268 



SCIENCE 



[N. S. Vol. XXVII. No. 685 



with a mirror of so gi'eat concentrating power, 

 which at the same time has possessed so 

 perfect a figure. 



The energy received from the sun can not 

 be determined from the data given without 

 further addition of a time-factor, and esti- 

 mates of the mass of material heated, and of 

 the accompanying losses of heat. As a simple 

 experiment in static equilibrium of tempera- 

 ture, however, this knowledge is not necessary. 



It is doubtful whether radiation formulae 

 obtained from measures through a limited 

 range of temperature for solid bodies, com- 

 posed of complex molecules, are applicable to 

 solar conditions at the photospheric level, 

 where it is improbable that any molecules re- 

 main undissoeiated. Extrapolations from 

 Stefan's law of the proportionality of total 

 radiation from a black body to the fourth 

 power of the absolute temperature, are there- 

 fore not certainly applicable to the problem, 

 -even though the law has been verified through 

 a range of some hundreds of degrees. But, on 

 the other hand, ISTewton's law, which is only an 

 approximation for a very limited range of 

 temperature, and which becomes entirely 

 erroneous when we pass to wider variations, is 

 even less trustworthy. 



If the exposed body were at the center of 

 a perfectly reflecting, hemispherical mirror, it 

 would receive as much heat as if it were 

 transported to the sun's surface, neglecting the 

 loss by atmospheric absorption. At the focus 

 of such a mirror, since the radiation received 

 or lost is proportional to the solid angle filled 

 by the mirror, or by the portion of the sphere 

 outside the mirror, respectively, the body 

 would receive more solar radiation than from 

 the actual mirror, subtending 29°, in the pro- 

 portion, versin 90° : versin 14°. 5 = 31.3 : 1. 



At the same time, the angle through which 

 loss of radiation from the heated body takes 

 place, having been diminished in the ratio, 

 1.968 : 1, the total radiant effect would be 

 altered in the ratio, 1 : 1.968 X 31-3 = 1 : 61.6. 

 Accepting the estimate of losses by absorption, 

 this ratio is to be further multiplied by 2.14, 

 giving 1 : 131.8. With the estimated tempera- 

 ture of 2,000° C. from solar rays with an 

 18-inch aperture, we get, if the sun radiates 



as a full radiator and Stefan's law holds, 

 effective solar temperature == i„ ■= (2,000* X 

 131.8)1 = 6,776°. This is a minimum value, 

 because the sun does not radiate as a body at 

 a single definite temperature, biit as a complex 

 radiator, since, even if the photosphere behave 

 like an' absolutely " black," or full radiator, 

 the atmospheric layers above the photosphere, 

 which are at a lower temperature and which 

 add their own radiations, can not be perfect 

 radiators, because they would then be perfect 

 absorbers also, and would completely absorb 

 and shut off the radiation from the photo- 

 sphere itself, becoming a new photosphere in 

 turn. 



We may presume that quite a notable 

 amount of radiation comes from these cooler 

 and impei'fectly radiating layers, enough, at 

 any rate, to cause the maximum in the spectral 

 energy-curve to move from the position cor- 

 responding to the photospheric temperature to 

 one appropriate to a body of lower tempera- 

 ture, through the addition of a disproportion- 

 ate amount of radiation of longer wave-length. 



To produce a given amount of radiation 

 from an imperfect radiator requires a higher 

 temperature in inverse proportion to the coef- 

 ficient of relative emissive power. Scheiner 

 has noted this in his treatise on the " Radia- 

 tion and Temperature of the Sun," and has 

 estimated that it may be necessary to almost 

 double the temperature which would be ob- 

 tained on the supposition that the sun is a per- 

 fect radiator. 



The complexity of the solar radiating layer 

 prevents the strict application of Paschen's 

 law connecting the wave-length of maximum 

 radiation and the absolute temperature, to the 

 problem of solar temperature ; but there is now 

 sufficient agreement in the different modes of 

 computing the solar temperature to indicate 

 that it is between 6,000° and 7,000°, or else 

 that there is a marked change in the law of 

 radiation at solar temperatures, a possibility 

 which has been suggested by Professor Bige- 

 low.° 



It does not seem demonstrable that the 

 effective solar temperature is as great as 66,- 



' Monthly Weather Review, December, 1902, p. 



