chest, the chyle becomes mixed with the chyme, and is conducted by this canal into the vein which passes under the left clavicle, and there becomes mingled with the venous blood. The composition of the chyle is the same with that of the blood, and the blood contains all the elements which are required for the nutrition and growth of every part of the body, as well as to repair that incessant loss which is going on in the system. Reparation is the end of nutrition; and if the chyle hold in a state of solution all the material elements of this reparation, then the reparation itself may be realised by the addition of the chyle to the blood. We have seen that the chyle gets into the venous system; and all that is now needful, is, that the venous blood should come into contact with the oxygen of the air in the lungs, to be transformed into arterial blood, and thus regain its own vital and vivifying property. QUESTIONS FOR EXAMINATION.

Can you describe the circulation in a plant, and in the lower kind of animals?

What does the blood in the human body represent when looked at in a chemical point of view?

Of what use are the teeth; and how are they divided?

What is the effect of eating our food too fast, and of drinking too much cold liquid?

What is the temperature necessary for digestion?

What change does the food undergo in the stomach?

What is the difference between the saliva and the gastric juice? What juices does the chyme meet with in passing into the duodenum ?

What important purposes are served by the bile?

In what vessel is the chyme found, and the lymph?

In what cavity do these lacteals and lymphatics empty them

selves?

Where does the thoracic duct arise; and what is its course?
How does the chyle get into the current of the blood?
How is venous blood converted into arterial?

Does the chyle contain all the elements of the blood; and how does the blood supply the various parts of the body?

SOLUTION OF PROBLEMS AND QUERIES. THE following is the complete solution of query 8, No. II. EUCLID, BOOK I. PROPOSITION XLVII. THEOREM. In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Let ABC (figs. 1 and 2), be a right-angled triangle, having the right angle BAC.

The square described upon the side BC, shall be equal to the squares described upon BA, AC.

On B C, describe the square вDEC (I. 46); and, on BA, A C, the squares G B, HC;

through A, draw A L parallel to Bn, or CE (I. 31);
and join AD, FC.

Then, because the angle B A C is a right angle (hyr.).

and that the angle BAG is a right angle id f. 30), the two straight lines AC, AG, UPON THE OPPOSITE SIDES & on the same side, of A B, m ke with it at the point A, THE ADN ALAN” ANGLIS, or the angles on the same side, two right angles;

therefore, CA IS IN THE SAME STRAIGHT LINE with A G, or 10.0 cides with it. (I.14.)

For the same reason, BA and AH are in the same straighila And, because the angle DBC 18 equal to the angle FBA, each of them being a right angle,

ADD TO, or subtract from, each of these equals, the angle Ar therefore, THE WHOLE, or the remaining, angle DBA is eam THE WHOLE, or the remaining, ang e PBC (ax. 2). And, because the two sides A B, RD, are equal to the two FF, BC, each to each, and the included angle ABD is equal to included angle PBC,

therefore, the base A D is equal to the base F C (I. 4), and the triangle ABD to the triangle FBC.

Now the parallelogram B Lis double of the triangle a B D (I. 41. because they are upon the same a D, and between the st parallels BD, A L;

also the square G B is double of the triangle F B C, because these also are upon the same F B, and between the st parallels FB, o C.

But the doubles of equals are equal to one another (ax. 6); therefore, the parallelogram B Lis cqual to the square a a

Similarly, by joining A E, BK, it can be proved

that the parallelogram CLis equal to the square и C.

Therefore, the whole square B DE C is equal to the two ques

а в, не (ах. 2).

and the square BDEC is described upon the straight licen and the squares GB, H C, upon the straight lines A B, A C: therefore, the square upon the side B c is equal to the squa upon the sides A B, A C.

Therefore, in any right-angled triangle, &c., Q. E. D.

In the preceding demonstration, which is taken from one of the latest and best editions of Euclid's Elements, we have only int duced, in italics, the words which refer exclusively to the secon figure; the words in small capitals referring EXCLUSIVELY to first figure, and the rest of the demonstration to beth figures It is evident to any one who attentively studies the first bock f Euclid, that the chief, if not the sole intention of the author, was?! establish the truth of the 47th Proposition, or, in other words, the Pythagorean Theorem, on the sure foundation of logical and re fragable demonstration. Many students of Geometry have ad this demonstration carefully-have admitted the truth establiert by it as convincing, provided the other propositions on which it r founded were true. They have then read the demonstrations these other propositions, and those also of the propositions en which the latter were founded, and thus in a regular series retraced the steps of his reasoning back to the very first proposition. I this way, they have discovered that the Greek Geometry, as de livered to us by Euclid, is one of the most perfect specimens ? pure and logical reasoning of which the human mind in this ser lunary state is found to be capable.

