20 THE POPULAR SCIENCE MONTHLY. 



We may, however, partially evade this difficulty by substituting as 

 the object of inquiry the sun's effective temperature : i. e., instead of 

 seeking to ascertain the actual temperature of different parts of the 

 sun's surface, we may inquire what tempei'ature would have to be 

 given to a uniform surface of standard radiating power (a surface cov- 

 ered with lampblack is generally taken as this standard) and of the 

 same size as the sun, in order that it might emit as much heat as the 

 sun actually does. In this waywe obtain a perfectly definite object 

 of investigation. But the problem still remains very difficult, and has 

 obtained as yet no entirely satisfactory solution. The difficulty lies 

 in our ignorance as to the laws which connect the temperature of a 

 surface with the amount of heat radiated per second. So long as the 

 temperature of the radiating body does not much exceed that of sur- 

 rounding space, the heat emitted is very nearly proportional to the ex- 

 cess of temperature. The extremely high values of the solar tempera- 

 ture asserted by Secchi and Ericsson depend upon the assumption of 

 this law (known as Newton's) of proportionality between the heat ra- 

 diated and the temperature of the radiating mass ; a law which direct 

 experiment proves to be untrue as soon as the temperature rises a little. 

 In reality, the amount of heat radiated increases much faster than the 

 temperature. 



More than forty years' ago the French physicists Dulong and Petit, 

 by a series of elaborate experiments, deduced an emj^ii-ical formula, 

 which answered pretty satisfactorily for temperatures up to a dull-red 

 heat. By applying this formula, Pouillet and Vicaire and others ar- 

 rived at the low solar temperatures assigned by them. It is, however, 

 evidently unsafe to apply a purely empirical formula to circumstances 

 so far outside the range of the observations upon which it was found- 

 ed, and, in fact, within a few years several experimenters, Rosetti espe- 

 cially, have shown that it needs modification even in the investigation 

 of artificial temperatures, like that of the electric arc. Rosetti, from his 

 observations, has deduced a different law of radiation, and by its aj^pli- 

 cation finds 10,000 Cent, or 18,000 Fahr. as the effective temperature 

 of the sun ; a result which, all things considered, seems more reason- 

 able and better founded than any of the earlier estimates. He consid- 

 ers that this is also pretty nearly the actual temperature of the upper 

 layers of the photosphere. The radiating power of the photospheric 

 clouds, to be sure, can hardly be as great as that of lampblack, but on 

 the other hand their radiation is supplemented by that of other layers, 

 both above and below. 



Besides the data as to the intensity of the solar temperature obtained 

 by calculation from the measured emission of heat, we have also direct 

 evidence of a very impressive sort. When heat is concentrated by a 

 burning-glass, the temperature at the focus can not rise above that of 

 the source of heat, the effect of the lens being simply to move the 

 object at the focus virtually toward the sun ; so that, if we neglect the 



