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Solar Radiation

SOLAR radiation is a subject which has more than scientific interest. It is the source of all the energy which maintains the economy of our globe. It lights and heats the other members of the planetary system. But, after accomplishing this, only an infinitesimal proportion of the total radiation has been used. The remainder, in so far as we know, is wasted by uninterrupted dissipation into space. The subject can be regarded and studied from either the solar or the terrestrial point of view. In terrestrial physics everything may be said to depend on the energy which, in one form or another, is supplied by the sun's rays. It is the revenue of the world, and it is of fundamental importance for us to know at what rate it falls to be received. Roughly speaking, the surface of the earth is occupied to the extent of one-fouth by land and three- fourths by sea. Therefore at least three-fourths of the surface which the earth presents to the sun is at the sea-level. Consequently the rate at which the sun's radiant heat arrives at the sea-level is the fact which it is of the greatest economical importance to ascertain. In considering this problem we have to answer two questions: What is the best experimental method of determining the heating power of the sun's rays at any place? and, What is the best locality for making the experiment? Let us take the last first. The energy which a radiation communicates to a surface is greatest when it strikes it perpendicularly. At every moment the sun is vertical over one spot or another of the earth's surface. Therefore our first step should be to choose a locality where the sun passes through the zenith at mid-day. Before reaching the sea-level the sun's rays have to pass through the whole thickness of the atmosphere. It is a matter of every-day observation that the atmosphere varies in transparency. The second condition is therefore to put ourselves in the position of greatest advantage as regards atmospheric conditions. Clouds and similar visible obstructions are of course excluded. The air should be motionless, the sky should be clear and of a deep blue color in the regions remote from the sun and should contain nothing that can be called haze, or that interferes with the definition of the sun or other heavenly bodies. From inspection alone we can only approximately ascertain what are the most favorable meteorological conditions. For this reason it is necessary to multiply observations and never to miss fine weather. In the end we cannot fail to approach nearer and nearer to the exact determination of the maximum heating power of the sun on the earth's surface at or near the sea- level, in so far as the degree of perfection of our instrumental resources permits. This limitation imposes on us the duty to continue observations, not only until the best natural conditions have been found, but also so long as the instruments or experimental methods appear to be capable of improvement. If we suppose for one moment that we have arrived at the point where no further improvement is possible, then the result of our work is the determination of the rate at which unit area of the earth's surface at or near the sea-level receives heat from the vertical sun in unit time. There is no question here of how much is lost on the way from the sun. All that is sought, and the most that is ascertained, is how much arrives. If we multiply this by the area included in the great circle of the earth we have the amount of radiant heat which we can count on as being supplied to the whole earth in unit of time. That is the constant which is of greatest importance in physical geography. When we have ascertained the supply of radiant heat which reaches the earth's surface, we have to inquire what becomes of it. If the heat were to accumulate the world would become uninhabitable. It cannot be doubted that long ago the earth, in this respect, arrived at a condition of equilibrium which is maintained with very slight oscillations. The fundamental principle of this state of equilibrium is that the heat which the whole earth receives from the sun in the course of a year also leaves it in the course of a year, so that, taking one year with another, the sum of the heat remains the same. When we study the details of the annual dissipation of heat we- find that the atmosphere, and especially the aqueous vapor in it, performs a very important part. Although practically transparent to the heat-rays passing from the sun to the earth, it is very opaque to those leaving the earth to pass outward. They are powerfully absorbed and the temperature of the atmosphere is tl ils raised considerably above that which it would have if it were as transparent to the leaving rays as it is to the entering ones. This has no effect in permanently detaining any of the year's supply; it still disappears in the year, but not before it has produced important climatic effects. We see in this differential behavior of the atmosphere toward the incoming and the outgoing rays