April 21, 1899.] 



SCIENCE. 



695 



mass at a given epoch. Consider the state of 

 affairs when the radius has become 1 1>. Gravi- 

 tational forces (per unit mass) will be quad- 

 rupled and, therefore, the pressure between two 

 contiguous portions of given mass will be quad- 

 rupled, but the area separating these portions 

 will be quartered so that the pressure per unit 

 area (p) will be 16 times as great. The volume 

 V of each portion will be J as great, so that pv 

 will be twice as great. But absolute tempera- 

 ture is proportional topv, therefore, the absolute 

 temperature will have been doubled when 

 the radius is halved. That is, 



T = 



constant 



" This remarkable formula," according to Dr. 

 See, " expresses one of the most fundamental of 

 all the laws of Nature." In simple truth it is an 

 interesting and suggestive formula, and it may 

 throw light upon some of the knotty questions 

 of celestial physics. 



Dr. See, in his Atlantic Monthly article, says 

 among other things : " It is somewhat remark- 

 able that, while the law of gravitation causes 

 bodies to describe conic sections, the law of 

 temperature for every gaseous body is repre- 

 sented by a rectangular hyperbola referred to 

 its asymptotes, and thus by a particular curve 

 of the same species." Now, it would have 

 been quite as well, or even better, for Dr. See 

 to have said frankly um-ta-rara-bum-te-a, or 

 words to that effect ; for, seriously, the object of 

 popular scientific writing is to develop proper and 

 significant associations, and the bane of popular 

 science is verbal sense tvhich by association becomes 

 absolute nonsense. 



In the Astronomical Journal for April 8th Dr. 

 C. M. Woodward calls attention to some of the 

 manifest inaccuracies of Dr. See's derivation of 

 the temperature formula. He points out that 

 the gaseous globe cannot be assumed to have a 

 bounding surface of definite radius p ; he calls 

 attention to the fact that the gravitational force 

 at a point does not determine the pressure, but 

 the pressure gradient at the point ; and he 

 claims that the hydrostatic pressure at a point 

 varies inversely with p', not with p', as indicated 

 in the above derivation of the temperature 

 formula. In the above derivation, however, 



the pressure is said to increase 16 times, not at 

 the same point in space, but at a point one-half 

 as far from the center. 



The objections raised by Dr. Woodward seem 

 to be removed as follows : Consider the gaseous 

 mass at the epoch t. Assume that during the 

 contraction the radius coordinate of every par- 

 ticle decreases in the same proportion (this is 

 what is meant in the above discussion by the 

 invariance of the density function.) Consider 

 the gaseous mass at a subsequent epoch t' when 

 the radius coordinate of every particle has been 

 reduced to one-half its initial value. The 

 density at a distance Ir from the center at epoch 

 t' is eight times as great as at distance r from 

 the center at epoch t, and the gravitational 

 force is four times as great. Therefore, the 

 weight per unit volume is thirty-two times as 

 great, and this weight per unit volume is the 

 pressure gradient. In integrating the pressure 

 gradients at epoch t and V, respectively, imagine 

 the paths of integration to be broken up into 

 homologous elements. The elements at epoch 

 t' are then half as long as at epoch t, and, there- 

 fore, the integral at epoch t' from infinity to ir- 

 is sixteen times as great as the integral at epoch 

 t from infinity to r. Therefore, the pressure at 

 homologous points is increased sixteen times 

 when the mass of gas has contracted to half its 

 initial dimensions, as stated in the above deriva- 

 tion. W. S. Franklin. 



NOTES ON INORGANIC CHE3IISTRY. 

 An attempt is described in the Chemiker 

 Zeitung, by Johann Walter, to concentrate solu- 

 tions by means of a centrifugal apparatus. But 

 while even very light and finely divided pre- 

 cipitates are rapidly separated by centrifugal 

 force, an examination of different portions of 

 a solution, taken while the machine was in 

 rapid motion, showed that the composition was 

 constant. The same was found true in the case 

 of gaseous mixtures, no tendency being found 

 for the denser constituent to collect in the most 

 rapidly rotating portion of the vessel. This 

 affords an interesting experimental confirma- 

 tion of what might have been theoretically ex- 

 pected from the laws of gases and of solutions. 



The heat of formation of anhydrous oxid of 



