of loudness appropriate to each passage. The exercises should établir son petit marché de vivres 12 près de cette église, ne be repeated till they can be executed with perfect precision, l'eut aperçue' et ne se fut senties touchée de compassion 13 so as to form a standard for all similar expression, in subse-pour la malheureuse enfant. Elle aussi avait des enfants! quent reading.

Exercise in Moderate' Force.

"An author represents Adam as using the following language. I remember the moment when my existence commenced: it was a moment replete with joy, amazement, and anxiety. I neither knew what I was, where I was, nor whence I came. I opened my eyes: what an increase of sensation! The light, the celestial vault, the verdure of the earth, the transparency of the waters, gave animation to my spirits, and conveyed pleasures which exceed the powers of

utterance.'

'Declamatory' Force.

C'est pourquoi elle s'empressa de prodiguer ses soins à la petite orpheline.15 Fodora ne savait comment lui témoigner sa reconnaissance.16 Elle devint bientôt pour sa seconde mère une aide fort intelligente. Peu à peu, elle apprit à comprendre sa bienfaitrice" et puti lui exprimer tout ce que son cœur renfermait de reconnaissance et d'amour.

Cepandant l'armée de Napoléon commença sa retraite 1 et la vivandière dut quitter Moscou. Les parents de Fœdora existaient-ils encore? C'est ce que rien n'était venu révéler.19 Fœdora partit donc avec l'armée française.20 Qu'on juge de ce qu'un enfant de cet âge eut à endurer “Advance, then, ye future generations! We bid you wel- pendant une pareille retraite! Au passage de la Bérézina, come to this pleasant land of the Fathers. We bid you wel- Fedora eut encore le malheur de se trouver séparée de sa come to the healthful skies, and the verdant fields of New bienfaitrice,21 soit que celle-ci eut péri dans les flots, soit England. We greet your accession to the great inheritance qu'elle crût la jeune enfant égarée! Quoiqu'il en soit, which we have enjoyed. We welcome you to the blessings l'orpheline ne la trouva plus,22 et elle se vit de nouveau of good government and religious liberty. We welcome you délaissée. to the treasures of science and the delights of learning. We welcome you to the transcendant sweets of domestic life, to the happiness of kindred, and parents, and children. We welcome you to the immeasurable blessings of rational existence, the immortal hope of Christianity, and the light of everlasting Truth!"

'Impassioned' Force.

"Shame! shame! that in such a proud moment of life,
Worth ages of history,-when, had you but hurled
One bolt at your bloody invader, that strife
Between freemen and tyrants had spread through the
world,-

That then,-Oh! disgrace upon manhood!-e'en then

You should falter,-should cling to your pitiful breath,Cower down into beasts, when you might have stood men, And prefer a slave's life, to a glorious death!

COLLOQUIAL EXERCISE.

1. En quelle année Napoléon 12. Que vint faire la vivandière
entra-t-il dans Moscou?

2. Quelle ville l'Empereur
menaçait-il de là?

3. Par quoi Rostopchin fut-il
poussé ?

4. Quelle résolution prit alors
le gouverneur ?

5. Où étaient les habitants ?
6. Que s'efforçaient-ils d'em-
porter ?

7. Qu'arriva-t-il à la petite fille

d'un négociant?

8. Que faisait la petite?
9. Où étaient son père et sa
mère ?

It is strange !—it is dreadful!-Shout, Tyranny, shout,
Through your dungeons and palaces, Freedom is o'er !'-10.
If there lingers one spark of her fire, tread it out,
And return to your empire of darkness once more."

FRENCH READING S.-No. X.

FEDORA.

SECTION I.

C'ETAIT en mila huit cent douze; Napoléon, à la tête des ses troupes victorieuses dans les plaines de la Moskowa, était entré dans l'antique capitale de l'empire des czars, et, de là menaçait la nouvelle ville fondée par Pierre-le-grand.2 Poussé par un patriotisme fanatique, le gouverneur de Moscou, Rostopchin, prit alors cette résolution qui a porté un coup si funeste au succès de nos armes, celle d'incendier la ville, dont l'empereur Alexandre lui avait confié la garde. Nous ne raconterons pas toutes les circonstances de cet épouvantable drame. Chassés de leurs demeures en feu, croulant sous les efforts des flammes, c'était un spectacle affreux que de voir tous les habitants mêlés à nos soldats, forcés de fuir en emportant ce qu'ils pouvaient dérober à la violence de l'incendie."

