1883.] On the Dependence of Radiation on Temperature. 173 



electrical energy absorbed can now be constructed. Taking the 

 abscissae of the curve proportional to the watts absorbed, and the 

 ordinates proportional to the temperatures in degrees Centigrade, the 

 dotted curve marked B represents the relation between the power 

 and the temperature for the results given in the tables. 



I have sought to express this relation by an empirical formula in 

 order to carry the curve to still higher temperatures. The equation — 



Temperature = A (log ^) 2 + B (log x) + C, 



where x represents watts, agrees with the experimental results. The 

 constants A, B, C have the values, 



A= -63. 

 B= 1177. 

 C = -1603. 



Mr. McFarlane, in a paper communicated to the Royal Society on 

 January 11th, 1872, has arrived at the equation — 



Bate of energy = a + bt + cfi, 



where a, b, c are empirical constants and t is the difference of tem- 

 perature, from his experiments made through a very limited range of 

 temperature, viz., about 60° C. (" Proc. Boy. Soc," vol. 20, p. 90, 

 1872). Professor James Dewar, from experiments extending from a 

 temperature of 80° to the boiling points of sulphur and mercury, also 

 ' deduces a parabolic formula. (" Proceedings of the Boyal Institu- 

 tion," vol. 9, p. 266.) 



Making use of the equation I have given, the rate of energy 

 absorbed for a temperature of 2780° C, is 155,000 watts, or sixty- 

 seven times the rate of absorption at a temperature of 1670° C. Since 

 1670° C. is not much below the temperature of an incandescent 

 filament (reverting to Sir William Thomson's calculation for the ratio 

 of the radiant power per unit of surface of the sun to that of the 

 incandescent filament), the temperature of the sun comes out to be 

 about 2780° ; which is in very close agreement with my former 

 estimate based on other grounds. The effect of absorption between 

 the sun and the earth would bring the two estimates into still closer 

 agreement. 



If we attempt to form a natural equation to the curve, it is apparent 

 that it will consist of two terms — 

 (i.) The term due to radiation, 



(ii.) The term depending on the convection and conduction of the 

 air. The conduction of heat by the wire into the terminals may be 

 neglected, as by taking a considerable length it becomes a small 

 quantity of the second order. The first term I take to be proportional 



