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may be made red-hot. Again, in the common process of striking a light with flint and steel, the heat is evolved by percussion; and to such an extent, as to determine a chemical combination between the minute fragments of metal separated, and the oxygen of the atmosphere. The elevation of temperature produced in metals by percussion, is said to be attended by conden sation; that is, their density is increased.
The best set of experiments on this subject has been made by Biot, Bertholet, and Pictet. The experiments were made upon pieces of gold, silver, and copper, of the same size and shape; and care was taken that all the parts of the apparatus had acquired the same temperature before the experiments began. It may be shortly stated, that copper evolved the most heat, silver was next in order, and gold evolved the least. The first blow produced the most heat in every instance, and it diminished gradually, and after the third blow was hardly perceptible. The heat acquired was estimated by throwing the piece of metal struck into a quantity of water, and ascertaining the change of temperature which the water underwent. The change of specific gravity in the metals, was found to be proportional to the heat thus evolved, thus shewing that condensation had accompanied the action; hence, when they could no longer be condensed, they ceased to evolve heat. In the rolling of metallic plates, and in the drawing of wires, considerable heat is evolved; and it is worthy of remark, that after the evolution of caloric from any metal by mechanical pressure or percussion, the metal is rendered more brittle, and will not afford any more heat by a repetition of the process, until after it has been again heated in the fire. In this particular the effect of friction seems to differ-the source of heat there appears inexhaustible.
The development of caloric by condensation is shewn most evidently, when aeriform fluids are exposed to mechanical operation. It had been observed, that a slight flash of light accompanied the discharge of an air-gun in the dark; this led to the construction of what is called the condensing tinder-box. This instrument consists of a brass tube about six inches long, closed at one end and open at the other. Into this tube there is fitted a piston, which, by means of a little silk or leather well greased, is made to fit the tube accurately. At the end of the piston, a fragment of a particular sort of tinder, called amadou, which is made of a species of fungus well beaten, steeped in a solution of nitre, and then dried, is fixed; and by one rapid and violent stroke
of the piston, this bit of tinder is in general ignited. Desmartiers has shewn that atmospheric air, or oxygen gas, are the only fluids with which condensation produces this effect. M. Biot, by condensation, effected the combination of oxygen and hydrogen gases, having compresed them violently by the piston of an air-gun. The heat evolved added so greatly to the expansive force of the gases, that, in two out of three experiments, the barrel was burst by the explosion.
That friction will evolve heat is well known, even among savage nations, who frequently kindle their fires by rubbing two pieces of dry wood smartly together. The wheels of carts and coaches, when not properly greased, will frequently take fire from the friction between the nave and axletree. In what manner then is caloric evolved or accumulated in these cases? Count Rumford instituted a series of most interesting experiments, to ascertain the cause of this phenomenon: in a work like this it would take up too much space to detail his various experiments, but the results may be briefly mentioned.
He found that the heat evolved by friction was not produced by increasing the density of the bodies rubbed against each other, as happens in cases of percussion; for heat is produced by rubbing soft bodies together, as any one may experience by rubbing his hand smartly against any woollen substance. Nor is it owing to the specific heat of the rubbed bodies decreasing, for the Count found that there was no sensible decrease; nor, if there were a decrease, would it be sufficient to account for the vast quantity of heat which is sometimes produced by friction. Neither is it owing to, or connected with, the decomposition of oxygen gas, for precisely the same results ensued when the apparatus was enclosed under an exhausted receiver, and also when buried in water.
In this last experiment, Count Rumford contrived to enclose a metal cylinder, bored to admit a blunt steel borer, in a wooden box filled with water, so as to effectually exclude all air. The borer was made to press upon the bottom of the cylinder with a weight equal to about 10,000 pounds avoirdupois, and the cylinder to revolve at the rate of thirty-two times in a minute. The quantity of water amounted to 18.77 pounds avoirdupois, and, at the beginning of the experiment, was at the temperature of 60°. After the cylinder had revolved for an hour, the temperature of the water was 107°; in thirty minutes more it arose to 178°; and in two hours and thirty
minutes from the commencement of the experiment, the water actually boiled.
