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tuity of the soil, the returns yielded to the farmer are most stalk is of such great height, as to present the appearance of abundant.

Fig. 1.

tree in miniature.

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countries it is sown on lands which are absolutely flooded for | namely, 144 and 64; find their difference, and the result is also weeks together; and when the grain has germinated, the 80. These results will take place with any two numbers; a fact, water is drawn off. The fields are left dry for a month or more, of the truth of which you may be satisfied, by trying as many pairs till the young plants are three or four inches high, when the of numbers as you please. This invariable result is expressed in plantations are again flooded, and left in that state for two or general terms, in the words of the following theorem :three weeks. This soaking destroys the weeds which have 1. The product of the sum and difference of any two numbers is sprung up with the rice. After this, the plants are left dry till equal to the difference of their squares. the ears are formed, (see fig. 3), being repeatedly hoed between and kept clear of weeds; the watering is again removed, and the flood is left on the ground till the grain is ripe. "The verdure of the young plant," says Heber, when visiting Ceylon, "is particularly fine; and the fields are really a beautiful sight, when surrounded by, and contrasted with, the magnificent mountain-scenery.'

Rye is used by several nations of Europe as bread-corn. It is not so much liked by birds as many other plants, and of this some farmers take advantage. They sow a narrow border of rye round their fields of wheat and other grain; and when thus fenced they are not attacked by poultry, nor even by the wild birds. As these seldom alight in the centre of corn-fields, but confine their depredations to the outer boundary, they visit the rye, and finding what they do not like they proceed no further. The bread made on the continent from rye, is very black, and as leaven is used instead of yeast it is sour, and to a stranger accustomed to better food extremely unpalatable. That which is sold in London by some bakers as rye-bread is, on the contrary, well-flavoured and very good; similar, in fact, to brown wheaten-bread.

In addition to the corn-plants already mentioned, there are others belonging to the large family of the grasses, which might be employed as food, and which are only neglected from the smallness of their seeds. None are unwholesome in their natural state except darnel, a common weed in many parts of England. This is one of the vegetable products reserved by Providence for other purposes.

How many plants, we call these weeds,
Against our wishes grow,

And scatter wide their various seeds
With all the winds that blow.

Man grumbles when he sees them rise,
To foul his husbandry;

Kind providence this way supplies
His lesser family.

Scattered and small, they 'scape our eye,
But are not wasted there;

Safe they in clefts and furrows lie,
The little birds find where.

Again, take any two numbers, say 12 and 8 as before, and find their sum and difference, namely, 20 and 4; then find the squares of these numbers, namely, 400 and 16. Next, find the squares of the two assumed numbers 12 and 8, and twice their product, namely, 144, 64, and 192. Find the sum of these two squares, namely, 208; then, add to this, the double product 192, and the sum is 400; subtract from it the same product, and the remainder or difference is 16. The same results will take place with any other two numbers you choose to try. Hence, we deduce the two following general theorems :

2. The square of the sum of any two numbers is equal to the sum of their squares, increased by twice their product.

3. The square of the difference of any two numbers is equal to the sum of their squares, diminished by twice their product. Our object in presenting these theorems, as well as those appended to the rule of subtraction, is to lead the student by degrees to the consideration of some general rules, which are equally true of all numbers, and are not confined to particular instances such as those by which they were illustrated. By help of a few new definitions, these theorems may be made a means of introduction to the universal language of algebra. In this science, the letters of the alphabet are employed to represent numbers, not fixed numbers, but any numbers whatever; and therefore, all theorems which can be demonstrated by means of letters, must be considered as universally true, and equally applicable to all numbers. In addition to the definitions, and explanation of signs already given in No. III., page 36, we may add the following relating to universal arithmetic.

