4 INTRODUCTION. 



Arctic explorations have given unusual interest. And, among other advantages, 

 light will be thrown upon geological researches relating to changes of the heat of 

 the globe at very remote epochs. 



It will be proper also to observe, that the method of summation, of which exam- 

 ples are given in the fifth and ninth sections, is more simple and direct than the 

 process of discontinuous functions. The general reader, however, passing over the 

 algebraic analysis, which is but a means for carrying out the leading conception 

 already stated, will find the conclusions which flow from it plainly discussed in 

 the remaining paragraphs of the several sections, and illustrated by tables and the 

 accompanying curves. 



At the close, the course of investigation has led to the development of a peculiar 

 inequality in the annual duration of sunlight. The like series of values for the 

 duration of twilight is also new, and will not be devoid of interest. But the main 

 design has been — distinguishing between the sun's intensity and terrestrial tem- 

 peratures — to carry out one comprehensive principle, by which the laws of the 

 sun's intensity of heat and light are obtained to some degree of completeness, as a 

 system, embracing the following topics in order: — 



Section I. Irradiated Surface upon the Planets. — Zone of Differential Radiation ; 

 its Breadth and Area; its Extension by Refraction; its Changes of Position. 



Section II. The Surfs Intensity upon the Planets, in relation to their Orbits. — 

 Intensity proportional to the true longitude described. Table of Relative Intensity 

 in equal times and in entire revolutions. Resemblance of the Earth to the planet 

 Mars. Equality of Intensities during the four Seasons. 



Section III. Law of the Stin's Intensity at any Instant during the day. — It is 

 proportional to the length of a perpendicular line from the Sun's Centre to the 

 Horizon. The Atmosphere. Causes of Climate. 



Section IV. The Su7i , s Diurnal Intensity. — It depends on the Latitude, the 

 Sun's Declination, Hour-angle, and Distance. Intensity upon the North Pole, 

 during Summer, greater than upon the Equator. Graphical comparison of Inten- 

 sities with Temperatures. Average Rate of Solar Intensity per hour. Retardation 

 of the effects of the Sun's Intensity. Indication of Equatorial, Tropical, and 

 Polar Calms. 



Section V. The Sun's Annual Intensity. — Formula for the Summation of Series 

 demonstrated. The Annual Intensity is measured by three Elliptic Functions. 

 Tabular Values. Annual Intensity upon the Polar Circle equal to one-half of that 

 upon the Equator. Analogy with the line of perpetual Snow. Graphical com- 

 parison of annual Intensities with annual Temperatures. 



Section VI. Average Annual Intensity upon a part or the whole of the Earth's 

 Surface. 