an example of Kirchoff's law, in virtue of which a body absorbs by preference the rays which it itself emits. It is exceedingly unlikely that any portion of the rays coming directly from the sun proceed from highly heated water or water vapors; we should therefore not expect the water vapor in the atmosphere to absorb them to any appreciable extent. When, however, they strike the surface of the earth, whether it be land or sea, they are abundantly absorbed. The blue water of the ocean transmits the sun's visible rays to a considerable depth. In experiments made by the writer on board the “Challenger,” a white surface, about four inches square, was clearly visible at a- depth of 25 fathoms. The total length of the path of the incident and refiected ray was 50 fathoms; therefore the sun's rays which strike the sea have a thickness of at least 100 meters to work on. When they strike the land, the direct effect is superficial, but the absorptive power of a surface of soil is very much greater than that of a surface of water, and it frequently attains a very high temperature. Even in the driest countries the soil is moist, and it may be that, ultimately, the surface of every ' particle of the soil is a water surface. Whether this be so or not, when a land surface cools, the heat of low refrangibility which it radiates proceeds to a very large extent from water, and it is accordingly abundantly absorbed by the water vapor in the lower layers of the atmosphere. In the absence of mechanical mixture by wind, these layers can lose it only by passing it on by radiation to higher layers which contain moisture, whence it ultimately escapes into space. This accumulating function of the atmosphere provides that while every portion of the earth's surface receives heat intermittently it loses it continuously. As the heat of the atmosphere is due to contact with. or radiation from, the surface, it must be taken from the supply that reaches the surface of the earth. Further, wind and all mechanical atmospheric effects are due to differences of density, and these are produced, not only by the thermal expansion and accompanying rise of temperature of the air, but also, and without change of temperature, by the mixture with it of a lighter gas. Such a gas is the vapor of water, and the water which supplies it is at the level of the sea. Therefore the sun's heat, which arrives at the surface of the earth at or near the sea-level, has to maintain not only the temperature of the surface of the globe, it has also to maintain all the mechanical manifestations of the air and the ocean. This is the ground for asserting, as above, that the only constant which is of interest in terrestrial physics is the rate at which the vertical sun heats unit area of the earth's surface at the sea-level. The instruments used for measuring the thermal effect of the sun's rays must fulfill certain conditions. The area of the sheaf or bundle of rays collected must be accurately known; and provision must be made for the exact measurement of the thermal effect produced by them in a given time. The' thermal effect produced is measured by a mass of some substance and either by the change of temperature produced in it or by the change of its state of aggregation. Actinometers, such as those of Herschel, Pouillet, Violle, Crova, are instruments of the first kind. The ice calorimeter used by Exner and Roentgen and the steam calorimeter of the writer are instruments of the second kind. The thermal mass of the substance affected is conveniently expressed in terms of the thermally equivalent weight of water, which is called its water value. In the actinometer the change of temperature is either measured by a separate thermometer or the actinometer is itself a thermometer, the calorimetric constants of which have been ascertained. In instruments of the second class no thermometer is required; the thermal effect is measured by the mass of water-substance which changes its state in a given time either from ice to water or from water to steam, both being at the same temperature. In the ice calorimeter the quantity of liquefaction is measured by the change of volume, as in Bunsen's calorimeter; in the steam calorimeter the generation of steam is measured by the weight or volume of the distilled water produced. The steam calorimeter was described recently in Nature (vol. lxiii. p. 548), and it is unnecessary to repeat it here. It acted quite satisfactorily in the writer's hands in Egypt in May, 1882, and it has since been giving good results in the hands of Mr. Michie Smith at the observatory of Kodaikanal in South India, at an elevation of about 7,000 feet above the sea. Theoretically, the ice calorimeter is as good as the steam calorimeter, but in applying it to the measurement of the sun's radiant heat it has a practical defect. At the moment before exposure, the ice, in the calorimeter is frozen to the inner surface of the metal plate, the outer surface of which receives the sun's rays. The first effect of exposure to the sun is that the ice is detached from the