Chase.] -jOO [April -21; 



3. The sums ot the logarithms of the reciprocals of deviation, which 

 indicate the aggregate relative probabilities of normal influence, are : 

 70.4555173 ; 89.2637807. 



4. The ratio of aggregate probabilities is, therefore, P^ : P.^ : : 1 : 64159 



(10)'*. The ratio of mean probabilities, P^^ is p^ : p., : : 1 : 2.1976. 



5. Testing the hydrogen unit in a like way, I find the average deviation, 

 (J3 ^=.0024: ; 2' log (1 -~ d-i) = 152.5459742 ; log. relative probability, taking 

 Pj, as the unit, 82.0904569. This gives, P^ = 12315 (10j'« ; p^ = 31.0852. 



6. In accordance with the principle of least squares, these values of p 

 should be reduced inversely as the fundamental divisors. This gives 

 P^--P2-P3-P*--'^ ■ l-'^l ■ 4.44 : 5.08 ; log {P., -- PJ = 12.8482860 ; log 

 (P^ ^ Pj) =, 35.6100415 ; log (P, -v- PJ = 38.8306765 ; p^ and P, being re- 

 spectively, the mean and aggregate probabilities of the phyllotactic 

 divisors (Note 181). The corresponding mean relative probabilities for 

 S-i, S.2, and Gerber's divisors are respectively, 2.78, 2.45, 4.72. 



211. Suggestions for Frn'tJier Investigation. 



The ratio between Pi and pg, in the foregoing note, has been gradually 

 diminished by successive approximations, and by making allowance for 

 theoretical considerations, which have seemed to justify the adoption of 

 some exact multiple or submultiple of an atomic weight which had been pre- 

 viously accepted. The ratio between p^ and p.^, favorable as it already is 

 for the latter, is based upon a comparison of the latest revision of the 

 atomic heats with the first crude application of the perissad and artiad divi- 

 sors. If Dulong and Petit's law is entitled to great weight in determi- 

 nations of atomicity, a still stronger claim may be urged in behalt of 

 divisors which have a mean probability that is more than 70 per cent, 

 greater. If Dumas's proposed modification of Front's hypothesis were 

 applied to Si and Cr, their atomicities would be very closely represented 

 by I X 8 and ^^^ >< § ; P is very nearly f X 8 X 7, or very nearly ^ of 

 the monatomic phyllotactic divisor ; Na is about 30 times the monatomic 

 divisor or 2 X H, H being the phyllotactic number which follows 7 in the 

 secondary series (Note 209) ;. Bo is 7.018 times its proper phyllotactic 

 divisor. Si, Cr, Na and P may, perhaps, have tendencies towards the 

 opposite group, perissad or artiad, the investigation of which may throw 

 light upon the beginnings of valency. 



212. Chemical Electricity. 



Davy's discovery of potassium laid the foundation of electrolysis, intro- 

 ducing polarity as an important modifier of chemical attraction. The at- 

 tractions and repulsions of Sir William Thomson's hypothetical vortex- 

 atoms involve gyroscopic tendencies to maintain uniform planes of rota- 

 tion, which must aid the normal arrangements of a-thereal particles {P-oc. 

 Am. Phil. 80c. , xii, 408) in the determination of axial and polar, centri- 

 fugal and centripetal relations. Hence arisp various combinations of 