1. When numbers are represented by letters, they are usually called quantities; when a particular value is given to them in any problem or question, they are then called known quantities; when their value is not given, but required in any problem or question, they are then called unknown quantities. The former are denoted by the initial (beginning) letters of the alphabet, as a, b, c, &c.; and the latter by the terminal (ending) letters of the alphabet, as z, y, x, &c. In expressing general theorems, however, either of these kinds of letters may be employed.

a

:

2. The arithmetical signs are used to denote that the arithmetical operations are to be performed upon the numbers represented by the letters. Thus the expression a+b=c, means that the sum of It is worthy also of remark that the tall sugar-canes and the two numbers represented by a and b is equal to the number represented by c. The expression a-b-c, means that the difference gigantic bamboos of tropical climates are only grasses on a of the two numbers represented by a and b is equal to the numlarger scale, agreeing with our own in every essential particu- ber represented by c. The expression axb-c, means that the lar, and differing mostly in size. They afford to the Indian savage almost all he wants, except the food which he derives product of the two numbers represented by a and b is equal to the from his rice or his maize. number represented by c. Very often, and mark this particularly, "With their lightest shoots he makes his arrows; the fibres of the wood form bow-very often the sign X is omitted; that is, ab≈e means the same as strings; and from the larger stems he fabricates a bow; a long a+b=c. The expressions a÷b=c, or =c, or a b=c, all and slender shoot affords him a lance-shaft, and he finds its hardened point a natural head for the weapon. With the mean the same thing,-namely, that the number represented by a hardened stems he builds the walls and roof of his house; its divided by the number represented by b, gives for a quotient the leaves afford him an impenetrable thatch; split into narrow number represented by c. strips, it gives him the material for weaving his floor-mats, and other articles of domestic convenience; its fibre furnishes him with twine, and its leaves provide him with paper, when he becomes sensible of the utility of such a material. Would he commit himself to the waves, the stems form the hull of his boat, which by a few skins stretched over it is rendered water-tight; they also give him masts, and their slips of wood become cordage or are woven into sails. In China, India, and Japan, bamboos are used for a great number of useful pur

poses.

LESSONS IN ARITHMETIC.-No. VIII.

3. When numbers or quantities are enclosed in a parenthesis, thus (a+b), (a-b), &c., the expression signifies that the number or quantities so included are to be treated as a simple number or quantity, or rather that the operation of the signs applied to them are to be performed, and that the result is to be treated, as it is in reality, like a simple number or quantity. Thus, the expression (a+b)xc=d, means that the sum of the quantities a and is to be multiplied by the quant ity c, and that the product is equal to the means that the sum of the quantities a and b, is to be multiplied quantity d. In like manner the expression (a+b)x(c+d)=e, by the sum of the quan tities c and d, and that the product of these sums is equal to e.

(1) (a+b)+(a-3)=2a

---

4. Applying these symbols of numbers and of operation to the IN our last number, we intended to annex to the Rule of Multi-general theorems in No.. V, page 67, they will stand thus :plication, some theorems of frequent occurrence, and of considerable use in practice. These we now proceed to give. Take any two numbers, say 12 and 8, and find their sum and difference, namely, 20 and 4; then, multiply these quantities together, and the product 80. Next, find the squares of the two numbers 12 and 8,

(2) (a+b)-(ab) = 2b

In these expressions a clenotes the greater number and the less, and reasoning upon them generally we shall be convinced of the univer sality of their applicatio n. Thus, in theorem (1), we are to add «+6

to ab; that is, we are first, to add b to a; second, to substract from a; and third, to add the results. Now, we know that if we add a to a, we shall have twice a, or 2a; but if we add something, viz., b to the one a, and take away the same thing, viz., b from the other a, we shall still have twice a or 2a; because what we add to the one we take away from the other, and therefore the sum will neither be increased nor diminished, that is, the sum will still be the same as if we had only added the two together.

5. Again, in theorem (2), we are to subtract ab from a+b; that is, we are first, to add b to a; second, to subtract b from a; and third, to subtract the latter result from the former. Now, we know that if we subtract a from a, we shall have nothing left; but, if we add something, viz., b, to the one a, and take away the same thing, viz., b, from the other a, we shall have twice b, or 26 left; because, what we add to the one, we take away from the other; and therefore, in taking the latter a away from the former a, we take away too much by the quantity b, and therefore we must add this b to the former b, in order to obtain the full remainder.