plate. The intervening water introduces perturbations which are not easily allowed for. The fundamental principle of the actinometer is analogous to Newton's second law of motion; when a body is engaged in the exchange of heat between itself and any number of other bodies, each exchange takes place independently of the others. The rate of exchange in each case depends on the difference of temperature between the two bodies and takes place on the principle that equal fractions of heat are lost or gained in equal times. A body cooling II the air is always subject to at least two quite independent sources of loss of heat, namely. radiation between itself and the surrounding objects and conduction between itself and the contiguous air. In ordinary circumstances the rate of loss of heat by radiation is subject to but little variation, but that due to conduction is subject to continual variation owing to the varying rate at which the air actually in contact with the thermometer is renewed. It is not to be expected that a body subject to at least two independent sources of loss of heat will cool in the same way as it would if exposed to only one, any more than it is to be expected that a body acted on by two forces will move in the same way as if it were impelled by only one of them. The composition of rates of cooling is like that of velocities in the same straight line; the resultant rate is the net, or algebraic, sum of all the rates. When the actino- meter is exposed to the sun, its temperature rises at first rapidly, and then more slowly until, if the experiment is sufficiently prolonged, it becomes stationary. The temperature is noted at equal intervals of time. The sun is screened off, either after the temperature has become stationary or beforehand, and the temperature is observed at equal intervals during cooling. Whenever the thermometer is at higher temperature than its inclosure, it is cooling. Therefore when it il! exposed to the sun's rays, and its temperature rises ever so little above that of the inclosure, cooling begins; and what is observed in the first operation is. not the rate of heating by the sun's rays. but that rate diminished by the rate at which the thermometer is cooling. Hence, when the two series of observations have been made and tabulated, the rate of rise of temperature when that of the thermometer is. say, 2 deg., 4 deg., or 6 deg. above that of the inclosure is found. Similarly, the rate of fall of temperature when the temperature of the thermometer is 2 deg., 4 deg., or 6 deg. above that of the inclosure during cooling is found. Three pairs of rates are thus obtained. The sums of all three pairs of rates should be alike, and each gives a value of the rate at which the temperature of the actinometer would rise when exposed to the sun if there were no cooling. The rule is the same whether the temperature is allowed to rise to the stationary point or not. A distinction is often made between the static method, when the experiment is continued until the stationary temperature is arrived at, and the fcinetic method, when it is interrupted before that temperature is reached. This distinction rests on no substantial difference; at the same time it is convenient to retain the designations to distinguish the manipulative processes. Were the protecting inclosures, such as the double spherical sh^l packed with melting ice, used by Violle, or the thick metal shell used by Crova, perfectly efficient. then it would not be necessary to make a separate cooling experiment in connection with every heating one. The necessity for it is due to the fact that. when the sun's rays are introduced, the temperature of the air in the inclosure no longer is, and it cannot be, at the temperature of the inclosing shell; nor can it remain motionless, as it is when at a constant temperature in the shade. These perturbations. which cannot be avoided, so long as there is air in the inclosure, make it impossible to apply a rate of cooling determined beforehand. It is necessary on each occasion to determine the actual integral rate of cooling during the particular experiment. If the actinometer be so arranged that the rate of cooling should not be affected by the introduction or exclusion of the sun's rays, the static method could be adopted without hesitation, and the instrument would become a valuable one for continuous self-recording observations. Their value would be mainly relative. The absolute value of the sun's heat radiation, as it reaches the surface of the earth, has to be determined by other means. When it has been ascertained in the most favorable circUmstances it does not vary, excepting in the annual cycle of the earth's revolution. The diurnal variation, as shown by registering actinom- eters, would have a great local importance. Crova, in the long series of valuable observations which he has made since 1875, at Montpelier, has, in fact, put this principle in practice. Very important observations have been made in the neighborhood of Chamonix by Violle and afterward by Vallot. The Annales de l'ObservatoirS