INTRODUCTION. 



The regular and almost uniform variations which meteorological tables exhibit, 

 indicate a periodical cause of change, which evidently resides in the sun. The 

 inquiry then arises, may not these variations be determined by theory from the 

 apparent course of the sun"? The first part of the present investigation thus sug- 

 gested by inspection of monthly temperatures, was published in Sillimari's Journal 

 of Science for 1850. Since then, considerable extensions have been made, includ- 

 ing expressions for annual values; a view of the whole of which is given in the 

 following pages. At some future time, the researches may be resumed in another 

 series. 



The object of the investigation here presented, is to resolve the problem of solar 

 heat and light, to the extent of the principle, that the intensity of the sun's rays, 

 like gravitation, varies inversely as the square of the distance, without resorting to 

 any other hypothesis. The principle is but a geometrical consequence of the 

 divergence of the rays. This elementary view thus presents the sun shining upon 

 a distant planet, and indicates the sum of the intensities received at the planet's 

 surface in all its various phases of position and inclination. 



In relation to the earth especially, the sum of the intensities must be referred to 

 the exterior limit of the atmosphere which surrounds the globe. This condition, 

 which is perhaps necessary in the present state of science, has the advantage of 

 rendering the formulas as rigorously accurate as are the propositions of geometry 

 and the conic sections. 



Poisson, in 1835, observed that, "for the completion of the theory of heat, it is 

 necessary that it should comprise the determination of the movements produced in 

 aeriform fluids, in liquids and even in solid bodies; but geometers' have not yet 

 resolved this order of questions, of great difficulty, with which are connected the 

 phenomena of the trade-winds, of certain currents observed in the sea, and the 

 diurnal variations of the barometer." The subject is believed to be now included 

 among the prize questions of the French Academy, and in the increasing number 

 of researches, it is hoped that its difficulties may at length be effectively obviated. 



The laws of Solar Intensity here derived a priori, have a general accordance with 

 physical phenomena, and will furnish instructive comparisons with analogous 

 values obtained by meteorological observations. The changes of the sun's inten- 

 sity upon the inaccessible regions of the Pole will be included, to which the late 



