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Chapter V.

THE METHODS OF MEASURING DIRECT OR DIFFUSE SUNSHINE AS TO INTENSITY OR DURATION.

Sunshine may be measured as to its quality or wave length, its intensity, or its duration. The methods used in measuring either of' these must be understood in order to intelligently compare the published observations with phænological phenomena. The following section considers some of the methods of measuring or registering the duration or intensity of sunshine, or the intensity of the skylight, at least in so far as these have been used in agricultural studies.

THEORETICAL RELATION OF DIRECT AND DIFFUSED SUNSHINE.

The relative intensity of any radiation may be measured by its heat or light or chemical effect. The insolation received by a horizontal surface, whether directly from the sun or diffusely from the sky, is subject in a general way to calculation, but the irregularities introduced by haze and clouds can not be so calculated and must be observed daily. The following table gives, for a clear blue sky, the values obtained by Clausius for the radiation (S) that falls upon a horizontal surface directly from the sun, and in the third column the diffuse radiation (C) that falls from the whole sky upon that same surface; the total radiation (S+C) is the sum of these two. If, however, the surface is normal to the sunlight, instead of horizontal, it receives the quantity in the fifth column (I) directly from the sun, and (c) which is less than the quantity (C) from the sky, depending upon the altitude of the sun, the total being, as before, the sum of these (I+c). The study of these columns shows us the maximum and minimum amounts of sunshine that may fall upon a given leaf surface, since a leaf will in general be in some position to receive the full sunshine normally to its surface, while others will be horizontal, or vertical, or in the shade, and receive only a part of the diffuse light from the sky.

It is assumed by Radau, in his actinometry (1877), as also by Marié-Davy, that the bright and black bulb thermometers in vacuo, or the so-called "conjugate thermometers," give us the total radiation (C+I) as for the horizontal surface, and that this is the quantity in which vegetation is interested.

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TOTAL INSOLATION, DIRECT AND DIFFUSED.

The value of the intensity of the direct solar rays incident normally to any unit surface, as determined by the absolute actinometers of Pouillet, Violle, and others, is not so applicable to the study of the growth of plants as is the sum of the radiation from the sky and other surroundings of the plant, added to the direct solar radiation. Comparative measures made in 1866 by Roscoe, at Manchester; Baker, at Kew; Wollkoff, on the summit of Koenigstuhl, near Heidelberg (altitude, 550 meters), and Thorpe, at Para, have given the following values of relative intensity of radiation at certain moments when the sun's altitude above the horizon was sensibly the same at all the stations. (See Marie Davy, 1882.)

Relative intensity of radiation for equal altitudes of the sun.

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At Manchester and at Paris the light that comes from the sky is more than double that which comes directly from the sun. When the sun is hidden by clouds, or even partially veiled, it is the radiation. from the sky that is of the most importance to agriculture, and in any case this radiation is far from being negligible.

The Arago-Davy actinometer (believed to have been invented by Arago before 1844, but improved by Marié-Davy and used at the

observatory of Montsouris ever since 1873) is an apparatus that is intended to determine the total solar plus sky radiation that is needed in agricultural physics. A theory of the action of this instrument was devised by Marié-Davy, but the proper method of calculating its results was first developed with exactness by Ferrel, in Professional Papers of the Signal Service, No. XIII (1884), and subsequently in his Recent Advances in Meteorology (Annual Report, Chief Signal Officer, p. 373). His formula will be given on page 88.

The Arago-Davy actinometer is composed of two mercurial thermometers with very fine tubes, and having spherical reservoirs of equal dimensions, one colorless and the other covered with lampblack. In the empty space above the mercury in the thermometer tubes there is a small quantity of hydrogen or other inert gas. The small quantity of gas left in the tubes of these thermometers has no other object than to prevent the mercury from falling in the tube by the force of gravity when the bulb is turned upward toward the sky. Each thermometer is inclosed in a larger glass tube or cylinder, terminated by a spherical enlargement, in the center of which is placed the center of the bulb of the thermometer. This tube and enlargement constitute the inclosure, and it is exhausted of air as perfectly as possible. The immovability of the thermometer, relative to the walls of its inclosure, is assured by a soldering at the upper extremity of the tube and, at the opposite end toward the reservoir, by two rings of cork held by friction between the interior tube and exterior cylinder. These thermometers, with their respective glass inclosures, are turned up with their bulbs toward the sky, and by means of double clamps fixed parallel to two metallic rods, arranged in the form of a V and turned, the one toward the east, the other toward the west. These metallic rods make an angle with each other of 60°-that is to say, of 30° with the vertical-and are fastened to a support of wood or iron 1.20 or 1.30 meters in height above the earth. The support is solidly planted in the ground in an open place, remote from buildings, plants, or any other obstacle capable of intercepting the direct radiation of the sun. The two thermometers, the envelopes of which are exposed near each other, have necessarily the same temperature and mark the same degree as long as they remain in perfect darkness; but hardly does day begin to break than the thermometer with the black bulb marks a higher temperature than that with a plain glass bulb. The difference in temperature of these two thermometers gives the “actinometric degree" for the moment of observation; that is to say, it serves to measure the intensity with which the radiation strikes the two thermometers and is absorbed by the black bulb; consequently, at least approximately, it serves to measure the intensity with which the

of his above-quoted work of 1884, on the Temperature of the Atmosphere and the Earth's Surface).

Until such a method has been perfected (see an article by Ferrel in Am. Jour. Sci., May, 1891, 3, Vol. XLI, p. 378) we will for the present quote the actinometric degrees and other figures as ordinarily published by Marié-Davy and others; but the reader must bear in mind that these results from the hypothesis assumed by Marié-Davy that the observed difference between the bright and black bulb is proportional to and therefore a proper measure of the intensity of the radiant heat that falls upon these thermometers; a hypothesis which, as Ferrel has shown, is far from being true. The error of this hypothesis is of such a nature that for a given difference or a given actinometric degree the true intensity of radiation is greater at high temperatures than at low temperatures. Probably the recorded actinometric degrees therefore give a rather low value for the solar and sky radiation during the hottest portions of summer days.

The accompanying table, as published by Marié-Davy, shows the actinometric degrees calculated for the clearest of skies at Paris at noon of each day. They are computed according to the preceding formula, viz, A=actinometric degrees 100X0.875; in which, as before said, the coefficient, 0.875, represents the penetration or the total heat which penetrates to the observer, both from the sun and the surrounding sky, and includes even that small part that is directly reflected from the surrounding grassy lawn or other surface when the sun is in the zenith; if there were no atmosphere present the total amount received would be 100. It will be less confusing if the reader will consider these so-called "actinometric degrees as "percentages of what would be received in the absence of the atmosphere."

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Columns 5, 6, and 7 of our table give the mean value of the five actinometric percentages observed on the clearest days at 6 a. m., 9 a. m., noon, 3 p. m., and 6 p. m.; in the absence of actual observations these means may be employed in our study, provided we make a proper allowance for the influence of hazy and cloudy skies. It is, however, always desirable that the actual observation of the actinometer should be available, and with it should be associated a simultaneous record of the cloud or haze as given by the sunshine recorder.

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.

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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.

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