mStSorologique du Mont Blanc contain, in vol. ii., several interesting reports on the results of these observations. They were made simultaneously at Chamonix and at certain stations on Mont Blanc. The first series of observations was made in 1887 on July 28, 29, and 30, and the instruments used were two “absolute actinometers” of Violle (Ann. Chim. Phys. (1879) [5], t. xvii.). The great advantage of such experiments is that they are made simultaneously at two stations situated at very different altitudes. At. the higher of the two the average barometric presure is 430 millimeters, so that 33-76 of the whole atmosphere are below the observer, and this portion contains nearly all the aqueous vapor. Above him there is a little more than one-half, and that much the simpler and purer half of the atmosphere. In it aqueous vapor is almost absent. The summit of Mont Blanc is 4.807 meters and the station at Chamonix is 1,087 meters above the sea.. The layer of the atmosphere separating them has. therefore, a thickness of 3,720 meters, and it can be visi^& at any point in its thickness. M. Vallot has^acquifed a personal acquaintance with this layer of air, which can only be obtained by devoting a number of years to living in it and observing it. It is this intimate and continuous acquaintance with so large a proportion of the earth's atmosphere that entitles the observations and conclusions of M. Vallot to especially great weight. The main results of Vallot's observations are as follows: The ratio between the heat received in the same time by the same area exposed perpendicularly to the sun's rays on Mont Blanc and at Chamonix was found to be 0.82 to 0.85, which agreed well with the proportion found by Violle in 1875. The value of the solar radiation found was, however, much lower than that found by Violle. The maximum values observed by Vallot were 1.56 gr. deg. C. on Mont Blanc and 1.33 gr. deg. C. at Chamonix, while Violle found 2.39 gr. deg. C. on Mont Blanc and 2.02 gr. deg. C. at' the Glacier des Bossons in the valley. Violle's observed values are therefore half as great again as Vallot's. No explanation of the cause of this discrepancy is offered, but it is pointed out that the values observed by Crova at Montpelier are more in accordance with Vallot's than with Violle's. They are interesting in themselves an'. are worth quoting. They relate to the year 1895, the summer of which was very hot. Intensity of solar radiation observed by M. Crova at Montpelier, in 1895, in gramme-degrees per 'Square centimeter per minute. Means. Season. Absolute maxima. Monthly. Seasonal. 1.02 1.12 1.15 1.09 1.82 January 28. Spring 1.20 1.13 1.13 1.15 1.8 May I:!. 1.22 1.14 1.19 1.-8 1.42 July 24. 1.80 1.20 117 l.41 September R. The subject was taken up again by Vallot in 1891. and this time he used the mercury actinometer o£ Crova (Ann. Chim. Phys., 1877 [5] xi., 461). The result of the experiments in 1891' was in the main confirmatory of those obtained in 1887. In the following table the intensities of solar radiation on September 19, 1891, are given as observed on Mont Blanc and at Chamonix: Hour. » a.m. 10. 11. Noon. l p.m. 2. 3. •3 J \ On Mont Blanc 1.84 1.30 1.84 1.83 1.81 ut. no ^ t At Chamonix 1.11 1.16 1.19 1.15 1.16 1.09 1.01 Ratio of intensities. 0.M 0.87 0JM 0.82 0.77 The mean value of the ratio of the intensities is 0.84. as before. The values of the intensity of radiation are rather lower than those found in 1887. In the year 1896 Prof. Angstrom, of Upsala, made observations on the peak of Teneriffe with a special form of actinometer depending on the heating of metal plates. He made observations at three different elevations, namely, at Guimar, 360 meters, Canada, 2,125 meters, and at the summit, 3,683 meters. Reduced to a uniform thickness of one atmosphere corresponding to a pressure of 760 mm., the intensity of radiation by the vertical sun was found to be at Guimar 1.39, at Canada 1.51, and at the summit 1.54 gramme-degrees per square centimeter per minute. These values agree more closely with the values found in 1887 by Vallot than with those of 1891. But the values found by Crova. Vallot, and Angstrom are all of the same order. The writer's observations with the steam calorimeter in Egypt in May, 1882, were undertaken with the object of ascertaining the maximum rate of distillation near the sea-level under the most favorable circumstances. This occurred during the forenoon of May 18, when the meteorological conditions were as favorable as they could be. The sun shone steadily in a cloudless sky, and the air was motionless. The shade temperature reached 40.5 deg. C. in the course of the day. Time was taken as portions of 5 cubic centimeters were distilled. The shortest time in which this quantity passed was 3m. 20s. This is at the rate of 1.5 c.c. per minute, and it occurred twice in the forenoon, namely, at 10h. 37m. and at 11h. 23m. As the collecting area of the refiector was 904 square centimeters, this corresponds to 16.6 c.c. distilled per minute per square meter. If we apply a correction for 20 