Dans quelle situation se trouva-t-elle à la pointe du jour ?

11. Se serait-elle réveillée ?

près de l'église ?

13. La vivandière eut-elle pitié
de la petite malheureuse?
14. Pourquoi eut-elle pitié de
Fœdora?

15. Que fit la vivandière?
16. Fedora parut-elle reconnais-

sante?

17. Qu'apprit-elle peu à peu? 18. Que fit l'armée quelque temps après ?

d

19. Avait-on découvert les pa
rents de Fodora?
20. Que fit-elle alors?
21. Qu'arriva-t-il au passage
la Bérézina?
22. L'orpheline retrouva-t-ell
sa bienfaitrice?

NOTES AND REFERENCES.—a. L. part ii., § 23, R. (5)-b. ça et là, here and there; L. S. 98, R. 3.-d. se prit á dormir, fell asleep; from prendre; L. part ii., p. 100.-e. from venir; L. part ii., p. 108.-f. L. S. 97, R. 4.-9. L. S. 97, R. 5.-4. from apprendre; L. part ii., p. 78.-i. from pouvoir; L. part ii., p. 100.-j. dut, was compelled to; from devoir.-k. soit, be it; from être.-l. from croire; L. part ii., p. 84.

ANSWERS TO CORRESPONDENTS.

persons

A. W. (Edinburgh): His solution to Prob. 60 in Algebra is correct; the friend Mary had been more successful, but hundreds of maturer years have others want improvement.-J. R. (Port of Monteith): We wish our young failed in the Four Ball Question.-B. K.: It is not the privilege of academic distinction, compared with the filling of the cranium.-W. Master who have matriculated only to wear gowns and caps; but this is a small (St. Ives): Electrotyping comes under Physics, and illuminating gas under Chemistry.-WARIN (East Dereham); G. SMITH (Manchester); H. D. DAVIS (Maida Hill): Solutions of algebraic problems received. We have received a great number of names to be attached to the Petition for removing the restrictions of the University of London in reference to graduates who do not belong to any of the affiliated colleges. The petition will be presented on the first Wednesday in April, and their names will be published immediately after the presentation.

We have received solutions of our Centenary of Algebraic Problems from a great many of our Correspondents, and we shall give their names and solutions a place in our pages very soon indeed.

La petite fille d'un négociant, à peine âgée de six ans, se trouva perdue dans le tumulte. Abandonnée, transie de froid, elle errait ça et là à travers les rues que le feu éparSon père et sa mère avaient disparu, et per-solved Geometrical Problems in "Cassell's Euclid," and others to be found gnait encore. We shall pay a similar debt to many of our Correspondents who have Sonne ne semblait vouloir la recueillir. La nuit se passa in the P. E. ainsi tout entière; et quand le jour commença à poindre, Fodora, exténuée de fatigue et de faim, s'affaissa devant la porte d'une église 10 et se prit à dormir.

We also propose a Quadratic Equation to be solved by the rules of simple equations or of pure equations, as some of our students seem to be ac quainted with more than we gave them credit for, in the interesting science of algebra. difference of their squares, and the sum of their squares equal to the differ PROBLEM.-Required two numbers such that their product is equal to the

Sans doute elle ne se serait plus réveillée, la mort serait venue la surprendre, si une vivandière, qui par harsard vintence of their cubes.

ON PHYSICS, OR NATURAL PHILOSOPHY.

No. XXXI.

(Continued from page 55.)

RADIATION OF CALORIC.

Propagation of Caloric in a Homogeneous Medium.-When a body is placed in a medium of which the temperature is higher or lower than its own, it is always observed that the temperature of the body rises or falls by degrees, until it has reached that of the medium by which it is surrounded; whence it is inferred that the body has gained or lost a certain quantity of heat-a quantity which it has taken from the medium, or which it has given to the same. Heat, therefore, is transmitted from one body to another, through space, in the same manner as light. The caloric which is thus propagated at a distance is called radiant calorie; and a ray of heat, or a calorific ray, is the straight line which caloric takes in its propagation.

Heat is also transmitted through the very mass of bodies; it is then an actual interior radiation from particle to particle which is produced, and which we recognise under the name of conductibility.

Laws of Radiation.-The radiation of caloric is presented to us under the three following laws :

1st. Radiation takes place in all directions around heated bodies. Thus, if we place a thermometer in different positions around a heated body, it will indicate in all of them an elevation of temperature.

