440 THE SCIENTIFIC PAPERS OF 



The curve of relation between the temperature of the wire and 

 the electrical energy absorbed can now be constructed. Taking 

 the abscissas of the curve proportional to the watts absorbed, 

 and the ordinates proportional to the temperatures in degrees 

 Centigrade, the 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 x) z + B (log z) + C, where .^repre- 

 sents watts, agrees with the experimental results. The constants 

 A, B,C have the values, A = - 63 ; B= 1177 ; = -1603. 



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

 on January llth, 1872, has arrived at the equation Rate of 

 energy = a + bt + ct* , where a, b, c are empirical constants and 

 t is the difference of temperature, viz., about 60 C. (" Proc. 

 Roy. 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 Royal Institution," 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 incan- 

 descent 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 to some power of the absolute temperature, the second 