6. As we have defined the square of a number in our last lesson, we may now inform the student how it is denoted, or marked on the number itself. As the same factor occurs twice in the product called the square, this occurrence is indicated by placing the number 2 on the right of the number or quantity, in a smaller character, and on a higher level than the latter; thus 6 denotes the square of 6, or 36; and a2 denotes the square of a, or axa. In like manner, (10+2) denotes the square of 10+2, or of 12; and (a+b) denotes the square of a+b, or of the sum of the quantities a and b. Again, (4+5+6) denotes the square of 4+5+6, or of 15; and (a+b+c)2 denotes the square of a+b+c, or of the sum of a, b, and c.

7. Applying the symbols of numbers and of operation to the general theorems, placed near the beginning of this lesson, they will stand thus:

(1) (axb)X(a—b) — a2 —b2
(2) (a+b)2=a2+b2+2ab.
(3) (a—b)2=a+b2-2ab.

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complete product of a by a that is wanted, but the product of the
difference between a and b by a; here, the general principle is
that the product of the difference of any two numbers by a third
number is equal to the difference of the products of those tw
numbers by the third number;* but this product a must be
diminished by the product of the same difference by b, as it is he
product of the difference (ab) by the difference of a and
is required. Now, if we multiply the difference (a—b) by
quantity b of the difference (ab), we shall have the pro
abb, as above; and subtracting this product from the for
product aab, we have a+b2ab; for, if we subtract
which makes a abab, or a2-2ab (since ab is to be s
tracted twice), we have subtracted too much by b; we
therefore add 63 to the result in order to obtain the true remane
viz., a2+b2— 2ab.

10. Another theorem of great importance, is necessary given here, as it is an extension shorems (2) and (3) of m 7, to the combination of severa ters by the signs of adm or subtraction: viz.—

The square of the sum of several numbers, is equal to the m of the squares of those numbers, and twice the product of the number by all that follow it; twice the product of the second nur by all that follow it; and so on, to the last number. Thus the several numbers, 4, 6, and 10; their sum is 20, and its is 400. Now, this square of 400, is equal to the sum of the of the numbers 4, 6, and 10; viz. 16, 36, and 100; with tw product of 4 by 6, and by 10, viz. 48 and 80; and twice the duct of 6 by 10, viz. 120; for 16+36+100+48+80+1204 Expressed symbolically, this operation stands as follow: ex 10)2 = 4 + 6 + 10 + (2×4×6) + (2×4×10)+(2x6x or, 20-400-16+36+100+48+80+120.

2

Applying to this theorem, the symbols of numbers and of pe tion, it will, in the case of four quantities, a, b, c, d, stand tis (a+b+c+d)2=a2+b2+c2+d2+2ab+2ac+2ad+2bc+2%2cd. The operation indicated here, is that the sum (a+b+ct be multiplied by itself; now, if we multiply (a+b+c+d In these expressions, still a denotes the greater number, and b the the first part, we have a+ab+ac+ad; if we multiply by less, and we may now reason upon them in a general way, as we second part, we have ab+b+be+bd; by e, the third part did on the expressions, taken from the theorems in page 67. Thus, have ac+be+c+cd; and by d, the fourth part, we have ad in theorem (1) we are to multiply the sum (a+b) of any two quan- cd+d. But, as the whole product is the sum of all these p tities a and b, by their difference (a-b), and find the product; we have first, a2+b2+c2+d2, the sum of the squares of the part now, if we multiply the sum (a+b) by one of the quantities a, of then, we have ab+ab, or 2ab; ac+ac, or 2ac; adtad, or the difference (ab), we shall have the product a2-ab; for axa= bc+be, or 2he; bd+bd, or 2bd; ed+cd, or 2cd; whence, we have a2, and b×a=ab; and adding these products, we have a+ab, second, 2ab+2ac+2ad+2bc+2bd+2cd, the sum of the prod by the general principle of Rule 4 in Multiplication. But this of twice each part by all that follow it. Hence, the comp product by a must be diminished by the product of the same sum square of (a+b+c+d) is a2+b2+c+d+2ab+2ac+200 by b, as it is the product of the sum (a+b) by the difference of a+od+2cd; and the truth of the principle is manifest. and b, that is required. Now, if we multiply the sum (a+b) The rule for squaring a quantity consisting of several parts by the quantity of the difference (a-b), we shall have the pro- duced from the preceding principle is simply this: Square duct ab+b2; for axb=ab, and b×b=b; and adding these pro-term, and multiply all the terms that come after it by twit ducts, we have ab+b2, by the general principle above mentioned. term; do the same with the second term; and so on, to i Subtracting this product, therefore, from the former product, we term. The sum of all these products is the answer. have a-b2; inasmuch as ab-ab=0; the principle of this operation being that the product of the sum of any two numbers by their difference, is equal to the difference of the products of the sum by each of the numbers. This principle is a natural conse-is quence of that given in Rule 4 of Multiplication, when applied to a multiplier divided into two parts.

