renders expression clear, by an attentive observance of appropriate pauses, and gives weight and effect to sentiment, by occasional impressive cessations of voice. It sheds light on the meaning of sentences, by the emphatic force which it gives to significant and expressive words. It avoids the "school tone of uniform inflections, and varies the voice upward or downward, as the successive clauses of a sentence demand. It marks the character of every emotion, by its peculiar traits of tone; and hence its effect upon the ear, in the utterance of connected sentences and paragraphs, is like that of a varied melody, in music, played or sung with ever-varying feeling or expression. arms, the tomahawk and scalping knife of the savage?-to call into civilized alliance the wild and inhuman inhabitant of the woods?-to delegate to the merciless Indian the defence of disputed rights, and to wage the horrors of this barbarous war against our brethren?-My lords, we are called upon as members of this house, as men, as Christians, to protest against such horrible barbarity!-I solemnly call upon your lordships, and upon every order of men in the state, to stamp upon this infamous procedure the indelible stigma of the public abhorrence!" ་ 2. Smoothness of Voice, or Purity' of Tone. The analysis of the voice, for the purposes of instruction and practice in reading and declamation, may be extended, in Smoothness of voice, in reading and speaking, is the same detail, to the following points, which form the essential proper-quality which, in relation to vocal music, is termed 'purity' ties of good style in reading and speaking. 1. Roundness. 3. Versatility, 4. Right Pitch. This property of voice is exemplified in that ringing fulness of tone, which belongs to the utterance of animated and earnest feeling, when unobstructed by false habit. It is natural and habitual in childhood; it is exhibited in all good singing, and in the properly cultivated style of public reading and speaking. To obtain roundness and fulness of voice, it is exceedingly important that the student observe the following suggestions. Be attentive to the position of the body. No person can produce a full, well-formed sound of the voice, in a lounging or stooping posture. The attitude of the body required for the proper use of the voice is that of being perfectly upright, without rigidness. The head must never be permitted to droop; it should be held perfectly erect. The back must be kept straight, and the shoulders pressed backward and downward. The chest must be well expanded, raised, and projected; so as to make it as roomy as possible, in order to obtain full breath and full voice. Breathe freely and deeply; keep up an easy fulness of breath, without overdoing the capacity of your lungs. Make your utterance vigorous and full, by giving free play to the muscles situated below the bony part of the trunk; these should move energetically, in order to drive the breath upward with due force, and thus give body to the sounds of the voice. Keep the throat freely open, by free opening of the mouth, so as to give capaciousness and rotundity to every sound. A round voice can never proceed from a half-shut mouth. The large and full effect of vocal sound, produced by the due observance of the preceding directions, forms what is called by great authorities in elocution, the 'orotund' (round, or, literally, round-mouthed) voice, which is considered the ample style of oratory, or public reading, in contrast with the limited utterance of private conversation. The attitude of body, and the position and action of the organs, demanded by 'orotund' utterance, is likewise highly favourable to health and to easy use of the voice; while stooping and lounging postures, a sunken chest, and drooping head, tend both to suppress the voice and injure the organs, besides impairing the health. Practice in the style of vehement declamation, is the best means of securing a round and full tone. The following exer. cise should be repeatedly practised, with the attention closely directed to the management of the organs, in the manner which has just been described, as producing the 'orotund,' or resonant quality of voice. Exercise on the 'Orotund.' "Who is the man that, in addition to the disgraces and mischiefs of the war, has dared to authorise, and associate with our of tone. This property of voice consists in maintaining an undisturbed liquid stream of sound, resembling, to the ear, the effect produced on the eye by he flow of a clear and perfectly transparent stream of water. It depends, like every other excellence of voice, on a free, upright, and unembarrassed attitude of the body, the head erect, the chest expanded. It implies natural and tranquil respiration (breathing); full and deep inspiration' (inhaling, or drawing in the breath); and gentle 'expiration' (giving forth the breath); a true, and firm, but moderate exercise of the larynx' (or upper part of the throat); and a careful avoiding of every motion that produces a jarring, harsh, or grating sound. 'Pure' tone is free from, 1. the heavy and hollow note of the chest ;-2. the guttural,' choked, stifled, or hard sound of the swollen and compressed throat;-3. the hoarse, husky, forcible expiration,' and too wide opening of the throat;-4. 