2nd. In a homogeneous medium radiation takes place in straight lines. For if we interpose a screen on the straight line which joins the source of heat and the thermometer, the latter will cease to be influenced by that source. But in passing from one medium into another, as from air into glass, the calorific rays, like the luminous rays, are generally deflected-a phenomenon which is denominated refraction, and of which we shall see the laws under the head of "Optics," these laws being the same both for light and for heat.

3rd. Radiant caloric is propagated in a vacuum as well as in air. This is proved by placing a small thermometer in an exhausted receiver. For if we bring a heated body near to it, we perceive the thermometer rising at its approach, a phenomenon which can only be ascribed to the radiation of heat in a vacuum; for we shall soon see that glass does not conduct heat sufficiently well to propagate it through the sides of the receiver and the stem of the thermometer.

1st. The intensity of radiant caloric is proportional to the temperature of its source.

2nd. This intensity is in the inverse ratio of the square of the distance.

3rd: The intensity of the calorific rays is less in proportion as their direction is more oblique in relation to the radiating surface from which they are emitted.

The first law is proved by presenting one of the bulbs of a differential thermometer to variable sources of heat, as a cubic vessel made of tin and filled successively with water at the temperatures of 30°, 20°, and 10o, on the Centigrade thermometer. In this case it is found that, at the same distance, the thermometer indicates temperatures which are in the same ratio as those just mentioned, viz., as the numbers 6, 4, and 2 are to each other.

In order to prove the second law by experiment, a differential thermometer is placed at a certain distance from a constant source of heat, and then at a double distance, and we find that the thermometer in the second position indicates a temperature four times less than in the former position. At a triple distance it indicates a temperature nine times less.

This second law is also proved by referring to the geometrical theorem that the surface of a sphere increases as the square of its radius. Thus, if we conceive a hollow sphere of any radius, at the centre of which is placed a constant source of heat, every unit of the interior surface receives a fixed quantity of heat. Now, if the radius of the sphere be doubled, its surface, according to the theorem just cited, would be quadrupled. The interior surface would therefore contain four times more units of surface; and as the quantity of heat emitted from the centre remains the same, every unit would necessarily receive four times less of it.

4th. The velocity of the propagation of caloric has not been yet ascertained with sufficient accuracy. It was generally considered, till very lately, that heat travelled with the same, or nearly the same, velocity as light. Modern experiments have led to the conclusion that the rate at which heat is radiated from the sun is only about four-fifths of the rate at which light is propagated from the same luminary, or about 160,000 miles per second. Von Wrede measured the velocity of heat in the following manner: he considered that if the heat and light in the sun's rays possessed unequal velocities, that the aberrations of these rays would also be unequal; and that consequently the image of the sun, formed in a telescope by the calorific rays and by the luminous rays, would not coincide, Moveable Equilibrium of Temperature.-Two hypotheses have but would be inclined to each other in a direction parallel to the been proposed as the principle of radiation; in the first it is ecliptic. One result of this would be, that the temperatures on supposed that, when two bodies of unequal temperature are the eastern and western edges of the image of the sun would near each other, radiation takes place only from the warmer nct be equal. By means of a thermo-electric calorimeter placed body to the other which is cooler than it, the latter emitting in the telescope, it was found that the temperature of the nothing towards the former, until the temperature of the eastern edge of the sun's image exceeded that of the western warmer body is gradually lowered and becomes the same as edge, and that consequently the velocity of the calorific rays that of the other body, and then all radiation ceases. This was less than that of the luminous rays. The mean of a great hypothesis has been replaced by the second, which is generally bumber of observations gave the proportion above mentioned; adopted in the present state of our knowledge, and is due to but this result requires confirmation by other experiments. M. Prevost of Geneva, viz., that all bodies, whatever be their Variation of the Intensity of Radiant Caloric.-Three causes temperature, are constantly emitting caloric in all directions. modify the intensity of radiant caloric; the temperature of the Then, a loss of temperature, that is a cooling, takes place in source of heat, its distance, and the obliquity of the calorific those bodies whose temperature is the highest, because that rays in relation to the surface which emits them. Thus, the the rays which they emit have a greater intensity than those three following laws on the intensity of radiant caloric are which they receive. On the contrary, a gain of temperature, recognised. that is a heating, takes place in those bodies whose tempera109

