411 



[Chase. 



251. Oscillatory Relations of Mercury. 

 The cardinal loci of Mercury show the following among other harmonic 

 relations : 



1. The locus of Mercury's semi-axis major (.3871) is the rupturing locus 

 for Venus's locus of incipient subsidence : (| of .7744 = .3872). 



2. Mercury's incipient rupturing locus (.2974) indicates phyllotactic in- 

 fluence at Venus's locus of incipient subsidence (.7744) 



.2977 : .7741 : : 5 : 13. 



3. Mercury's incipient rupturing locus (.2974) is also near the extremity 

 of the linear pendulum, which has Mars's incipient subsidence locus 

 (1.7365) for its point of suspension, and Venus's incipient subsidence locus 

 (.7744) for its centre of oscillation : 



(3 X •'?'?44 — 1.7365) -f- 2 == .2934. 



4. If we divide Earth's semi-axis major by the phyllotactic product 2x3 

 X 3 X 13, we find approximate indications of Earth's harmonic influence 

 on Mercury's cardinal loci. 



70 a .298 Mercury 



Earth 

 252. Improbability of Accidental Harmonies. 



Schuster's harmonic investigation (Note 141) appears to have been 

 grounded on the hypothesis, which others have also entertained, that har- 

 monies such as are found in spectral lines and planetary positions may be 

 accidental. In note 244, I spoke of such an hypothesis as "wrongly as- 

 sumed," and I believe that it is only calculated to hinder scientific pro- 

 gress. Professor Peirce, in the Howland will case, showed that the rela- 

 tion of each individual position to all the possible positions which it might 

 assume, as well as the relative positions of the lines among themselves, 

 should be considered in calculations of mathematical probability. In the 

 Iliad problem, the bare improbabilitj^ of the accidental arrangement of the 

 letters in their orderly sequence is a", a representing the number of 

 letters in the alphabet and n the number of letters in the poem. Let p be 

 the number of readily distinguishable positions which each letter can as- 

 sume, and the adverse probability against the accidental occurrence of the 

 actual positions would be {apy. The improbability would be likewise 

 increased by considerations of the spaces between the letters, the word 

 spaces, the orderly arrangement of lines and pages, the probable frequency 

 of errors, and countless other particulars which are indicative of plan and 

 purpose. Finally, the adequate explanation which is furnished by the 

 simple hypothesis of human contrivance, wholh'- removes the question 

 from the realm of chance, and makes the improbability infinite. 



PROC. AMER. PHILOS. SOC. XX. 112. 2z. PRINTED KOVMEBEK 15, 1882. 



