I 



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On the Variation of Entropy, 251 



fluorescent than the basal planes, exce})t in the case of one 

 crystal. One of the basal planes of this was very fluorescent, 

 the other not. It was thouoht at first that this was a proof 

 that the crystal possessed hemimorphic symmetry, like tour- 

 maline. But the other crystals showed no such difference 

 between the ends of the optic axis. It is probable that the 

 diffc'rence was due to some kind of decomposition which had 

 only affected one end of the crystal. 



A number of other fluorescent crystals, including various 

 platinocvanides, aponhyllite, calcite, felspar, and scheelite were 

 tried. But they did not exhibit any difference of fluorescence, 

 depending on which face was exposed to the rays, or on the 

 orientation of the face. 



Another experiment may be briefly mentioned. It is known 

 that crystallized calcium tungstate, whether natural or arti- 

 ficial, is brightly fluorescent under the rays. The amorphous 

 precipitated tungstate is scarcely at all so. It was thought 

 worth trying wdiether prolonged boiling with water would 

 effect the change to the crystalline fluorescent modification. 

 Experience showed that this was so. Some of the precipi- 

 tated tungstate was divided into two parts. One of them 

 was boiled for four days with excess of water. On drying it 

 was found to be much more fluorescent than the untreated 

 portion, though less so than natural crystallized scheelite. 



XXX. On the Variation of Entropy as treated in Willa^'d 

 GiObs' 'Statistical Mechanics/ By S. H. BuRBURY, F.B.S* 



1. XN a former paper in this Magazine (May 1900), I 

 X considered the question whether there exist in nature 

 systems of which the motion is irreversible, and entropy tends 

 to a limit, although they consist of parts, the motion of each 

 of which is reversible separately. This was with especial 

 reference to Boltzmann^s H theorem, the best known example 

 of such a process. In a later paper (February 1902), I con- 

 sidered Planck^s treatise Ueher irreversible Strahlungsvor gauge 

 in the same relation. Boltzmann^s and Planck^s theories 

 depend ultimately on certain algebraic theorems, of which 

 we may take as a type that, given '%x, 2.i' log cC has its least 

 vakie when x is constant throughout the summation, or, in 

 another form, given ^e"" dx, \.e^xdx has its least value when 

 X is constant throuo'hout the inteo-ration. But these theorems 

 of |)ure mathematics do not alone determine the question of 

 irreversibility, or the tendency of entropy to a limit. To 

 * Communicated by the Author. 