The third law can be proved by the following experiment: Fix horizontally on a support, a tube made of pasteboard blackened in the interior, and about twenty inches long. At one of its extremities place the bulb of a differential thermometer, and at the other a cubic vessel made of tin, filled with boiling water, and arranged so that one of its faces may be perpendicular to the axis of the tube. The calorific rays which reach the bulb of the thermometer being necessarily directed in a straight line parallel to this axis, it is evident that they are perpendicular to the face of the cube. When the thermometer becomes stationary, note the number of degrees which it indicates; then, without altering the distance of the parts of the apparatus, turn the cube slightly in such a manner that the face, which was perpendicular to the axis, may now be more or less inclined to it. In this new position the rays of heat, which always take that direction in the tube which is parallel to the axis, are now inclined to the face of the tube, at the same time the portion of this face from which the radi ation proceeds to the thermometer-bulb is increased. In the first case, in fact, this portion of the face was equal to the interior section of the tube parallel to the axis; in the second case it is equal to an oblique section of that tube. The radiant surface is thus increased, and the tube is traversed by a greater number of calorific rays. Now, the differential thermometer continues to indicate the same temperature; therefore the oblique rays are less intense than the perpendicular rays. The doctrine of forces shows that the intensity of the rays is proportional to the sines of the angle which their direction makes with the radiant surface.

YOL. V.

THE REFLECTION, EMISSION AND ABSORPTION OF
CALORIC.

Laws of Reflection.-When the calorific rays fall on the surface of a body, they are generally divided into two sets; the one set penetrates the mass of the body, the other set rises as if it were driven from the surface in the manner of an elastic ball, a phenomenon which is described by saying that it is reflected. Thus, if m n, in fig. 166, represents a plane reflecting surface; AB a ray of heat, called the incident ray; BD a straight line perpendicular to the surface m n, called the normal to that surface; and B C the ray of heat thrown off the surface, called the reflected ray; then the angle A B D is called the angle of incidence, and the angle DBO is called the angle of reflection. Now, as the reflection of caloric takes place in the same manner as the reflection of light, the following laws hold good in the former as well as in the latter :

Fig. 167.

such a manner that their axes coincided. At ▲, fig. 168, the focus of one of them, is placed a small iron-wire basket of red-hot coals, and in the focus of the other, at B, is placed an inflammable body, as a piece of amadou or tinder. Then, the rays emitted from the source of heat, at A, are reflected, the first time, from the mirror at whose focus this source is placed; and taking, in consequence of this reflection, a direction parallel to the axis, these rays are reflected the second time from the other mirror and meet at its focus B. This is proved at once by the result; for the piece of tinder placed at this point is set on fire: but either above or below the focus this phenomenon does not take place.

This experiment proves that heat and light are reflected according to the same laws. Moreover, if we place at the focus A a lighted candle, and at the focus в a piece of ground glass, there will be seen in the latter a luminous focus exactly in the place where the tinder was set on fire. This shows that a luminous focus and a calorific focus are formed at the same point; the reflection takes place, therefore, in both cases, according to the same laws.

ice, the surrounding air being at 12° or 15o Centigrade, and
in the focus of the other a differential thermometer, this
instrument will indicate a reduction of several degrees of
temperature. This phenomenon seems, at first sight, to be
the effect of the frigorific rays emitted from the ice; but this
apparent reflection of cold, as it is called, is explained on the
principles, above stated, concerning the equilibrium of tempe-
rature which bodies always tend to establish between each
other. There is still an exchange of caloric, just as in the
experiment of the setting of the tinder on fire, only the parts
of the phenomenon are changed; and in this case it is the
thermometer which is the warm body. As the rays which it
emits are stronger than those emitted by the ice, there is no
compensation between the heat which it gives and the heat
which it receives; whence its reduction of temperature. It
is on the same principle that we explain the cold which is felt
when we are near walls in plaster, stone, or marble; and, in
general, when we are close to any body whose temperature is
lower than our own.
Reflecting Power.-The property which bodies possess of

Fig. 168:

B

feet.