From the incidental remark of the editor of his works, whic led to the query solved in the preceding demonstration, we have

discovered not only his mistake, but the deficiency even of Euclid's werk, although it be a masterpiece. It is evident that he never contemplated the construction of the squares on the interior sides of the triangle, as shown in fig. 2, otherwise he would have found it necessary to alter the enunciation of the 14th proposition of the first book into the following;

:

If at a point in a straight line two other straight lines make the two angles on opposite sides of it, or the two angles on the same side of it, either two right angles, or together equal to two right angles, these two straight lines shall be either in the same straight line, or shall coincide with each other.

It will be a useful exercise for some of our more advanced readers to demonstrate the truth of this proposition under its new phase. In the printed arrangement of the preceding demonstration, we have adopted the very useful method followed by Mr. Potts in his edition of Euclid; where the text is "so arranged as to exhibit to the eye of the student the successive steps of the demonstration, ad thus to facilitate his apprehension of the reasoning."

In conclusion, we remark, that although the above demonstraon is complete as regards the construction of the squares on the interior sides of the triangle, we shall not now consider the demonstration of the Pythagorean theorem absolutely complete, until our geometrical correspondents have actually solved all the possible cases of construction, which are the following six:

1. The squares on the three cxterior sides of the triangle. 2. The squares on the three interior sides of the triangle.

3. The two smaller squares on the exterior sides, and the greater an the interior side.

4. The two smaller squares on the interior sides, and the greater on the exterior side.

5. The greater and one of the smaller squares 'on the exterior sides, and the other on the interior side.

6. The greater and one of the smaller squares on the interior side, and the other on the exterior side.

The first case is that given by Euclid. The second is that given above, and solved by many correspondents. The third we have repeatedly seen. But we should like to see a demonstration adapted to all the cases at once, with such necessary differences as are given in the preceding one.

PROBLEM.-To describe an isosceles triangle, such that each of its legs shall be double the base or third side.

Let A B be the given base. It is required to describe an isosceles triangle on AB, such that each of its legs shall be double a B.

From the points A and B as centres, with radius A B, describe the circles B D E, AFG; produce A B both ways to E and G; then, from the point A, as a centre with radius A o, describe the circle & CH; from the point B, as a centre with radius BE describe the circle ECI; and from the point c, where the circles intersect, draw CA, CB; then CA B is the triangle required.

Because A E is equal to A в (I. Euc. def. 15), therefore B E is double of A B; for the same reason, A G is double of A B. Because A is the centre of the circle G CH, therefore a C is equal to AG (I. Euc. def. 15); but AG is double of A B, therefore A Cis double of AB; in like manner it may be shown that BC is double of AB; wherefore AC and BC are each double of A B; they are, therefore, equal to each other (I. Euc. ax. 6), and the triangle ACB is the isosceles triangle required.

Of this problem we have received many correct solutions exactly similar to the above. Owing to the problem being put without reference to a given base, we have received a number of solutions

of a different kind, but equally correct. Others, however, have not confined themselves within the prescribed limits; and therefore their solutions, though correct in themselves are not so in reference to these limits.

PROBLEMS AND QUERIES.

1. Draw a straight line at right angles to a given straight line from one of its extremities without producing it, and give a demonstration with as few propositions from Euclid as possible, but still geometrically correct.

2. If sound travels at the rate of 1,142 feet per second, and a stone falls through the height of 16 feet 1 inch per second, from what height would a stone fall, which should occupy the same time in falling through it, that sound would occupy in ascending it ?E. J. R. B.

3. In the figure of the 47th Proposition of the First Book of Euclid's Elements (see figs. 1, 2, preceding page), if the points FD, GH, and KE, of the squares BG, CH, and CD, be joined, they will form three triangles-F B D, G A H, and K C E, which are all equal to one another; required the proof.

4. In the same figure, prove that the straight lines FC, BK, intersect cach other and the straight line a L in the same point. 5. Show how the squares B G and C H, if made of paper or pasteboard, must be cut, so that the pieces may be laid upon the square B E, and made exactly to fit or cover it, without leaving any space under or over.

Lessons on Politeness, and our social duties to friends and foes, male A correspondent, E. C., earnestly suggests to us the utility of giving and female, somewhat in the Chesterfield style. He draws a contrast between foreign manners and our own, to the disadvantage of the latter; and instances a case where, on two afternoons in the week, the children in schools are lectured on the art of politeness, and their social bearing towards all classes of society,-namely, in the Grand Duchy of Baden. He relates an anecdote of what he witnessed and was ashamed of in the conduct of some of his countrymen on the quay at BAmerican politeness invited English on-lookers to inspect a ship. males as well as males availed themselves of the offer. The female descent of the ladder in returning after inspection, excited the risibility of an English crowd to the degree called the horse-laugh; while American politeness, in the shape of a common sailor, at once removed the cause, and prevented the repetition of the insult.

