The changes in the amount of light due to the altitude of the sun are produced by the earth’s atmosphere. The absorption of light rays is greatest near the horizon, where their pathway through the atmosphere is longest, and it is least at the zenith. The absorption, and, consequently, the relative intensity of sunlight, can be determined at a given place for each hour of any sunshiny day by the use of chart 13. This chart has been constructed for Lincoln, and will serve for all places within a few degrees of the 40th parallel. The curves which show the altitude of the sun at the various times of the day and the year have been constructed by measurements upon the celestial globe. Each interval between the horizontal lines represents 2 degrees of the sun’s altitude. The vertical lines indicate time before or after the apparent noon, the intervals corresponding to 10 minutes. If the relative intensity at Lincoln on March 12 at 3:00 P.M. is desired, the apparent noon for this day must first be determined. A glance at the table shows that the sun crosses the meridian on this day at 9 minutes 53 seconds past noon at the 90th meridian. The apparent noon at Lincoln is found by adding 26 minutes 49 seconds, the difference in time between Lincoln and a point on the 90th meridian. When the sun is fast, the proper number of minutes is taken from 26 minutes 49 seconds. The apparent noon on March 12 is thus found to fall at 12:37 P.M., and 3:00 P.M. is 2 hours and 23 minutes later. The sun’s altitude is accordingly 36°. If the intensity of the light which reaches the earth’s surface when the sun is at zenith is taken as 1, the table of the sun’s altitudes gives the intensity at 3:00 P.M. on March 12 as .85.
For places with a latitude differing by several degrees from that of Lincoln, it is necessary to construct a new table of altitude curves from the celestial globe. It is quite possible to make a close approximation of this from the table given, since the maximum and minimum meridional altitude, and hence the corresponding light intensity, can be obtained as indicated above. For Minnehaha, which is on the 105th meridian, and for other places on standard meridians, i. e., 60°, 75°, 90°, and 120° W., the table of apparent noon indicates the number of minutes to be added to 12 noon, standard time, when the sun is slow, and to be subtracted when the sun is fast. The time at a place east or west of a standard meridian is respectively faster or slower than the latter. The exact difference in minutes is obtained from the difference in longitude by the equation, 15° = 1 hour. Thus, Lincoln, 96° 42′ W. is 6° 42′ west of the standard meridian of 90°; it is consequently 26 minutes 49 seconds slower, and this time must always be added to the apparent noon as determined from the chart. At a place east of a standard meridian, the time difference is, of course, subtracted.
Fig. 13. Chart for the determination of the sun’s altitude, and the corresponding light intensity.
The actual differences in the light intensity from hour to hour and day to day, which are caused by variations in the sun’s altitude, are not as great as might be expected. For example, the maximum intensity at Lincoln, June 22, is .98; the minimum meridional intensity December 22 is .73. The extremes on June 22 are .98 and .33 (the latter at 6:00 A.M. and 6:00 P.M. approximately); between 8:00 A.M. and 4:00 P.M. the range in intensity is from .90 to .98 merely. On December 22, the greatest intensity is .52, the least .20 (the latter at 8:00 A.M. and 4:00 P.M. approximately). If the growing season be taken as beginning with the 1st of March and closing the 1st of October, the greatest variation in light intensity at Lincoln within a period of 10 hours with the meridian at its center (cloudy days excepted) is from .33 to .98. In a period of 8 hours, the extremes are .65 to .98, i. e., the greatest variation, .3, is far within the efficient difference, which has been put at .9. For the growing period, then, readings made between 8:00 A.M. and 4:00 P.M. on normal sunshiny days may be compared directly, without taking into account the compensation for the sun’s altitude. Until the efficient difference has been determined for a large number of species, however, it seems wise to err on the safe side and to compensate for great differences in time of day or year. In all doubtful cases, the intensity obtained by the astronomical method should also be checked by photometric readings. A slight error probably enters in, due to reflection from the surface of the paper, and to temperature, but this is negligible.
