328 METEOROLOGY. 



it follows that the sun shining for sixteen hours from an altitude of 

 30°, would exert the same heating effect upon a plain as when it 

 shines during eight hours from the zenith ; since sin 30° is 0.5, and 

 sin 90° is 1. At least, such were the result independently of radiation 

 from the earth. 



By some writers, the measure of vertical intensity, as the sine of the 

 sun's altitude, has been stated without limitation. Approximately it 

 may apply at the habitable surface of the earth, when the influence of 

 the atmosphere is neglected ; yet it is strictly true only at the exterior 

 of the atmospheric envelope which encompasses the globe, or at the 

 outer limit where matter exerts its initial change upon the incident 

 rays. 



- The distinction here explained has not only engaged the attention 

 of the most eminent meteorologists of modern times, but was equally 

 adopted in ancient philosophy, as appears in the following passage 

 fram Plato's Phasdon, LVIII : " For around the earth are low shores, 

 and diversified landscapes and mountains, to which are attracted 

 water, the cloud, and air. But the earth, outwardly pure, floats in 

 the pure heaven like the stars, in the medium which those who are 

 accustomed to discourse on such things call ether. Of this ether, the 

 things around are the sediment which always settles and collects upon 

 the low places of the earth. We, therefore, who live in these terra- 

 queous abodes, are concealed, as it were, and yet think we dwell 

 above upon the earth. As one residing at the bottom of the sea might 

 think he lived upon the surface, and, beholding the sun and stars 

 through the water, might suppose the sea to be heaven. The case is 

 similar, that through imperfection we cannot ascend to the highest 

 part of the atmosphere, since, if one were to arrive upon its upper 

 surface, or becoming winged, could reach there, he would on emerg- 

 ing look abroad, and, if nature enabled him to endure the sight, he 

 would then behold the true heaven and the true light." 



In modern times, the researches of Poisson led him to the philo- 

 sophic conclusion now generally received, that the highest strata of 

 the air are deprived of elasticity by the intense cold ; the density of 

 this frozen air being extremely small. Theory de la (Jhaleur, p. 460. 

 An atmospheric column resting upon the sea may thus be regarded 

 as an elastic fluid terminated by two liquids, one having an ordinary 

 density and tenjperature, and the other a temperature and density 

 excessively diminished. 



Although the sun's intensity, which is here the subject of investi- 

 gation, is the principal source of heat, yet its effects are modified by 

 proximate causes of climate, of which the following nine are enume- 

 rated by Malte Brun : 



1st. — Action of the sun upon the atmosphere. 



meter of the disk. Hence, generally, A^ sin A, expresses the sun's intensity at any given in- 

 stant during the day. 



To determine the value of sin A by spherical trigonometry, the sun's angular distance from 

 the pole, or co declination, the arc from the pole to the zenith, or co-latitude, and the included 

 hour-angle from noon are given to find the third side or co-altitude. Writing, therefore, sines 

 instead of the co-sines of their complements, / 



sin A =:: sin L sin D -\- cos L cos D cos II. 

 a2 sin Azzz ^~ sin L sin I) -\- a'^ cos L cos D cos H. 