Fe

As another instance, which we have often witnessed ourselves, he mentions that of a gentlemen and lady walking on the pavement, the lady being next the kerb, and forced off into the dirty street by persons standing in a knot on the pavement, or walking and talking together, without any regard to the comfort and convenience of others. He also wishes the masses to be taught, how to settle disputes among themselves by arbitration, as is done among the upper classes, rather than by "fighting it out," as the phrase is. We think our correspondent is right, to a considerable extent, and we hope his abstract of his remarks will be taken in good part by those for whom it is intended.

LITERARY NOTICES.

The EMIGRANT'S HANDBOOK, a Guide to the Various Fields of Emigration in all Parts of the Globe, is now ready, price 6d.

The ILLUSTRATED EXHIBITOR and MAGAZINE OF ART, is in

course of issue in Weekly Numbers, price 2d.; Monthly Parts, price 9d.; or if containing five weekly numbers, price 11d. The fourth Monthly Part, price 9d., contains a Portrait of the late J. M. W Turner, R.A., drawn by J. Gilbert, and engraved by W. J. Linton together with upwards of forty other choice illustrations. The first half-yearly volume of this truly National Illustrated Work will be published July 1st, in a style of binding in strict accordance with the character of the work, price 6s. 6d. It may with safety be asserted that this volume will contain a larger number of first class engravings, executed in the most finished manner, than has ever previously appeared in works of three times the cost.

SCRIPTURE LIBRARY FOR THE YOUNG, in Shilling Volumes.-The first two volumes of this instructive series of works, "The LIFE of JOSEPH," illustrated with sixteen choice engravings and maps, and "The TABERNACLE, its PRIESTS, and SERVICES," with twelve engrav. ings, are now ready.

An admirer and student at Newcastle is rather sharp on our English grammarian; but Lennie is no authority, neither is Cobbett; and Murray is on the wane. Use has the power to alter a language, and use will do it too. As to mathematical instruments, we can only give him our own experience,-viz.. that with a pair of small bow compasses, and a common ruler, or straight-edge, we carefully constructed all the figures of the Elements of Euclid. And, with the addition of the diagonal scale, we solved many practical questions and problems deducible from the same, in mensuration, surveying, trigonometry, &c. The price of the small compasses, about three inches in length, which served us for a geometrical pen, a pair of dividers, and various other purposes, was 18. 6d. The common ruler, was the bevelled edge of a diagonal scale, which cost about 18.; so that, for about half-a-crown, we had a couple of instruments that served our purpose for many a long day.

AMY (Northwich).—A friend, under this name, suggests that it would be well to render the French exercises more useful, by substituting the qualities of different objects, their origin, use, &c., for unconnected sentences, for instance, using the verb "avoir" and "un œuf." What has an egg? It has an outside, an inside, a surface, a shell, a porous membrane, the white, the yolk, the embryo or germ. What shape has the egg? It has an oval shape. How many eggs has the hen? She has thirteen, and perhaps wil! have twelve chickens, &c. Then with "être." Where is the hen's nest? It is in the poultry yard, where the cock is also. What colour is the egg-shell? It is white. What are its qualities? It is hard, yet porous. And so on, till the whole egg was examined, thus giving connexion and precision of ideas, at the same time that accurate words were acquired. Afterwards the same object might be recapitulated with other verbs and thus well fixed in the memory, with facts and observations worth treasuring up. It is quite possible to pack a multitude of materials in a small box, if skilfully disposed; why not written ideas and words in the mind?

R. A. (Dublin).-His suggestion is a very good one indeed; but we fear our subscribers would soon get tired of it, and that would defeat our purpose. There are many cheap publications on the subjects he mentions, but they are subjects upon which we intend to have papers ourselves.

J. P. Cox-A list of the best books on the subjects of which the various papers or articles treat will be a desideratum which we shall endeavour to supply; but this must be deferred to the close of each series, as we wish our own work to be first and specially consulted in reference to any subject of which it treats.

J. WN (Newtown).-When our treatise on the French language is completed, we shall consider it sufficient in itself to educate a pupil in that language.

F. BLANKLEY.-His idea of an intercommunication page is very good, and so is the sample; but we prefer the idea of correspondence, notes and queries, under our own control and management, in order to prevent the circulation of error.