86. Table for determining apparent noon
| DATE | TIME EQUATION | LINCOLN NOON | |||
|---|---|---|---|---|---|
| Sun slow: + | 26m. | 49s. | |||
| January | 1 | 3m. | 47s. | 12:31 | P.M. |
| „ | 6 | 6 | 7 | :33 | |
| „ | 11 | 8 | 12 | :35 | |
| „ | 16 | 10 | 3 | :37 | |
| „ | 21 | 11 | 35 | :38 | |
| „ | 26 | 12 | 48 | :40 | |
| „ | 31 | 13 | 41 | :40 | |
| February | 10 | 14 | 27 | :41 | |
| „ | 20 | 13 | 56 | :41 | |
| March | 2 | 12 | 18 | :39 | |
| „ | 7 | 11 | 10 | :38 | |
| „ | 12 | 9 | 53 | :37 | |
| „ | 17 | 8 | 29 | :36 | |
| „ | 22 | 6 | 59 | :34 | |
| „ | 27 | 5 | 27 | :32 | |
| April | 1 | 3 | 55 | :31 | |
| „ | 6 | 2 | 27 | :29 | |
| „ | 11 | 1 | 3 | :28 | |
| Sun fast: − | |||||
| „ | 16 | 0 | 13 | :27 | |
| „ | 21 | 1 | 20 | :25 | |
| „ | 26 | 2 | 16 | :24 | |
| May | 1 | 3 | 0 | :24 | |
| „ | 16 | 3 | 48 | :23 | |
| „ | 31 | 2 | 33 | :24 | |
| June | 5 | 1 | 45 | :25 | |
| „ | 10 | 0 | 49 | :26 | |
| Sun slow: + | |||||
| „ | 15 | 0 | 13 | :27 | |
| „ | 20 | 1 | 18 | :28 | |
| „ | 25 | 2 | 22 | :29 | |
| „ | 30 | 3 | 22 | :30 | |
| Sun slow: + | 26m. | 49s. | |||
| July | 5 | 4m. | 19s. | 12:31 | P.M. |
| „ | 10 | 5 | 7 | :32 | |
| „ | 20 | 6 | 6 | :33 | |
| August | 4 | 5 | 53 | :33 | |
| „ | 14 | 4 | 30 | :31 | |
| „ | 19 | 3 | 28 | :30 | |
| „ | 24 | 2 | 13 | :29 | |
| „ | 29 | 0 | 48 | :28 | |
| Sun fast: − | |||||
| September | 3 | 0 | 45 | :26 | |
| „ | 8 | 2 | 25 | :24 | |
| „ | 13 | 4 | 9 | :23 | |
| „ | 18 | 5 | 55 | :21 | |
| „ | 23 | 7 | 41 | :19 | |
| „ | 28 | 9 | 23 | :17 | |
| October | 3 | 10 | 59 | :16 | |
| „ | 8 | 12 | 26 | :14 | |
| „ | 13 | 13 | 43 | :13 | |
| „ | 18 | 14 | 48 | :12 | |
| „ | 23 | 15 | 37 | :11 | |
| November | 2 | 16 | 20 | :10 | |
| „ | 12 | 15 | 45 | :11 | |
| „ | 17 | 14 | 54 | :12 | |
| „ | 22 | 13 | 44 | :13 | |
| „ | 27 | 12 | 14 | :15 | |
| December | 2 | 10 | 25 | :16 | |
| „ | 7 | 8 | 21 | :18 | |
| „ | 12 | 6 | 5 | :21 | |
| „ | 17 | 3 | 41 | :23 | |
| „ | 22 | 1 | 12 | :26 | |
| Sun slow: + | |||||
| „ | 27 | 1 | 17 | :28 | |
87. Place. The effect of latitude upon the sun’s altitude, and the consequent light intensity have been discussed in the pages which precede. Latitude has also a profound influence upon the duration of daylight, but the importance of the latter apart from intensity is not altogether clear. The variation of intensity due to altitude has been greatly overestimated; it is practically certain, for example, that the dwarf habit of alpine plants is not to be ascribed to intense illumination, since the latter increases but slightly with the altitude. It has been demonstrated astronomically that about 20 per cent of a vertical ray of sunlight is absorbed by the atmosphere by the time it reaches sea level. At the summit of Pike’s Peak, which is 14,000 feet (4,267 meters) high, the barometric pressure is 17 inches, and the absorption is approximately 11 per cent. In other words, the light at sea level is 80 per cent of that which enters the earth’s atmosphere; on the summit of Pike’s Peak it is 89 per cent. As the effect of the sun’s altitude is the same in both places, the table of curves on page [57] will apply to both. Taking into account the difference in absorption, the maximum intensity at sea level and at 14,000 feet on the fortieth parallel is .98 and 1.09 respectively. The minimum intensities between 8:00 A.M. and 4:00 P.M. of the growing period are .64 and .71 respectively. The correctness of these figures has been demonstrated by photometer readings, which have given almost exactly the same results. Such slight variations are quite insufficient to produce an appreciable adjustment, particularly in structure. They are far within the efficient difference, and Reinke[[5]] has found, moreover, that photosynthetic activity in Elodea is not increased beyond the normal in sunlight sixty times concentrated. In consequence, it is entirely unnecessary to take account of different altitudes in obtaining light values.
The slope of a habitat exerts a considerable effect upon the intensity of the incident light. If the angle between the slope and the sun’s ray be 90°, a square meter of surface will receive the maximum intensity, 1. At an angle of 10°, the same area receives but .17 of the light. This relation between angle and intensity is shown in the table which follows. The influence of the light, however, is felt by the leaf, not by the slope. Since there is no connection between the position of the leaf and the slope of the habitat, the latter may be ignored. In consequence, it is unnecessary to make allowances for the direction of a slope, viz., whether north, east, south, or west, in so far as light values are concerned. The angle which a leaf makes with its stem determines the angle of incidence, and hence the amount of light received by the leaf surface. This is relatively unimportant for two reasons. This angle changes hourly and daily with the altitude of the sun, and the intensity constantly swings from one extreme to the other. Moreover, the extremes 1.00 and 0.17, even if constant, are hardly sufficient to produce a measurable result. When the angle of the leaf approaches 90°, there is the well-known differentiation of leaf surfaces and of chlorenchym, but this has no relation to the angle of incidence.