deg. zenith distance it becomes 17.04 c.c. The evaporation of 17.04 grammes of water at 100 deg. C. requires 9,116 gr. deg. C. of heat, so that the heat actually collected and used in making steam was at the rate of 9,116 gr. deg. C. per square meter or 0.9116 gr. deg. C. per square centimeter per minute. Converting 9,116 gr. deg. C.. into work at the rate of 0.425 kilogramme-meter per gramme-degree, we obtain as the realized working value 3,875 kilogramme-meters per minute or 0.87 horse power per square meter. The refiector consists of one mirror inclined at an angle of 45 deg. to the axis of the instrument. This mirror throws all the refiected rays normally on the surface of the axial boiler. The larger mirror outside and the smaller mirror inside of this one throw their refiected rays inclined at small angles to the normal. Taking all the refiected rays together their mean normal component is 94 per cent of the total refiected rays. It is therefore legitimate to increase the above figures in the proportion of 94: 100, giving 0.93 horse power or 9,700 gr. deg. C. per square meter per minute. The mirrors are not perfectly refiecting; nor is the blackened surface of the boiler perfectly absorbing. An allowance of 7 per cent for these deficiencies will liot be thought extravagant, and we have in round numbers the work value of the sun's vertical rays on the surface of the earth at or near the sea-level as 1 horse power per square meter; the equivalent of this in heat is 10,300 gr. deg. C. per square meter per minute, or 1.03 gr. deg. C., taking the square centimeter as the umt of area. Mr. Michie Smith informs the writer that the highest rate which he has observed is 1.754 c.c. distilled per minute at a height of 7,000 feet above the sea. This is exactly seven-sixths of the maximum rate observed on the banks of the Nile. If we imagine that in tile most favorable circumstances the radiation as determined in Egypt might be improved in this proportion we get 1.17 horse power per square meter and 1.202 gr. deg. C. per square centimeter per minute as a value of the heating power of the sun at the sea-level, which is probably very near the truth. Comparing these results with those already quoted. we see that they agree with Crova's summer values as determined at Montpelier and lie midway between Vallot's (1891) value!! for Mont Blanc and Chamomx. We arrive therefore at the conclusion that the rate at which the surface of the earth at the level of the sea receives heat in the most favorable circumstances from the vertical sun is 1.2 gr. deg. C. per square centimeter per minute, or 1.17 horse power per square meter. In discussing questions of terrestrial physics it would not be prudent to postulate a more abundant supply. If we ascribe to the atmosphere a coefficient of trans mission no greater than two-thirds, the value of the soZar constant, or the heating power which the sun's rays would exert on a surface of one square centimeter exposed to them for one minute at a point on the earth's orbit, is 1.8 gr. deg. C. As the transmission coefficient is probably greater than two-thirds, the value of the solar constant is probably less than 1.8. Vallot, by giving. elIect to the rate of absorption actually observed in the air separating his two stations, arrives at 1.7 gr. deg. C. as the most probable value. These values are in substantial agreement with the older ones, such as those of Herschel and Pouillet; but there is a feeling at present that not much weight is to be attached to these results, and much higher figures seem to be more readily accepted. In a recent work, “Strahlung und Temneratv'l del' Sonne,” p. 38, J. Scheiner sums up the discussion of this subject by giving 4 as the most probable value of the solar constant. As we have seen, the heat which arrives at the sea-level has to support the temperature of the land and that of the sea; it has also to supply the energy for all the mcvempnts of the ocean; it has to warm and expand the air, and to furnish the latent heat represented by the aqueous vapor in the atmosphere, and it is mainly accountable for 'finds and storms. All this is maintained on less than 1.5 gr. deg. C. per square centimeter per minute. But when the above catalogue of functions has been repeated, there is nothing left to be accounted for. If the sun's rays enter at the top of the atmosphere with an intensity of 4 and come out at the bottom of it with an intensity of only 1.5, how is the loss to be accounted for? It represents nearly double the energy which reaches the sea-level and produces such far-reaching elIects. If it really entered the atmosphere it must still be there, either as heat or its equivalent. But we know that the air is not made appreciably warmer by it, and we see no mechanical manifestations which can in any way be put forward as an equivalent. We conclude therefore that there is no excess of heat of this order to be accounted for, consequently values of the solar constant of the order of 4 are exaggerated. J. Y. Buchanan.

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