8. In like manner, in theorem (2), we are to multiply the sum (a+b) of any two quantities a and b, by the sum (a+b) of the same quantities, and find the product; now, if we multiply the sum (a+b) by one of the quantities a of the sum (a+b), we shall have the product a+ab, as before; but this product by a must be increased by the product of the same sum by b, as it is the product of the sum (a+b), by the sum of a and b that is required. Now, if we multiply the sum (a+b) by the quantity of the sum (a+b), we shall have the product ab+b2, as before; and adding this product to the former product, we have a+b+2ab, for ab+ab =2ab.

9. Lastly, in theorem (3) we are to multiply the difference (a —b) of any two quantities a and b, by the difference (a-b) of the same quantities, and find the product. Now, if we multiply the difference (ab) by one of the quantities a of the difference (ab), we shall have the product a2-ab; for, axa = a2, and ba=ab; and subtracting the latter product from the former we have a2 —ab; that this subtraction is necessary, is obvious, because it is not the

QUESTIONS ON THE PRECEDING LESSON.

1. What is meant by a quantity? How is it represented?
meant by a known quantity? How is it represented? W
meant by an unknown quantity? How is it represented?
the sum of two numbers or quantities is added to their differ
what is the result? When the difference of two number
the sum and difference of two numbers or quantities are mul
quantities is taken from their sum, what is their result?
together, what is their product? What is the square of the
of two numbers or quantities equal to? What is the square
difference of two numbers or quantities equal to? What
square of the sum of several numbers or quantities equal to?
Add the quantities z+y and x-y together.
Subtract the quantity x-y from the quantity ty.
Multiply ty by x-y, and tell the product.
Find the squares of x+y and of x-y.

Find the squares of x+y++m, and of a+b+ctate
What are the sum and difference of m and n ?
What is the product of the sum and difference of m anda!
What are squares of the sum and difference of m and a!
What are the factors of p2-q2p

What are the factors of p2+g+2pq and of p2+q2-2p1

This principle is merely a generalisation of that given in the process i paragraph.

BIOGRAPHY.-No. III.

JAMES BRINDLEY.

JAMES BRINDLEY was born at Tunsted, in the county of Derby, in the year 1716. The extreme poverty to which his father had reduced himself by his dissipated habits, exposed his family to great privation and suffering;-a case which should operate as a warning against the commission of such an evil, since he who indulges in it, not only does harm to himself, but often inflicts incalculable injury on others. One consequence of his father's vicious life was, that James had scarcely any instruction; and even to the end of life, after having been raised by his talents and energy to very different circumstances, he was hardly able to read, while his ability to write went but little beyond the power of signing his name. In childhood, and in youth, he was employed in ordinary country labour, but conscious that he was fitted for something better, he bound himself apprentice to a millwright, named Bennet, who was living at Macclesfield, not far from Tansted. He had now a special opportunity for that thoughtfulness to which he appears to have been strongly inclined, as well as for all the skill he could put forth; for even in the early part of his apprenticeship, his master left him for weeks together to execute works for the execution of which he had received no instructions. It is easy to imagine how indolent and careless some young men would have been in such circumstances; not only would work intrusted to them have made Little or no progress, but they would have been at "the shop" as little as possible, while business would have fallen off, and injury in various ways have been inevitably sustained. The contrary was the case with Brindley; for on his master's return from time to time, he not only found the work done, but was astonished at the improvements his apprentice made in doing it, and frequently asked him how he could have gained his knowledge. The wise answer was, doubtless, that he was always thinking about his work, and turned whatever he met with on any subject to the utmost advantage. Observation, combined with sagacity, is often the seed-corn of a rich and plenteous harvest.

wished him to return to the inferior position he had previously occupied. Brindley refused to do so; and the result was, that the entire work was committed to him, and he completed it with his usual distinguished ability. Among his ingenious contrivances was one for cutting all his tooth and pinion wheels by machinery, instead of having them executed by hand, thus enabling him to accomplish as much of that kind of work in one day as had previously been done in fourteen. At length he was applied to by the Duke of Bridgewater, in reference to a project, which, thenceforward, formed the chief part of his pursuits.

