68 TWENTIETH ANNUAL KEPORT ON THE STATE CABINET. 



and uninterrupted radiation may produce an intensity of cold far 

 beyond what is indicated by the figures in the table ; and in the 

 continued sunshine of summer there is likely to be an intensity 



day and latitude by the correction for the day and altitude obtained as 

 above, for a third term, or the antecedent of the second ratio, we have, 

 with 80 deg. Fahrenheit, the average temperature at the equator, a formula 

 for obtaining the temperature in degrees of Fahrenheit for the day and lati- 

 tude for which the third term was made. 



When we reach the Polar circle, however, a modification of the formula 

 becomes necessary. Within that circle the sun does not set or reach a 

 zero of altitude at all ; and it becomes necessary, in order to get our ave- 

 rage for the correction for absorption, to integrate the values of A between 

 the limits of the maximum altitude for the day, that is, the altitude for 

 noon, and the minimum of the altitude for midnight ; and to the average 

 thus obtained, we must add the value of the midnight altitude. The figure 

 that denotes the sun's heat for the day under these circumstances, becomes 

 a semi-ellipse resting on a paral- c 



ielogram as in the annexed figure, 

 in which AB represents the sun's „ 



altitude at its minimum, and the 



distance HC its altitude at mid- A H e 



day; the base AE or BD having now become constant, and equal to double 

 its length at the equator, where the days are only and constantly twelve 

 hours long. 



But in winter, December 21st, the sun never rises within the Polar circle. 

 Hence a new expedient must be resorted to. I have taken the angular 

 depression of the sun at midday as the minimum, and its depression at mid- 

 night as the maximum or superior limit within which to integrate for the 

 average to be used as a correction. This implies that radiation of heat 

 from the earth, or the cooling process, goes on at the same rate as the re- 

 ception of heat from the sun, or the warming process, other things being 

 equal. This is proved to be the case by two considerations : 



1. Otherwise, that is, in case either heating or cooling were in excess, 

 the earth would be growing cooler or warmer, not from season to season as 

 it now does from summer to winter, but from year to year ; a process which, 

 if it exists at all, must be very slow, as no observed facts prove it to be 

 taking place. 



2. A comparison of temperatures as observed at evening and at morning 

 during the year, averaged for several years, shows, of course, that the air 

 is cooler in the morning than at evening ; but there is no difference in 

 this respect between summer and winter, that indicates the operation of a 

 different law. Hence I infer that, although the nights are much shorter 

 in the summer than the days, and longer than the days in the winter, yet 

 the radiation must take place so much faster in the summer when the earth 