M. Haldot repeated the experiments of Count Rumford, and obtained the same results. He found that different metals gave different degrees of heat; zinc evolved the greatest degree of heat, then brass and lead, and afterwards tin, which only produced of the heat evolved during the friction of lead. By quadrupling the pressure, the heat evolved was seven times greater than before. When the rubber was rough, it produced but half as much heat as when smooth. When the apparatus was surrounded by bad conductors of heat, or by non-conductors of electricity, the quantity of heat evolved was diminished. Mr. Wedgwood found, that by pressing a piece of window-glass against a revolving wheel of grit, the glass became red-hot at the point of friction, and gave off sparks capable of igniting gunpowder. Sir H. Davy contrived to melt ice by friction, within an atmosphere which was not suffered to rise above the temperature of 32° of Fah
The most obvious properties of caloric are radiation, reflection, absorption.
Radiation may be defined to be the free motion of heat; that is, those philosophers who suppose caloric to be an existent material fluid, suppose that the particles of which this fluid is composed, are endued with a vast idio-repulsive force, and that they move in right lines with unmeasured velocity in appropriate media, wherein no resistance is opposed to them.
The earliest experiments usually cited upon this subject, are those of Mariotte. He states that "the heat of a fire reflected by a burning mirror is sensible in its focus; but if a glass screen is interposed between the mirror and the focus, the heat is no longer sensible." Scheele is the first who made use of the term radiant heat, and shewed that it did not communicate warmth to the air through which it was made to pass. He proved also, that its passage through a space filled with air, was not changed in direction by a current in that air, and that its intensity was not diminished by violent agitation taking place in the air. By the interposition of a pane of glass between the fire and his hand, he found the heat was intercepted, though the light was transmitted, and might afterwards be concentrated to a focus by a lens. He states that a glass mirror reflects the light of a fire, but not the heat; that a polished metallic surface reflects both the light and the heat. The metallic reflector, therefore, may be opposed to the fire, and held in the hand
with safety; but by blackening its surface, the reflecting power was destroyed, and in four minutes it became too hot to hold: thus shewing that the calorific rays proceeding from a common fire, follow, in some measure, the same law with those proceeding from the sun.
From the experiments of Herschell, it would, however, appear, that the calorific rays which accompany the solar light, and those which issue from heated bodies, though similar in some points, have some dissimilarity; for the former pass through transparent media with much greater ease than the latter. On exposing two thermometers of equal sensibility, the one covered with glass, the other uncovered, first to the solar rays, and afterwards to those of a candle, he found that a greater proportion of calorific rays were intercepted in the latter case than in the former.
The experiments of Saussure and Pictet seem to prove that the calorific rays exist independently of the luminous ones; that they proceed in right lines from heated bodies; and that they are capable of reflection from polished metallic substances. These gentlemen placed two concave mirrors of polished tin, each a foot in diameter, at a distance of twelve feet apart; the focal length of the mirrors was four and a half inches each. In the focus of one was the bulb of a thermometer, and in the focus of the other they placed a ball of iron two inches in diameter, which was first heated red, and then suffered to cool until it ceased to be visible in the dark. Another thermometer was placed at the same distance from the heated ball as the former one, but without the focus of the reflecting mirror. Upon the introduction of the heated ball to its place, the thermometer instantly rose, and in six minutes indicated an increase of temperature of 10°.5 of Reaumur, while that not in the focus advanced only 29.5. Here the two thermometers, being at equal distances, may be supposed to have been equally affected by the direct rays from the hot ball; but the one in the focus of the mirror received in addition the reflected rays, and of course rose much higher.