'harsh,' 'reedy,' and grating style, which comes from too the nasal twang, which is caused by forcing the breath against the nasal passage, and, at the same time, partially closing it;-5. the wiry, or false ring of the voice, which unites voice of the mouth, which is caused by not allowing the due the guttural and the nasal tones;-6. the affected mincing proportion of breath to escape through the nose. The natural, smooth, and pure tone of the voice, as exhibited in the vivid utterance natural to healthy childhood, to good vocal music, or to appropriate public speaking, avoids every effect arising from of the chest, of the throat, or of any other organ, and, at the an undue preponderance, or excess, in the action of the muscles same time, secures all the good qualities resulting from the just and well-proportioned exercise of each. A true and smooth utterance derives resonance from the chest, firmness from the throat, and clearness from the head and mouth. Without these qualities, it is impossible to give right effect to the beauty and grandeur of noble sentiments, whether expressed in prose or in verse. and fixing, in permanent possession, the good qualities of Childhood and youth are the favourable seasons for acquiring agreeable and effective utterance. The self-taught cannot exert too much vigilance, nor take too much pains, to avoid the encroachments of faulty habit in this important requisite to a good elocution. practised, with a view to avoid every sound which mars the The subjoined exercise should be frequently and attentively purity of the tone, or hinders a perfect smoothness of voice. Exercise in Smoothness and Purity' of Voice. "No sooner had the Almighty ceased, but all Their crowns, inwove with amaranth and gold.— The various passions and emotions of the soul are, to a great extent, indicated by the 'quality' of the voice. Thus, the malignant and all excessive emotions, as anger, hatred, revenge, fear, and horror, are remarkable for guttural quality,' and strong aspiration,' or 'expiration,' accompanying the vocal sound, and forming 'impure' tone; substituting a 'harsh,' husky, aspirated utterance, for the 'orotund,' or the 'pure' tone; while pathos, serenity, love, joy, courage, take a soft and smooth oral, or head tone, perfectly pure, or swelling into 'orotund. Awe, solemnity, reverence, and melancholy, take a deep, 'pectoral' murmur; the voice resounding, as it were, in the cavity of the chest, but still keeping perfectly 'pure' in tone, or expanding into full 'orotund.' The young student cannot be too deeply impressed with the importance of cultivating, early, a pure and smooth utterance. The excessively deep 'pectoral' tone sounds hollow and sepulchral; the guttural' tone is coarse, and harsh, and grating to the ear; the nasal' tone is ludicrous; and the combination of guttural' and 'nasal' tone is repulsive and extremely disagreeable. Some speakers, through excessive negligence, allow themselves to combine the pectoral,' 'guttural, and nasal' tones, in one sound, for which the word grunt is the only approximate designation that can be found. Affectation, or false taste, on the other hand, induces some speakers to assume an extra ne, or double distilled, oral tone, which minces every word in the mouth, as if the breast had no part to perform in human utterance. The tones of serious, serene, cheerful, and kindly feeling, are nature's genuine standard of agreeable voice, as is evinced in the utterance of healthy and happy childhood. But prevalent neglect permits these to be lost in the habitual tones of boys and girls, men and women. Faithful advisers may be of much service to young students in this particular. 3. Versatility, or Pliancy of Voice. Signifies that power of easy and instant adaptation, by which it takes on the appropriate utterance of every emotion which occurs in the reading or speaking of a piece characterised by varied feeling or intense passion. To acquire this invaluable property of voice, the most useful course of practice is the repeated reading or reciting of passages marked by striking contrasts of tone, as loud or soft, high or low, fast or slow. The following exercises should be repeated till the student can give them in succession, with perfect adaptation of voice in each case and with instantaneous precision of effect. Exercises for Versatility, or Pliancy of Voice: "And dar'st thou, then, To beard the lion in his den, The Douglas in his hall? And hop'st thou hence unscathed to go? No! by St. Bride of Bothwell, no! Up, drawbridge, groom! What! warder, ho! Very Soft. "I've seen the moon climb the mountain's brow, "I had a dream, which was not at all a dream, "I awoke-where was I?-Do I see "In every period of life, the acquisition of knowledge is one of the most pleasing employments of the human mind. But in youth, there are circumstances which make it productive of higher enjoyment. It is then that every thing has the charm of novelty; that curiosity and fancy are awake, and that the heart swells with the anticipations of future eminence and utility." Contrast this pitch with that of the pieces before quoted, as examples of 'high' and 'low.' IL DUE QUANTITY, OR LOUDNESS. The second characteristic of good reading, is the use of that degree of loudness, force, 'volume,' or 'quantity,' of voice which enables those to whom we read or speak, to hear, without effort, every sound of the voice; and which, at the same time, gives that degree of force which is best adapted to the utterance of the sentiments which are read or spoken. and an All undue loudness is a great annoyance to the ear, injury to the expression; while a feeble and imperfect utterance fails of the main purposes of speech, by being partly or entirely inaudible, and consequently utterly unimpressive. The failure, as regards loudness, is usually made on passages of moderate force, which do not furnish an inspiring impulse of emotion, and which depend on the exercise of judgment and discrimination, rather than of feeling. It is of great service, however, to progress in elocution, to possess the power of discriminating the various degrees of force which the utterance of sentiment requires. The extremes of very 'loud' and very soft,' required by peculiar emotions, have been exemplified in the exercise on 'versatility' of voice. There are three degrees of loudness, all of great importance to the appropriate utterance of thought and feeling, required in the usual forms of composition. These are the following: moderate, forcible,' and 'impassioned.' The first, the 'moderate,' occurs in the reading of plain narrative, descriptive, or didactic composition, addressed to the understanding, rather than to the feelings: the second, the 'forcible,' is exemplified in energetic declamation: the third, the impassioned,' occurs in the language of intense emotion, whether in the form of poetry or of prose. Watchful attention will be required, on the part of the student, in practising the following examples, so as to enable him to detect, and fix definitely in his ear, the exact degree 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! 