W. Ferret — Law of Thermal Radiation. 5 



the body radiates on the one side through the atmosphere into 

 space, the imperfect inclosure is equivalent to a perfect one of 

 the temperature at which the body would stand in the shade, 



3. Again, using the same notation as above except the abso- 

 lute temperatures T and T instead of r and r , if we put 



(•) H=J!LT. f 



this, in the special case of <?=4, becomes the expression of 

 Stefan's law. From this we get 



(7) H-H i=i ^ 5 (T--T i -)=m fl r «(j«-l) J 



in which the quotient 



T T 



q= Y , and q=^. 



From this form we get 



(8) U=A{q e — l, in which (9) A= n ™q e . 



Hence, for different temperatures of the inclosures, A varies 

 as q °, or as the e power of T . In the special case of a spheri- 

 cal body we have 



■ ,. 3 m 



9') A=— q*. 



\ i red 



4. The law of Dulong and Petit is based upon the results 

 of their noted experiments upon the rate of cooling of a large 

 glass bulb filled with mercury within an inclosure of the tem- 

 perature of melting ice and several other temperatures, and 

 the expression (4) in the special case of «=l - 0077 perhaps rep- 

 resents the observed rates at different temperatures within the 

 limit of the probable, at least the possible, errors of observa- 

 tion. At the time of these experiments, however, it was not 

 understood that the thermal conduction of gases is independent 

 of pressure except at very low tensions, and it was supposed 

 that the conduction at the tensions of 2 or 3 mm , at which the 

 experiments were made, was very small. Dulong and Petit's 

 formula for expressing the rate of cooling Y in calories per 

 minute due to both convection and conduction, was based upon 

 experiments made at pressures of 720, 360, 180 and 45 mm . 

 From these the following formula was deduced : 



(10) V=0-00919y 45 d v - z3 , 



in which p is the pressure of the air in meters Their observed 

 rates of cooling at the low air tension of their experiments 

 were corrected by deducting the rates given by this formula, 

 in order to obtain those due to radiation alone. But Stefan 

 has shown that this formula, based upon observations at high 