The duke, having considered the pecuniary advantage he should derive from a canal connecting his estate at Worsley, which contained valuable coal-mines, with the town of Manchester, as well as the benefit that would accrue to others, called in the advice and practical ability of Brindley. An Act of Parliament was consequently obtained in 1759, to carry a canal over the river Irwell, near Barton-bridge, in Manchester, and to conduct a branch to Longford-bridge in Stratford. One peculiarity was to mark this work. A lock is the barrier of a canal which confines the water-consisting of a dam, banks, or walls, with two gates, or pairs of gates, which may be opened and shut at pleasure. By means of such locks vessels are transferred from a higher to a lower level of water, or from a lower to a higher. Whenever a canal changes its level on account of an ascent or descent of the ground through which it passes, the place where the change occurs is usually commanded by a lock. But this canal was to be accomplished without the aid of locks, by preserving the same level throughout the course of the canal. After many difficulties had been surmounted, of sufficient magnitude to deter an ordinary man from the undertaking, Brindley commenced that which was by far the most gigantic part of the work; to carry the canal over the river Irwell, at a height of thirty-nine feet above the surface of the water.

Confident as Brindley felt of the practicability of the design, he wished the Duke to take the opinion of some eminent engi neer before making the attempt; for, though such an enterprise has since been common, it was at that time an absolute A fact which occurred at this time is not a little significant novelty. The scheme appeared, however, to the gentleman of his future progress. Bennet was engaged to make the consulted, as rather calling for ridicule than deliberation, and machinery of a paper-mill, and as he had never seen one, he he is stated to have said, "he had often heard of castles in the took a journey for the purpose of inspecting a mill that might air, but was never before shown where any might be erected." serve as a model; but it appears he might as well have But neither Brindley's confidence nor that of the duke, in his remained at home, for on his return, a stranger, who observed judgment, was shaken by the reply; and the work was happily what he was doing, remarked in the neighbourhood that he completed. The canal began at Worsley-mill, where a basin was only throwing away his employer's money. This gave was cut, capable of holding not only all the boats required to rise to various reports, which led Brindley on hearing them to carry the coals, but a great body of water, which serves as a determine what he would do; he started on Saturday evening reservoir or head of the navigation. The canal runs through to see the mill which his master had visited in vain, returned a hill by a subterranean passage, large enough for the admison Monday morning, having accomplished the journey of sion of long flat-bottomed boats, which are towed by handfifty miles on foot, and in due time completed the machine-rails on each side, near three-quarters of a mile under ground, with many improvements of his own-to the entire satisfaction to the coal-works. There the passage divides into two chanof Bennet's employer. nels, one of which goes five hundred yards to the right, and the other as many to the left; both being left to be continued at pleasure. The ingenuity displayed in carrying forward this great work is worthy of remembrance. The smith's forges, and carpenter's and mason's workshops were covered barges, which floated on the canals, and followed the work as it went on, so that there was no hindrance of business; and as the duke had all the materials in his possession-timber, stone, and lime for mortar, as well as coals from his own estate, all close by, he was at little expense besides labour. Nor was this all: the refuse of one part of the work was made to serve in the construction of another; thus the stones dug up to make the basin for the boats, at the foot of the mountain, as well as others taken out of the rock to make the tunnel, were hewn into the proper forms to build bridges over rivers, brooks, and highways. And the clay, gravel, and earth, taken up to preserve the level of one place, were carried down the canal to raise the land in another, or reserved to make bricks for other uses. In this way grandeur and elegance were successfully combined with economy. The aqueduct at that time a most astonishing work-was completed in about ten months. The canal was then extended to Manchester, where Brindley's ingenuity in diminishing labour by mechanical contrivances was exhibited in a machine for landing coals on the top of a hill,

