36 INTENSITY OF SUN'S HEAT AND LIGHT. 



the summer of 1807, the heat was excessive, and the spots of vast magnitude. 

 Warm summers, and winters of excessive rigor have happened in the presence or 

 absence of the spots." 1 



Proceeding now to investigation, our first inquiry will relate to changes of the 

 sun's annual intensity upon the earth's surface regarded as one aggregate. In Section 

 II, formula (10), let the accented letters refer to the earth at an antecedent or future 

 epoch ; then, since Astronomy proves that the semi-transverse axis A is invariable, 



we have for the proportion of intensity at the secular epoch I 5 . (42.) 



In the Connaissance des Terns, for 1843, Leverrier has exhibited the secular values 

 of most of the elements of the planetary orbits during 100,000 years before and 

 after Jan. 1, 1800. The eccentricity of the earth's orbit at the present time being 

 .0168, the value 100,000 years ago, and the greatest in that interval was .0473. 

 Substituting these in the preceding expression, we find that the sun's annual 

 intensity at the former epoch was greater than at present by one-thousandth part. 

 Now this fraction of 365.24 days, counting the days at twelve hours each in respect 

 to solar illumination, amounts to between four and Jive hours of sunshine in a year ; 

 and by so small a quantity only has the sun's annual intensity, during 100,000 years 

 past, ever exceeded the yearly value at the present time. Nor can it depart from 

 its present annual value by more than the equivalent of five hours of average sun- 

 shine in a year, for 100,000 years to come. 



The superior and ultimate limit given by Leverrier, to which the eccentricity of 

 the earth's orbit may have approached at some very remote but unknown period or 

 periods, is .0777. At such epoch, the annual intensity is computed, as before, to 

 have exceeded the intensity of the present by thirteen hours of sunshine in a year. 

 On the other hand, the inferior limit of eccentricity being near to zero, indicates 

 only /b«<? - minutes of average sunshine in a year, less than the present annual amount. 

 Between these two extreme limits, all annual variations of the solar intensity, 

 whether past or future, must be included, even from the primitive antediluvian era, 

 when the sun was placed in his present relation to the earth. By the third law of 

 Kepler, on which equation (10) is based, these results are rigorous for siderial 

 years; and by reason of the slight but nearly constant excess, the same may be 

 concluded of tropical or civil years. For the annual variation of the tropical year 

 is only — Od.OOO 000 066 86. 



The preceding conclusions, it is proper again to observe, refer to the whole earth's 

 surface collectively. Let us, in the next place, inquire concerning changes of annual 

 intensity upon the different Latitudes of the earth. According to formulas (30) and 

 (31), this variation will be a function of the eccentricity e, and the obliquity a. For 

 the present, let it be proposed to compute the annual intensity for an epoch 10,000 



1 Professor Henry was the first to show, by projecting ou a screen in a dark room the image of the 

 sun from a telescope with the eye glass drawn out, that the temperature of the spots was slightly less 

 than that of the other parts of the solar disc. The temperature was indicated by a delicate thermo- 

 electrical apparatus. Professor Sechi, of Italy, afterwards obtained the same result. — See Silliman's 

 Journal, Yol. XLIX, p. 405. 



