644 



SCIENCE 



[N. S. Vol. XXXIV. No. 



Jo) 



Fig. 1. A side view of the helix drawn to scale. The four graphs below have been changed, 

 the alkalis and match closely the four double octaves, the two octaves and the half octave. The 



the same ratio is true of the circles of which 

 these triads are a part. So, omitting gases 

 and the abnormal glucinum, we have for the 

 carbon octave .52 and for the silicon octave 

 .80. Thus we get, without forcing, the fol- 

 lowing average values for D/Y for each of the 

 seven circles 



E Nu C Si Fe Bu Se Pt 



(0) (1/3) 1/2 2/3 1 3/2 2 3. 



This agrees with Victor Goldschmidt's law of 

 complication' which shows that the law of in- 

 creasing longitudinal condensation in the 

 elements deduced above is the same as the 

 law of the octave in music, and the funda- 

 mental law of crystallography, and the first 

 ° V. Goldsehmidt, ' ' Ueber Harmonie und Com- 

 plication, " Berlin, 1901. 



two values given above are extrapolated in 

 accordance with Goldschmidt's law. 



Instead of omitting any elements as sug- 

 gested above, a different and perhaps more 

 useful line of thought may be followed. It 

 may be assumed that the true relations would 

 appear only when the specific gravities were 

 taken under common conditions, say at 

 — 273°, since the elements expand unequally 

 and sometimes diversely with change of 

 temperature, so that we can obtain only ap- 

 proximate results from specific gravities 

 taken at ordinary temperatures. We find the 

 law most perfectly realized at the bottom of 

 each circle at the point of greatest condensa- 

 tion. 



Thus C as graphite is .5, Si as quartz ia 