14 quent reading. C'est pourquoi elle s'empressa de prodiguer ses soins à la petite orpheline.15 Fedora ne savait comment lui téElle devint bientôt pour Exercise in Moderate' Force. 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. "An author represents Adam as using the following lan-moigner sa reconnaissance.16 guage. 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. "Advance, then, ye future generations! We bid you welcome to this pleasant land of the Fathers. We bid you welcome to the healthful skies, and the verdant fields of New England. We greet your accession to the great inheritance which we have enjoyed. We welcome you to the blessings of good government and religious liberty. We welcome you 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,- It is strange !-it is dreadful!-Shout, Tyranny, shout, 3 C'ETAIT en mil 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." 9 Cepandant l'armée de Napoléon commença sa retraite 18 et la vivandière dut quitter Moscou. Les parents de Fœdora existaient-ils encore? C'est ce que rien n'était venu révéler.19 Fodora partit donc avec l'armée française.20 Qu'on juge de ce qu'un enfant de cet âge eut à endurer pendant une pareille retraite! Au passage de la Bérézina, Fedora eut encore le malheur de se trouver séparée de sa bienfaitrice, soit que celle-ci eut péri dans les flots, soit qu'elle crût la jeune enfant égarée! Quoiqu'il en soit, orpheline ne la trouva plus,22 et elle se vit de nouveau délaissée. COLLOQUIAL EXERCISE. 21 12. Que vint faire la vivandière 13. La vivandière eut-elle pitié 15. Que fit la vivandière ? 17. Qu'apprit-elle peu à peu ? 19. Avait-on découvert les pa- 21. Qu'arriva-t-il au passage d 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.-h. 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. A. W. (Edinburgh): His solution to Prob. 60 in Algebra is correct; the others want improvement.-J. R. (Port of Monteith): We wish our young friend Mary had been more successful, but hundreds of maturer years have failed in the Four Ball Question.-B. K.: It is not the privilege of persons academic distinction, compared with the filling of the cranium.-W. MASON who have matriculated only to wear gowns and caps; but this is a small (St. Ives): Electrotyping comes under Physics, and illuminating gas under DAVIS (Maida Hill): Solutions of algebraic problems received. Chemistry.-WARIN (East Dereham); G. SMITH (Manchester); H. D. 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 épargnait encore. Son père et sa mère avaient disparu, et per-solved Geometrical Problems in "Cassell's Euclid," and others to be found 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. 11 Sans doute elle ne se serait plus réveillée, la mort serait venue la surprendre, si une vivândière, qui par harsard vint 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 acquainted with more than we gave them credit for, in the interesting science of algebra. PROBLEM.-Required two numbers such that their product is equal to the difference of their squares, and the sum of their squares equal to the difference 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 caloric; 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. 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 game, 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, but would be inclined to each other in a direction parallel to the ecliptic. One result of this would be, that the temperatures on the eastern and western edges of the image of the sun would nct be equal. By means of a thermo-electric calorimeter placed in the telescope, it was found that the temperature of the eastern edge of the sun's image exceeded that of the western edge, and that consequently the velocity of the calorific rays was less than that of the luminous rays. The mean of a great number of observations gave the proportion above mentioned; but this result requires confirmation by other experiments. Variation of the Intensity of Radiant Caloric.-Three causes modify the intensity of radiant caloric; the temperature of the source of heat, its distance, and the obliquity of the calorific rays in relation to the surface which emits them. Thus, the three following laws on the intensity of radiant caloric are recognised. VOL. V. 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 10°, 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. 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. Moveable Equilibrium of Temperature.-Two hypotheses have been proposed as the principle of radiation; in the first it is supposed that, when two bodies of unequal temperature are near each other, radiation takes place only from the warmer body to the other which is cooler than it, the latter emitting nothing towards the former, until the temperature of the warmer body is gradually lowered and becomes the same as that of the other body, and then all radiation ceases. This hypothesis has been replaced by the second, which is generally adopted in the present state of our knowledge, and is due to M. Prevost of Geneva, viz., that all bodies, whatever be their temperature, are constantly emitting caloric in all directions. Then, a loss of temperature, that is a cooling, takes place in those bodies whose temperature is the highest, because that the rays which they emit have a greater intensity than those which they receive. On the contrary, a gain of temperature, that is a heating, takes place in those bodies whose tempera109 ture is lowest. Consequently there is a period when the temperature is the same in both; but then there is still an exchange of caloric between the bodies, only that each receives as much as it emits; and thus the temperature remains constant. This particular state of the bodies is denoted by the name of the moveable equilibrium of temperature. Newton's Law of Refrigeration.