LIVER.-The subject he mentions will be begun as soon as possible. He is quite right in his Latin lessons. Amare, to love, to be fond of, expresses generally the love of affection, whether with or without reflection or consideration; hence it is distinguished from diligere, to value, to have an affection grounded on esteem, as the etymology of the word implies; for diligere is derived from dis and legere; now dis is a preposition only used in composition, that is, in union with other words; and it means separately or apart; legere means to gather or collect, (from the Greek lego, to lay), that is, to lay together; but as whatever is laid together or collected apart is peculiarly esteemed or loved, it naturally follows that the verb diligere signifies to love in a more rational manner than amare does, which merely implies an affection of the mind without particular regard to the grounds or the consequences of the passion. This correspondent deserves high commendation for his laudable desire to improve himself, and for the means which he proposed to employ for that purpose. We are glad to think that our journal is likely to prove so serviceable to him.

J. PARSELLE (Kennington).-His solution of the 8th query in No. II. is complete, and similar to that inserted in this number. JOSEPHI WEBSTER.-His ingenious communication is under consider

ation.

H. H. M. D. CAMBRAY (Cheltenham).-His communication had falien aside. We now state that without some further explanation we cannot give a decided answer on the subject to which he refers, of course, the subject he is anxious about will appear.

WM WALTON.-He is right in his cbjection; the want he compisins of must be supplied.

INDOCTUS. We shall make some inquiry about the biographia! subject he speaks of.

A HARD WORKER AND THINKER-The omission will be supplied. The subjects he mentions will be treated of in our pages.

A Subscriber, at Bishop-Auckland, puts in a word or two for the ladies' department of our pages. With every wish to serve the fair KX we fear that the great objects we have in view, namely the improveme of the mind, and the elevation of the character, by the diffusion of literature and science among the people, will preclude our attemptag to meet her wishes for some time to come. Still, if she can really us by her own efforts, to disseminate the kind of information she proposes, in a way that we can heartily approve of, we shall be glad to give be some encouragement in the attempt.

C. BATES. The simplest method of ascertaining the circumference of the earth at any latitude (by which tee understand the length of any parallel of latitude), is to multiply the circumference of the earth at the equator, or rather its mean circumference, by the cosine of the pr latitude. Otherwise: in "Keith on the Globes," there is a table of ar the length of a degree of longitude, in geographical miles, correspoming to every degree of latitude, from the equator to the pole, appended i the ninth problem on the terrestrial globe. Take the number from the table, corresponding to the given latitude, and multiply it by 360, te product will be the circumference required in geographical miles. I. convert them into British miles, very nearly; take a tenth part of the geographical miles, and the half of this tenth part; then add these parts and the whole together, and the sum will be the required answer, wina a small fraction of the truth.

C. L.-There is a mistake in the VOCABULARY, in page 35, column ! No. III., for vincio, I conquer, read vincio, I bind. In the same pag stay is a misprint for slay. As to amare and diligere, they both mean w love. The errors have been corrected in later impressions.

W. P. (Dublin).-The syllables are written according to the provsi ciation. Why should our Dublin friends want them spelt in the Ita language? Not many others, we are persuaded, have any desire to se puzzled with Italian spelling in their music lessons. The change d Si (See) for Te, is already explained.

CANTABO (Hounslow).-The monochord could not be used to set the "pattern," unless you could "stop" the strings at the appointed pinoss very rapidly. Pianos are very commonly tuned more" sweet," that a more correctly, in the keys most used, being, in proportion, all the mre out of tune in the others. The best "pattern" is the voice of a curre singer. An equally accurate one is the notes of a well-played vio If you can strike the right notes on the piano (taking care of the flats o sharps peculiar to the different keys), you can set yourself the "pattern" from that instrument. But let it be only a pattern. Do not sing res the piano. Though few persons can say where precisely the piano nas are wrong, or to what extent, by the ear alone, yet almost any one can feel, as the general effect, that they are not so true and satisfactory ar "concert of sweet voices." It is easier and more natural to sing a perfect tune than in "temperament." Therefore you will soon becom more perfect than your piano-pattern, especially if you study the "mental effect of notes," of which more anon. A piano tuned by "equal temperament," would be most nearly right on the sa, thr fourth, and the second of the scale. The third (Me), the sixth (Lat. and the seventh (Te), would be considerably too sharp. dion" or "German concertina," which gives only one key, and tha tuned "sweet," would be useful for giving the pattern in the ear lessons. If you observe and think you will soon grow independent of the pattern, and a pattern in one key would serve you for any other. MICH, RAFFERTY.-The memory, like other powers of the mind, strengthened by exercise. He should endeavour to learn some asem rules by heart, and the effort itself would assist greatly in producing the power of concentration in the mind. He should, however, proceed br degrees, and not attempt too much at first. Let him begin by carryng the calf, and he will ere long be able to carry the bull.

Anr

others.

London.-May 15, 1852.