INTENSITY OF SUN'S HEAT AND LIGHT. 17 



The following cases under the general formula may here be specified : — 



First, at the time of the Equinoxes, D is 0, and consequently II is 6 h ; substitut- 

 ing these values in (13) and converting into units, 



u = k A 2 cos L. (15.) 



Hence the sun's daily intensity for all places on the earth is then proportional to 

 the cosine of the latitude. As the equinoxes in March and September lie intermedi 

 ate between the extremes or maxima of heat and light in summer, and their 

 minima in winter, the presumption naturally arises that the same expression will 

 approximate to the mean annual intensity. The coincidence is accordingly worthy 

 of note, that the best empirical expression now known for the annual temperature 

 in degrees Fahrenheit, given by Sir David Brewster, in the Edinburgh Philosophical 

 Transactions, Vol. IX, is 81.°5 cos L, being also proportional to the cosine of the 

 latitude. It is remarkable that Fahrenheit, in 1720, should have adjusted his 

 scale of temperature to such value, that this formula applies, without the addition 

 of a constant term. 



Secondly, for all places on the Equator, the latitude L is ; and H is 6 h , or 

 the sun rises and sets at six, the year round, exclusive of refraction. Consequently 

 the Sun's diurnal intensity varies slowly from one day to another, being proportional 

 to the cosine of the meridian Declination, or, 



v! = k A 2 cos D. (16.) 



Thirdly, at the South or the North Pole, the latitude L is 90° ; and since tan 90° 

 is infinite, the astronomic relation cos H = — tan L tan D is illusory, except when 

 D is 0. The physical interpretation of this feature is, that at the North Pole, the 

 sun rises only at the vernal equinox in March, and continues wholly above the 

 horizon, till it sets at the autumnal equinox. Thus to either Pole, the sun rises 

 but once, and sets but once in the whole year, giving nearly six months day, and 

 six months night. Now suppose the six months day to be divided into equal 

 portions of twenty-four hours each; then, in reference to formula (13), if is 12\ 

 and the intensity during twenty-four hours of polar day is proportional to the sine of 

 the Declination at the middle of the day ; or, 



u" = k A 2 it sin D. 



This term varies much faster than the cotemporary value on the equator. And 

 comparing the two expressions, it appears that during the summer season, in each 

 twenty-four hours, the Sun's intensity upon the Equator is to that upon the Pole, 

 in the following proportion : — 



v! : u" : : 1 : 7t tan D. (1^0 



Fourthly, at the summer solstice, when the intensity on the Pole is a maximum, 

 D is 23° 28', and the preceding ratio becomes as 1 to 1.25 ; or the Polar intensity 

 is one-fourth part greater than on the Equator (Plate IV). The difference evidently 

 arises from the fact that daylight in the one place lasts but twelve hours out of 

 twenty-four, while at the Pole the sun shines on through the whole twenty-four 

 hours. 



It were interesting to find when this Polar excess begins and ends, which may 

 be ascertained by equating the last two terms of (IT). The condition n tan D = 1, 

 thus gives D equal to 17° 40', which is the sun's Declination on May 10th, and 

 3 