-A body placed in a vacuum is only cooled or heated by radiation. In the atmosphere a body is cooled or heated by radiation and by contact with the air. In both cases the velocity of cooling or heating, that is, the quantity of heat lost or gained in a second, is proportional to the difference of temperature. Newton has stated the following law on the cooling or heating; of bodies:-The quantity of heat which a body loses or gai per second, is proportional to the difference between its temperature and that of the surrounding medium. MM. Dulong and Petit have shown that this law is not general, as Newton supposed, and that it is only applicable to difference of temperatures which do not exceed 15 or 20 Centigrade. Beyond this the quantity of heat lost or gained is greater than the law indicates. The following are consequences of Newton's law : 1st. When a body is exposed to a constant source of heat, its temperature is not raised to an indefinite extent, for the quantity of heat which it receives in equal times is always the same, whilst that which it loses increases with the excess of its temperature above that of the surrounding air. A period will, therefore, arrive when the quantity of heat emitted is equal to that which is absorbed, and the temperature is then &ationary. 2nd. The law of Newton, applied to the differential thermometer, shows that the indications of this instrument are proportional to the quantities of heat which it receives. For instance, let one of the bulbs of a differential thermometer receive rays of heat emitted from a constant source; the instrument will at first indicate increasing temperatures, then it will become stationary; and this will be indicated by the fixed position which the index assumes. At this instant the quantity of heat which the bulb receives is equal to the quantity which it emits. But the quantity is, according to the law of Newton, proportional to the excess of the temperature of the bulb above that of the medium, that is, to the number of degrees marked on the the mometer. Therefore, the teinperature indicated by the dential thermometer is also proportional to the quantity caloric which it receives. 1st. The angle of reflection is equal to the angle of inci. dence, 2nd. The incident ray and the reflected ray are in the same plane which is perpendicular to the reflecting surface. These two laws are proved by means of concave mirrors, Fig. 166. D B Reflection of Concave Mirrors.-Spherical or parabolic surfaces made in metal or in glass, and constructed so as to concentrate in the same point luminous or calorific rays, are called concare mirrors or reflectors. Let us consider the case of spherical mirrors. In fig. 168 are represented two of these mirrors, and in fig. 167 a vertical and focal section of one of them. The centre, c, (fig. 167) of the sphere to which the mirror belongs (that is, of which it would form a part), is called the centre of curvature; the point ▲, the middle of the reflector, is the centre of figure; and the straight line, A B, drawn through these two points, is the principal axis of the mirror. In order to apply to spherical mirrors the laws of reflection which belong to plane surfaces, they are considered as formed of an infinity of plane surfaces each infinitely small-a hypothesis which admits of our demonstrating geometrically that the normals to these small surfaces all meet in the centre of curvature. Thus, on the axis A B of the mirror MN, let a source of heat be supposed to be situated at a distance sufficiently great, so that the rays EK, PH, etc., which emanate from it, may be considered as parallel to AB and to each other. According to this hypothesis, that the mirror is formed of an infinite number of plane surfaces each infinitely small, the ray EK is reflected from the element K as from a plane mirror; whence, the straight line cK being normal to this element, the ray takes a direction, K F, such that the angle CKF is equal to the angle C K E. The other rays, PH, GI, etc., being reflected in the same manner, all these rays, after reflection, sensibly meet in the same point, F, situated in the middle of Ac, as demonstrated in " Optics." There is, therefore, at the point a THE REFLECTION, EMISSION AND ABSORPTION OF meeting of the calorific rays, and consequently a greater eleva 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: tion of temperature there than at any other point. Whence the name focus (Latin, a fire) has been given to this point. The distance FA of the focus from the mirror is called the focal distance. In the accompanying figure, the caloric is propagated along the lines EKF, LDF, etc., in the direction of the arrows; but conversely, if the heated body is placed at F, the caloric is propagated along the lines FKE, FDL, etc., so that the rays emitted from the focus become, after reflection, parallel to each other and to the axis AB; whence it follows that the heat which is transmitted does not lose its intensity. Conjugate Mirrors.-The following experiment, made nearly at the same time by Scheele in Sweden, and by Pictet at Geneva, proves the existence of the foci, and also the laws of the reflection of caloric. Two reflectors of the same size were arranged about four or five yards apart from each other, is Fig. 167. H |