To prove that the calorific rays exist independently of the luminous ones, and that they can only proceed in right lines, M. Pictet made use of a lighted candle in place of the heated ball. The candle was put in one focus; and when it had raised the thermometer in the opposite focus from 2° to 12°, a plate of glass was interposed, and in nine minutes the thermometer fell to 5°.7, and rose again on the removal of the glass. Here was an instance of a trans
parent body, which freely admitted the rays of light to pass through it, stopping the calorific rays; but that caloric was not entirely intercepted, is evident from the circumstance of the thermometer not falling below 5o.7. Another proof that the calorific rays exist independently of the luminous ones is, that the same results took place when a flask of boiling water was used instead of the candle. When a concave mirror of glass was substituted in place of the metallic reflector, little effect was produced upon the thermometer; thus proving the inferiority of glass as a reflector of
M. Pictet endeavoured to ascertain the velocity with which the calorific rays moved, and for this purpose he placed the reflectors at a distance of sixty-nine feet from each other, having in the one focus a heated ball, and in the other a delicate air thermometer. A cloth screen was interposed between the reflectors, upon the removal of which the rise of the thermometer was instantaneous; so that, within this distance, no perceptible interval elapsed between the passage of the calorific rays from one point to the other.
Absorption, as applied to caloric, implies that power which substances possess, of retaining the heating rays which impinge upon them, and thereby of acquiring an elevation of temperature. The absorptive powers of substances are very different, and may be roughly said to vary directly as the power of radiation. As far as the calorific effect of the sun-beam is concerned, it has been shewn, that the power of the absorbent body greatly depends upon its colour.
Mr. Powell, who has written several papers on the nature of caloric in the Philosophical Transactions, has thus stated his views on the subject.
1. "That part of the heating effect of a luminous hot body, which is capable of being transmitted in the way of direct radiation through glass, affects bodies in proportion to their darkness of colour, without reference to the texture of their surfaces.
2. "That which is intercepted produces a greater effect in proportion to the absorptive nature or texture of the surface, without respect to colour. These two characteristics are those which 'distinguish simple radiant heat at all intensities.
"Thus, when a body is heated at lower temperatures, it gives off only radiant heat, stopped entirely by the most transparent glass, and acting more on an absorptive white surface than on a smooth black one.
"At higher temperatures the body still continues to give out radiant heat, possessing exactly the same characters. But at a certain
point it begins to give out light precisely at this point, it begins also to exercise another heating power, distinct from the former; a power which is capable of passing directly through transparent screens, and which acts more upon a smooth black surface than on an absorptive white one."
It seems to be the general tendency of caloric, to become so diffused among matter of every kind, as to produce uniformity of temperature. That bodies differ greatly in the facility with which they permit the motion of caloric, or transmit its effects, is matter of daily observation. The transmission of caloric in free space, or through aeriform fluids, seems to be instantaneous, but in solids and liquids the case is very different. It may be stated as a general fact, that the conducting power of any body is in proportion to its density; thus, metals are better conductors than glass, glass than wood, and wood than feathers, wool, and other light substances, &c. The bad conducting power of these latter bodies, depends upon the quantity of air enclosed within their interstices, and the force of attraction by which this air is confined. If their imperfect conducting power depended on the difficulty with which caloric passes through their solid matter, the relative degree of that power would be as to the quantity of that matter. The reverse, however, is the case. Thus, the reason is evident, why wool, down, furs, &c. form such warm articles of clothing; because, in the ordinary state in which they are employed, the effect of their own bad-conducting property, and that of the air retained in their interstices, prevents the abstraction of caloric from the body. From its porous nature, snow is a very bad conductor, and thus forms an admirable mantle for the protection of vegetables from the more intense cold of winter.
As liquids are very easily heated, it may at first sight appear that their conducting power is considerable. The very opposite is, however, the true state of the case. The mobility of their particles is the chief cause of their power of transmitting heat, as may be seen from attending to the manner in which caloric acts upon them. If heat be applied to the lowest surface of any vessel containing a liquid, the first effect produced will be the expansion of the particles immediately in contact, by which their specific gravity being diminished, they will ascend through the mass of fluid, and a fresh stratum of particles will descend to occupy their place. By a repetition of this process, the whole body of fluid soon becomes heated. But if heat be applied to the upper
surface of a liquid, no such effect can take place; the heated and lighter particles continue at the surface; and the caloric, if it proceed downwards at all, will do so very slowly, and must do so on the principle of absorption.