Already the millers, wherever Brindley was at work, chose him in preference to any other artisan; and, before his apprenticeship expired (at which time Bennet, who was advanced in life, grew unable to work), he kept up the business with credit, and even supported in comfort his master and his family. He subsequently started in business on his own account; but, for some time, he was only known in the neighbourhood of the place where he lived; gradually, however, his connexions became more extensive, and at length he undertook all kinds of engineering. Still there were difficulties in his way; he was a sort of intruder in his present profession, for which he had not been regularly trained; and, if some regarded him with feelings of jealousy, others did not treat him with the confidence to which he was fully entitled,

In 1752 he erected a water-engine for draining a coal mine at Clifton, in Lancashire; a work of great difficulty, and v hich he accomplished by bringing the water, as the moving power of the engine, through a tunnel cut in the solid rock, a distance of six hundred yards. About three years after, Brindley was engaged to make the larger wheels and other parts of a new silk-mill at Congleton, in Cheshire, while another person was appointed to execute the superior portions of the work. He however committed various mistakes which Brindley was employed to rectify; but having done this, the proprietors

Many and great were the advantages obtained by this canal, | After certain intervals of consideration, he noted down the afterwards extended to Liverpool. Before it was commenced, result at which he had arrived in figures, and then proceeded the price of water-carriage by the old navigation on the rivers to work out the complete solution, and, strange to say, he was Mersey and Irwell, from Liverpool to Manchester, was twelve generally right. Those who knew him well highly respected shillings per ton; land-carriage was forty shillings per ton; him for his uniform and unshaken integrity, as well as for the and not less than two thousand tons were carried, on an vast range of his understanding. He appears also to have average, yearly. Coals were retailed to the poor at Manches- cherished kindly and liberal dispositions, in accordance with ter at sevenpence per hundredweight, and often at a still his conduct to his master and his family when rising into life. higher charge. The cost of carriage by the duke's canal was six shillings per ton-the conveyance was much quicker-and the poor had their coals supplied at threepence-halfpenny for a hundredweight of seven score.

In the execution of every part of this remarkable navigation, Brindley displayed extraordinary skill; and he produced many valuable machines to facilitate the object he had in view. His economy and foresight were peculiarly discernible in the stops or floodgates, fixed in the canal, where it is above the level of the land; these being so constructed that, if any of the banks were to give way, and occasion a current, the adjoining gates would rise merely by that motion, and prevent any other part of the water from escaping but that which was near the breach between the two gates.

LESSONS IN NATURAL HISTORY.-No. II.

THE TIGER.

THE animal next in order in the Feline or cat-tribe, which claims the attention of the naturalist, is the tiger. Like the lion it is carnivorous; and for size and fierceness little inferior. In height and general conformation the tiger resembles the lioness; while in the features and outward appearance it is pre-eminently feline. In fact, the domestic cat may be taken as a miniature resemblance of this fierce and revengeful quadruped. The neck of the tiger is short, and the skin, which is soft and smooth and of a tawny-brown colour, is marked Encouraged by the results that had now been achieved, all over in spotty stripes. The eyes are small, round, and other enterprises were commenced and carried out by different bright; the teeth, twenty-eight in number, are sharp and persons, but under Brindley's direction. Among these were strong; the feet, like those of the cat, are furnished with the Grand Trunk Canal-forty-six miles in length-connecting crooked claws; and the tail, long and slightly tapering, is altoBristol with Liverpool and Hull; a canal from Birmingham-gether deficient of the shaggy tuft which distinguishes the twenty-six miles in length-uniting with the Staffordshire lion. The tiger is maneless, with a flat head and retreating and Worcestershire canal, near Wolverhampton; and the frontal bone; the ears are short and set far back from the eyes; canal from Droitwich to the Severn. He planned also the the jaws are large, powerful, and furnished with strong pliable Coventry navigation; and a short time before his death he muscles; while the suppleness of its spine and the freedom of began the Oxfordshire canal, which, uniting with that at its limbs render it eminently fitted for attack or retreat. To Coventry, serves as a continuation of the Grand Trunk navi- the sagacity and agility of the cat is added the strength and gation to Oxford, and from thence by the Thames, to London. ferocity of the lion: it is distinguished by a cruel and revenge Such was Brindley's established reputation, that few works ful disposition, and is altogether deficient of the noble and of this kind were undertaken without his advice; but his magnanimous spirit said to characterise the king of beasts. labours are too numerous to be particularised. It may, how- The female tiger has generally two cubs at a birth; and, unlike ever, be added, that he gave the corporation of Liverpool a the lioness, appears to entertain but little affection for its plan for clearing their docks of mud, which was successfully young, having been known to devour its offspring even when practised; and prepared a method, no less effective, of build- possessing plenty of food in its den. ing walls against the sea without mortar. His last invention was a machine for drawing water out of mines by a peculiar kind of bucket, which he afterwards employed with advantage in raising coals.

