Solar radiation plus sky radiation expressed as actinometric percentages according to Marié-Davy, calculated for skies as clear as at Montsouris and for various latitudes. THEORETICAL FORMULÆ FOR ACTINOMETER. In reply to some criticisms of Violle, Marié-Davy (1880, p. 245) gives the only statement that I have seen of his theory or explanation of the working of his conjugate thermometers. It is about as follows: Let a be the absorbing power of the bright bulb. 7 the absorbing power of the black bulb. c a numerical coefficient for converting degrees of temperature into a quantity of heat. 7 the quantity of radiation or heat falling per minute on the black bulb and also on the bright bulb. a q the quantity of radiation absorbed by the bright bulb. lq the quantity of radiation absorbed by the black bulb. e the emissive power of the black bulb. e' the emissive power of the bright bulb. t and t' the temperatures of the black and bright bulbs, respectively, when they come to the stationary temperature that indicates equilibrium between absorption and emission. T the temperature of the glass envelopes within which the thermometers are inclosed in a space that is an approximate vacuum. On the assumption of the Newtonian law of radiation, viz, that the quantity of heat emitted is proportional to the excess of temperature, we have the following relations: q=ce (t −T) aq=ce' (t'-T) From these expressions we can, by elimination of T, find the following expression for 4-that is to say, the quantity of solar radiation per unit of time that is at that moment falling on the two thermometers, at least in so far as this radiation is capable of being transformed into heat by absorption into the bulbs of the thermometers: Marié-Davy, in the absence of exact knowledge of these coefficients a, c, e, e', prefers to attempt to determine only relative measures of the intensity of radiation. He therefore assumes that the expression cee' is equal to 5.88 units, and the values for q thus obtained he e-a e calls actinometric degrees, since on the very clearest days in Paris they accord well with the assumption that the so-called solar constant of radiation is 100 actinometric degrees, and that the coefficient of transmission of sunshine through the atmosphere is 0.875. Ferrel (1884), in his memoir on the temperature of the atmosphere (p. 41), has improved upon Marié-Davy's theory, in that he has applied to the conjugate thermometers the law of radiation, established by Dulong and Petit in 1817, which is applicable to a much larger range of temperatures than the Newtonian law adopted by Marié-Davy. Ferrel's formula may be written: q=4.584 km t' (m t-t'—1) where the notation is the same as before, except that m is the number 1.0077, as determined by Dulong and Petit and k is a factor that varies with the quality of the bright bulb, whose absolute value is usually greater than 7, but whose relative value may by preference be determined by referring each pair of conjugate thermometers to an adopted standard pair. Ferrel's formula is especially devised for thermometers having spherical bulbs, measures made by it at high and low temperatures give results that are comparable with each other; for absolute results the numerical coefficients may need some modification, but as it stands it gives the values of q approximately in calories per minute per square centimeter. Omitting for the present the factor k in Ferrel's formula, which must be specially applied for each thermometer, we have the values of q in calories as given in the following table (see Ferrel, p. 37), which also presents the corresponding values given by the formula of Marié-Davy in actinometric degrees. In a critical study of observations reduced by these two methods we have to recall that MariéDavy's actinometric degrees are really fractions of a calorie, or units of heat so small that 100 of them are equivalent to the absolute radiation of the sun received at the outside of an atmosphere whose coefficient of transmission is 0.875; whereas Ferrel's calories have been adopted without predicating anything as to the solar radiation or atmospheric absorption, concerning which his observations show that the solar radiation constant is between 2 and 2.25 calories per minute per square centimeter and the atmospheric coefficient of transmission to be used with the conjugate bulbs is 0.72. Solar radiation deduced from observations with the conjugate thermometers. Marie Ferrel, calories per minute per square centimeter for the respective Davy, actino bright-bulb temperatures. t-t'. 20. 10.... 58.8 339 .352 .366 .380 .395 .410 ° C. 5.... 29.4 0.166 0.172 0.179 0.186 0.194 0.201 0.209 0.217 0.226 .761 35.. 40.. 45. .652 .678 .538 .559 .581 .604 .627 .426 .443 .460 .704 .791 1.007 1.848 1.920 1.995 2.073 INTENSITY AND DURATION OF SUNSHINE AT MONTSOURIS. In order to have at hand data that will enable one to approximately infer some of the relations between the temperature of the air and of the soil and of the solar radiation, one may consult the tables for the observations at Montsouris, given by Marié-Davy in his Annuaire for 1887. As those who can not make use of the actinometric degrees deduced by Marié-Davy from his observations of his conjugate bulbs will necessarily have to use either the simple observations of clear sky and cloudy sky, as given by the sunshine recorder, or the equivalent personal observations of the clouds, I give the following tables, which show how nearly parallel these two phenomena may be. Evidently in our study of the influence of insolation on crops in America from year to year we may use the sunshine recorder or the ratio between the actual and the maximum possible duration of sunshine without much error, at least in the growing season. Mean of five daily actinometric observations at Montsouris, expressed in MariéDavy's actinometric degrees or percentages of maximum possible intensity. Month. 1875. 1876. 1877. 1878. 1879. 1880. 1881. 1882. 1883. 1884. 1885. April. May June 46.0 July. August September. Average 44.1 40.1 36.3 35.4 28.6 38.9 33.0 39.7 36.8 34.5 34.1 41.5 40.6 50.3 48.9 47.4 45.9 46.3 40.3 43.2 46.1 43.4 49.4 Mean of five daily observations of the cloudiness at Montsouris expressed as ratio of the actual duration of sunshine to the maximum possible duration. Month. 1875. 1876. 1877. 1878. 1879. 1880. 1881. 1882. 1883. 1884. 1885. RELATIVE TOTAL HEAT RECEIVED FROM SUN AND SKY DURING ANY DAY, BY HORIZONTAL SURFACES. A more accurate way of considering the amount of insolation at any locality is to compute the total radiation (expressed by its equivalent heat in calories) received by a horizontal surface in the natural daytime of that day and latitude, taking account of the absorption by the atmosphere. (See Annales Agronomique, 1878, IV, pp. 270–296, or Ann. Report Chief Signal Officer for 1881, pp. 1200-1216.) This has been done by Aymonnet by a graphic method. He assumes that if the sun were in the zenith then the unit of horizontal earth's surface would, because of atmospheric absorption, receive only 0.75 of the heat that it would receive if it were outside the atmosphere. Of the remaining 25 per cent one-half reaches this horizontal unit by way of the diffuse reflection from the sky, so that with the sun in the zenith the unit receives 0.875 of the original solar heat. For a point on the equator during twelve hours this would amount to 0.875×12X60X60 of the total possible if the sun were in the zenith. Using this as a basal datum, Aymonnet obtains the relative numbers given in the following table or the ratio of the heat actually received during one day to that which would have been received if the sun had stood for twelve hours in the zenith. Thus on June 20, at latitude 30°, the horizontal unit receives 0.347 of that corresponding to the ideal sun in the zenith all day, while at the north pole on the same day the horizontal unit received during twenty-four hours 0.328 of what it would had the sun stood in the zenith for twelve hours. In fact the amount of heat received by horizontal surfaces is nearly uniform for all latitudes for the days June 15-July 28. These relative numbers or ratios may be turned into absolute calories by multiplying them by the so-called "solar constant," whose value is probably between two and three calories per minute per square centimeter. Relative quantities of total heat received on specified days from the sun and sky at different latitudes by a unit surface of horizontal ground during one cloudless day, allowing for the absorption and diffuse reflection of ordinary clear air, as computed by Aymonnet. |