Decembek 20, 1907] 



SCIENCE 



877 



select. It usually discourages a student some- 

 what to buy a large text -book, one half or one 

 third of which is used in his classes, and the 

 rest omitted. W. J. Beal 



SPECIAL ARTICLES 



THE PROBABLE ORIGIN AND PHYSICAL STRUCTURE 

 OP OUR SIDEREAL AND SOLAR SYSTEMS* 



Mainly because of the very high, and for 

 certain reasons inadmissible, temperature 

 heretofore obtained when Newton's law of 

 radiation is employed, astronomers and phys- 

 icists hold that this law can not be used for 

 determining the effective surface temperature 

 of the sun. 



That Newton's law of radiation is just as 

 true for the sun as is the law of gravitation, 

 and that the sun's surface temperature can 

 only be determined by means of this law will 

 now b« demonstrated. 



Let us conceive that the sun's, total radiant 

 energy S (per unit of time) is concentrated 

 in an ether vibration at the sun's center. 

 Let the temperatures t„ and t be taken as 

 the measures of the intensity of vibration at 

 the distances r„ and r; we can then at once 

 write 



hence 



Wo'} \tr')' 



(1) 



(2) 



Now let us conceive that a thin spherical 

 shell of lampblack having the radius r„, and 

 coinciding with the sun's surface, receives 

 and transmits in each unit of time the total 

 energy S, the temperature t^ of this shell will 

 then be the same as the temperature of the 

 sun's surface, and the temperature t in any 

 exterior similar shell of radius r must neces- 

 sarily be such as to satisfy equation (2), for 

 to assume any gain or loss through the sub- 

 stitution of the total energy S given out by 

 the surface shell in place of the energy S 

 given out by the central vibration would be 

 contrary to the law of the conservation of 

 energy. 



Now to find i„ the temperature i, at the 

 ' Extract from a still unfinished paper. 



earth's distance from the sun, must first be 

 found, and just here is where inadmissible 

 errors have leen committed in past determi- 

 nations. 



I offer the following extremely simple meth- 

 od for determining the absolute temperature 

 of space: 



Let D denote the diameter of a mirror (or 

 objective) having the focal length F, the 

 linear diameter d of the sun's focal image 

 will then be d = 2F tan 9, in which is the 

 angular semi-diameter of the sun. (For our 

 present purpose d depends only on F and 6 

 and is independent of D.) Let T denote the 

 measured absolute temperature in the sun's 

 focal image, then, if we neglect for the present 

 the effects due to atmospheric absorption, we 

 can at once write for a theoretically perfect 

 telescope 



The expression for the absolute temperature 

 of space is therefore 



-ay 



(4) 



Now let a denote the factor by which T must 

 be multiplied in order that the product shall 

 equal the surface temperature t, of the sun; 

 we then have 



-f-«(?y=7"-(a' 



from which we find 



in which all the quantities are known. The 

 expression for the effective surface tempera- 

 ture t„ of the sun is therefore 



(5) 



(6) 



'.='(a' 



:ar. 



(7) 



My observational work has been carried on 

 with the aid of three mirrors which I con- 

 structed to continue investigations under way 

 at the time of my departure from the Lick 

 Observatory. The first two of these telescopes 

 are briefly described in No. 539 of the As- 

 tronomical Journal; the third mirror has an 

 aperture of two feet and a focal length of 

 three feet. The definition of this last-men- 



