracic Duct.] Colon Small Intestine The process of digestion being thus advanced, there are, on the walls of the intestines, what are called ABSORBENT VESSELS, which gradually withdraw the nutritious portion from the con tents of the intestine, and this is carried by the circulating Cæcum current into the most remote tissues of the body. These s. iliac absorbent vessels are called LACTEALS, on account of the milky appearance of the fluid which is formed in them. This fluid is the chyle, and these vessels, in their course form larger trunks, which converge and pour their contents into a cavity, known by the name of the RECEPTACULUM CHYLI, or chyle-receptacle, which arises in the front and lower part of the spine. Into the same cavity are poured the contents of another system of vessels, which, from the transGreat Intestine parency of their fluid or lymph, is called the LYMPHATIC possible to recognise in the chyme the aliment out of which it system, which, in its general design and end, is very closely has been formed. In quitting the stomach, the chyme passes allied to the lacteals. În the THORACIC DUCT or CANAL, which into the DUODENUM, where it comes into contact with two new passes upwards in front of the spine, from the belly into the |