Such was the euthusiasm of this extraordinary man in all that related to inland navigation, that it is said, when he was asked, at an examination before the House of Commons, for what purpose he thought rivers were created, he replied, "to feed navigable canals." He refrained from what are ordinarily regarded as amusements," on the ground that they unfitted his mind for business. On the works intrusted to him, stupendous as many of them were-and frequently the first attempted of their kind-he was constantly intent, and to the persevering and sagacious employment of his remarkable powers, he was indebted entirely for his success and his fame. His labours appear, however, to have overtasked his frame; he suffered from a hectic fever, with little or no intermission for several years, and his earthly course was terminated in the fifty-sixth year of his age.

There can be little doubt that his want of early instruction rendered his labours far more wearisome and exhausting than they would otherwise have been. As he had no resource except in his surprisingly inventive mind, this was constantly and violently tasked. It was his practice when engaging in a new project to retire to bed for one, two, or three days, there completely to arrange all his plans, and this being done he rose and set scores or hundreds of men to work, without any memorandum of what he had determined, nor did he ever use a drawing or a model, except for the satisfaction of his employers. His memory thus largely trusted must have been proportionately burdened. Arithmetic, had he known it, would have been of immense value, but this was an attainment he had not been able to make, as the poor, hardworking son of a drunken and profligate father, at a time when instruction was not easily procured. In his calculations of the powers of any machine, therefore, he was accustomed to pass through some mental process which none knew but himself, and which, perhaps, he would have been unable to communicate to others.

The tiger is found in Asia, Africa, and America; but in each continent it differs slightly in its outward appearance. The East Indian tiger is fallow-coloured on the back, grey on its sides, and white beneath; marked with numerous black stripes, the largest of which is not less than an inch broad. Some of the stripes are disposed in the form of a girdle round its body; but in general they are short, irregular, and slanting forward from the tail. One of this kind was killed by Captain Hamilton in the Sundah Rajah's dominions, and when dead was measured. Its length, from the tip of the nose to the extremity of the tail, was five feet nine inches; its height, from the end of its fore paw to the top of its shoulder, was three feet seven inches; and the fore leg, measured directly under the shoulder, was above two feet and a half in circumference, the rest of the body being large in proportion. The tail was two feet ten inches in length, and nine inches in thickness at the largest part, gradually decreasing to the extremity, which was very slender. It was encompassed with irregularly-marked rings of the same colour as the rest of the body, but of a darker hue. Its head was fifteen inches and a-half in length, and ten in diameter: the two sides of the forehead appeared to rise up above the skull, leaving a considerable cavity in the centre, which ran down from the ears to the muzzle. The lower part of the neck was covered with a long narrow stripe, whence several others of a rather lighter tawny colour proceeded, turning downwards towards the legs. The top of the trunk was marked with a series of disjointed blackish stripes; which, dividing and parting from each other from the centre of the back downwards, reunited in a single stripe in the middle of the upper part of the neck. The mouth was very large, furnished with teeth of formidable dimensions, and being decorated on each side with large feelers or whiskers like those of the cat. The East Indian, or Asiatic tiger, is common to many parts of China and the uncultivated jungles of the tropics. It is a fierce, cruel, and rapacious beast; possesses immense strength, and is considered the largest and most ferocious of its tribe.

The American tiger is also a very fierce and mischievous

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