NovEMBiai 10, 1911] 



SCIENCE 



645 



Co mtrilcatlon 



Law of CondenfiBlInn ^ 

 Vibration Period 



Paf rflctivltv 



in size only, to match the diagram. It will be seen that the apices of the same point exactly to 

 table showing the longitudinal octave relations is placed below. 



.66, iron is 1, rhodium is 1.5, all exactly fol- 

 lowing the law. The next circle is not de- 

 termined and osmium is 2.8 + instead of 3. 

 Moreover, all the elements in the lower part 

 of each curve keep close to this average, but 

 as we pass up the left side of the curves into 

 the region of lessened density we come upon 

 a sudden sharp divergence from the law in the 

 sulphur and halogen series, caused by the 

 polymerization or allotropic states of these ele- 

 ments. If we divide the numbers of the sul- 

 phur and the first half of the halogen series 

 by two and bromium and iodine by three we 

 obtain numbers closely coinciding with the 

 law in every case thus: 



ri Cl Br I s Se Te 



Obtained by division .55 .65 1 1.7 5 1.1 1.5 



Eequired by the law .5 .67 1 1.5 67 1 1.5 



We may further strengthen the argument 



for this polymerization by the following tabu- 



lation of the monovalent specific gravities or 

 specific gravity 



valence 

 octant : 



of the elements in the carbon 



.3 .3 



coal 

 .58 .5 .5 



graphite 

 .9 .9 .9 1.1 



diamond 



As carbon crystallizes as graphite at normal 

 pressures we may take that as the normal form 

 and .5 as the normal monovalent specific grav- 

 ity. There is a partially known graphitic 

 form for boron and we may divide all the 

 numbers in the lower row by two to get ap- 

 proximately the specific gravity of these ele- 

 ments in a form analogous to graphite. With 

 these two changes we get averages of all the 

 elements in each circle as follows: 