Count Rumford exemplified this carrying power of liquids by a very pleasing experiment. He made a solution of potash and water of the same specific gravity with amber; then strewing in it some roughly powdered amber, he enclosed the whole in a proper glass vessel, and, after exposing it to a considerable heat, placed it in a window to cool. As the sun shone upon the vessel, it illuminated the particles of amber, and the whole liquid was seen to be in most rapid motion, running swiftly in opposite directions, upwards and downwards at the same time. The ascending current occupied the axis, the descending current the sides of the vessel. When the sides of the vessel were cooled by means of ice, the velocity of both currents was accelerated. It diminished as the liquid cooled; and when it had acquired the temperature of the room, the motion ceased altogether. These currents were evidently produced by the particles of the liquid going individually to the sides of the vessel, and giving out their caloric. The moment they did so, their specific gravity being increased, they fell to the bottom, and of course pushed up the warmer part of the fluid, and so on in continuity. Count Rumford likewise found, that, by mixing a small quantity of starch with the water, so as to diminish the fluidity, it took nearly double the time to reach a certain temperature, that it did when pure water was used. Eider down was likewise mixed with water, which could only tend to embarrass the motion of the particles, and a rather more powerful effect was speedily produced.
It is principally by the agency of fluids, elastic and non-elastic, that the distribution of caloric over the globe is regulated, and great inequlaities of temperature are guarded against; and this agency is exerted chiefly by the circulation of which their mobility renders them susceptible.
Thus, the atmosphere, with which the earth is surrounded, serves the important purpose of moderating the extremes of temperature in every climate. When the earth is heated by the sun's rays, the stratum of air reposing on it receives part of its caloric, is rarefied, and ascends. At the same time, from a law which attends the rarefaction of elastic fluids, that they become capable of containing a greater quantity of caloric at a given temperature, as they become more
rare; this heated air, though its temperature falls as it ascends, retains the greater part of its heat; its place at the surface is supplied by colder air, pressing in from every side; and by this constant succession, the heat is moderated, that would otherwise become intense. The heated air is, by the pressure of the constantly ascending portions, forced towards a colder climate; as it descends to supply the equilibrium, it gives out the heat it had received, and this serves to moderate the extremes of cold. There thus flows a current from the poles towards the equator, at the surface of the earth, and another superior current from the equator to the poles; and though the directions of these are variously changed, by irregularities in the earth's surface, they [can never be interrupted, but, produced by general causes, must always operate, and preserve, with greater uniformity, the temperature of the globe.
Water is not less useful in this respect in the economy of nature. When a current of cold air passes over the surface of a large collection of water, it receives from it a quantity of caloric; the specific gravity of the water is increased, and the cooled portion sinks. Its descent forces up a portion of warmer water to the surface, which again communicates a quantity of caloric to the air passing over it; and this process may be continued for a considerable time, proportioned to the depth of the water. If this is not very considerable, the whole is at length cooled to 40°, below which, the specific gravity not increasing, the circulation ceases, and the surface is at length so far cooled as to be covered with a coat of ice.
The quantity of caloric afforded by water is exceedingly great. Count Rumford says, "the heat given off to the air by each superficial foot of water, in cooling one degree, is sufficient to heat an incumbent stratum of air forty-four times as thick as the depth of the water, ten degrees. Hence, we see how very powerfully the water of the ocean, which is never frozen over except in very high latitudes, must contribute to warm the cold air which flows in from the polar regions." From this cause, currents must exist in the ocean similar to those formed in the atmosphere. The water, which in the colder regions is cooled at the surface, descends, and, spreading on the bottom of the sea, flows towards the equator, which must produce a current at the surface in the opposite direction; and thus the ocean may be useful in moderating the excessive heats of the torrid zone, as well as in obviating the intense cold of the polar climates.
ON THE CONIC PROJECTION OF THE SPHERE.