It is owing to the high temperature which can be obtained | by means of the foci of concave mirrors that they have been called burning mirrors. It is related that Archimedes set on fire the vessels of the Romans before Syracuse by the application of such mirrors. M. Buffon constructed burning mirrors of such power as to prove that the fact ascribed to the ingenuity of Archimedes was possible. These mirrors were formed of a great number of pieces of silvered glass about eight inches long and six inches broad. They could be turned independently of each other in any direction, so that the reflected rays could be made to meet in the some point. With 128 pieces of glass and a burning summer's sun, Buffon set on fire a tarred plank of wood at the distance of about 220 Reflection in a Vacuum.-Caloric is reflected in a vacuum as well as in air. This was proved by Sir Humphrey Davy by the following experiment. Under the exhausted receiver of an air-pump, two small mirrors were placed facing each other; in the focus of the one there was a very sensible thermometer, and in the focus of the other a source of electric heat, consisting of platinum wire, which was rendered incandescent by making the current of a voltaic pile pass through it; the thermometer rose immediately, by several degrees, on the application of the current- a phenomenon which was only due to the reflected caloric, for the thermometer would have experienced no elevation of temperature had it not been exactly in the focus of the second mirror.

Apparent Reflection of Cold.If two reflectors are arranged facing each other, as represented in fig. 168, and instead of red-hot coals we place in the focus of one of them a piece of

reflecting a greater or less portion of the heat which falls upon them, is called their reflecting power. This power varies considerably in different substances. In order to ascertain experimentally the reflecting power of a variety of substances without constructing a number of reflecting mirrors, Sir John Leslie arranged his experiments in the manner represented in fig. 169.

The source of heat is a hollow cube, м, filled with boiling water. On the axis of a spherical reflector, between the focus and the mirror, is fixed a plate, A, formed of the substance whose reflecting power is required. With this arrangement, the rays emitted from the source and reflected the first time, fall on the plate A, and are thence reflected a second time, forming their focus between the plate and the mirror, in a point where the bulb of a thermoscope is placed. Now, the mirror and the thermoscope remaining unchanged, and the water in the cube being kept always at 100° Centigrade, the temperature indicated by the thermoscope varies with the nature of the substance of which the plate A is formed when subjected to the experiment; whence we deduce not the absolute reflecting power of a body, but the ratio of this power to that of another body, assumed as a standard of comparison; that is, in conformity with what has been said on the application of Newton's law, the temperatures indicated by this instrument are proportional to the quantities of heat which it receives. Thus, if a plate of glass causes the differential thermometer to rise 1°, and a plate of lead causes it to rise 6°, we conclude that the heat reflected by lead is six times greater than that reflected by glass; for the quantity of heat emitted by the source is the same, the concave mirror reflects

the same portion of it to each, and the difference can only depend on the reflecting power of the plates at A. According to this mode of experimenting, and by representing the reflecting power of brass by 100, when taken as a standard of comparison, Leslie constructed the following table of the relative reflecting powers of different substances:

100
90

80

:

M. Melloni has also investigated the reflecting powers of Relative Reflecting Powers. bodies, and it follows from his experiments and those of Leslie, that the reflecting power of metals is much greater than that of other bodies, as shown in the preceding table. M. Melloni has proved, by means of his apparatus, that of all the metals, mercury has the greatest reflecting power. There are causes, however, which modify the reflecting power of the same body.

70

60

13

Fig. 169.

LESSONS IN CHEMISTRY.-No. XXX.

As a preliminary to our cupelling operations, we shall require a small piece of lead, say a shot, a piece of wood charcoal, and a blowpipe. First excavate in the smooth surface of the piece of charcoal a slight depression, and into this deposit the lead; which being done, direct upon the lead the continuous outside halo of a blowpipe-flame, as represented by the accompanying sketch, fig. 27.

The metal will fuse at first; then, becoming converted into oxide, the surface of the charcoal, to the extent perhaps of a quarter of an inch all round, will assume a yellowish or reddish aspect, due to the presence of oxide of lead. By continuing sufficiently long the blowpipe operation, all the metal admits of being oxidised. Careful attention of the phenomena which present themselves during the operation of fusion, will moreover show that the oxide of lead thus produced is remarkably fusible; will show that the oxide becomes, in point of fact, quite liquid, soaking into the substance of the charcoal, where it may be observed on breaking the latter across. It follows, therefore, that if instead of charcoal we had employed some other material of greater absorbent power, all the oxide might have been removed; filtered away, thus to speak, so soon as formed. We are beginning to see the principle upon which depends the cupelling operation. Let the student now assume a general case. Let it be assumed, I say, that instead of lead alone exposed to an oxidising heat, we had to deal with an alloy of lead and some other metal, the latter being capable of fusion but not oxidation; then it follows theoretically, that separation of the two metals might be effected by taking advanIn other tage of the chemical peculiarity just mentioned. words, while all the lead should be susceptible of oxidation and absorption, all of the second metal remained behind. Let us now proceed one step further in our theoretical investigation