the Sun's direct Rays in high than in low Latitudes. 183 



intensity* of radiant heat emanating from a particular surface 

 at the temperature 0° be expressed by i, the intensity at any 

 other temperature, /, will be expressed by ia*\ the quantity a 

 being constant for the same thermometric scale, and i for sur- 

 faces having the same radiating power. 



Hence it may be concluded that if radiant heat, at what- 

 ever distance from its source, have an intensity expressed by 

 ia x , it is equal to the initial intensity of heat emanating from 

 a surface the radiating power of which is r, and its tempera- 

 ture x. 



Again, suppose the bulb of a thermometer radiating heat 

 of a given intensity, ia' 9 to be exposed during a short period, 

 such as a minute, to the influence of solar heat of some su- 

 perior intensity, ix*, and that the velocity of heating, as mea- 

 sured by the number of degrees which the thermometer rises 

 during the given time, is represented by v, then, according to 

 Dulong and Petit f, the relation between these quantities may 

 be expressed by the equations 



v = m {a x —a t ) (1.) 



«'+ — = a?, (2.) 



where m is constant for the particular instrument by which v 

 is measured. 



From these equations it follows : 



1st, That the intensity of the sun's rays being the same, 

 their calorific effect ought to increase as the temperature of 

 the air diminishes. 



2ndly, That the intensity of the sun's rays is proportional 

 not simply to the increment of temperature which they impart 

 to a thermometer in a given time, but to that increment added 

 to the quantity which expresses the intensity of the thermo- 

 meter's radiation. 



But there are two objections to which these equations may, 

 perhaps, be thought liable, namely, 



1st, That the quantity a*, being small compared with a*, 

 may be neglected, and both equations be reduced to the form 



v = ma* (3.) 



2ndly, That in the particular case when it becomes = 0, 

 the intensity of radiation is still expressed by 



* The terms " intensity" and " density" may here be regarded as con- 

 vertible. 



•j- When v is determined by Sir John Herschel's very beautiful and sim- 

 ple method, every condition supposed in the reasoning of MM. Dulong 

 and Petit is complied with. 