ON THE CONIC PROJECTION OF THE SPHERE.
Of the several methods of projecting the surface of the earth, or of a sphere, on a plane, the globular is most esteemed, as giving the most faithful and correct representation of its surface, exhibiting it with equidistant meridians and parallels; it is, therefore, preferable to the other methods, because the different countries, &c. are represented more proportional to their dimensions as they stand on the globe.
If, however, a cone be inscribed in a hemisphere, and the various circles, lines, &c. as also the different continents and islands on its surface, be transferred to the convex surface of the cone; this will be a nearer approximation to the surface of a sphere than the globular projection, or than any other projection on a plane surface. Two such cones, so placed that their bases may coincide with the equator, and their axes with the axes of the sphere, will represent the whole surface of the earth, or the northern and southern hemisphere.
If the surfaces of each of these cones be unwound, they will present two plane surfaces, or great segments of circles, whose semidiameters are the slant heights of the cones; and if they be placed so that the chords of the arcs may coincide, the four sides of the sectors, or semidiameters of the circles, will form a rhombus, or diamond square, in the middle of the figure, in which the name of the map or other particulars may be written.
Such a map may be constructed as follows:
To find the length of the arc of the sectors; suppose the diameter of the circle to be 1, then the slant height of the cone will be 5, hence, by Euclid, 47th P. of .353 is the semidiameter
of the base of the cone, and .353 × 2 × 3.1416 2.217 the length of the arc : now as 3.1416 360°:: 2.217: 254° 9' = length of the arc in degrees, and 360° 254° 9' 105′,, 50' the length of the deficient arc. Therefore, with any radius draw a circle, cut off from the proper side of it 105°,, 50', next draw the two radii or sides of the sector; then, with the length of the radius from the points of section, describe arcs intersecting one another on the outside of the sectors; from the points where they intersect, circumscribe the arc of the other sector, meeting, or cutting the former; and then finish the rhombus, by drawing the sides of the sector.
Divide each of the arcs into 360 degrees for the longitude, and at proper distances
2D. SERIES.-NO. 6.
draw straight lines from the centre to the circumference, for meridian lines. The degrees of latitude must be marked on the sides of the rhombus; but as they are not of equal length, the points of division may be found as follows:-make the sides of the rhombus, chords of the arcs of quadrants, divide each of the arcs into 90 degrees, and through the points of division, to the vertex of each quadrant, draw straight lines, and the points where they cut the chords or sides of the rhombus, are the points of division for the degrees of latitude.
These divisions may be found arithmetically as follows:-there are given the base of a triangle, or radius of the quadrant, and both the angles at the base, and, therefore, that at the vertex, to find one of the sides, one angle at the base being the given latitude, and the other always 45°; hence, the sine of the angle at the vertex, is to the base or radius, as the sine of the latitude is to the required side or part of the chord corresponding to the given latitude. When the divisions of the latitude are found, arcs must be drawn through them, parallel to the equator, for the parallels of latitude, at proper distances from each other.
Thus much for maps of the world; but for maps of any part of the earth's surface, either in the northern or southern hemisphere:-in order to obtain the nearest approximation to the surface of a sphere, the surface of the spherical zone, lying in the latitude of the map, should be transferred to the surface of the frustrum of a cone, the semidiameters of whose greater and lesser bases, are the cosines of the latitudes of the bottom and top of the map. · Let S,s, be the sines of the latitudes of the top and bottom of the map, and c, C, their cosines; C-c2 + S—s = the slant height of the frustrum, and by sine ▲s, as C C-c: C +S
S :: C:
S s the slant height of the whole cone or radius of the greatest parallel of latitude, whose length is 3.1416 x 2 C, a proportional part of which must be taken for the width of the map. The divisions of the degrees of latitude may be found by the former trigonometrical analogy, observing that the given base, or side of the triangle, is equal to the radius of the sphere, in the zone of which the frustrum of the cone was supposed to be inscribed, and one of the angles at the base being the difference of the latitude of the bottom of the map, and the given latitude whose distance 150.-VOL. X