1S82.] ■it)< rChase. 



that it causes the observed discrepancy between the theoretical and 

 observed accelerations of the Moon " (op. cit. p. 147). 



244. Scientific Skepticism. 



Hesitation in the acceptance of alleged results, in any new line of scien- 

 tific research, is an obvious duty on the part of those who are fitted and 

 expected to be on the watch against the promulgation of hasty general- 

 izations which would needlessly cumber the field of knowledge. There is 

 danger, however, that even faithful watchmen may sometimes hinder 

 scientific progress by failing to keep their skepticism within proper bounds. 

 The fact of harmony, and especially of coordinated harmony, transcends 

 all mathematical tests of probability. It would be a tedious, but not a 

 difficult task, to find in how many ways the letters of the Iliad could be 

 arranged, and it is often wrongly assumed* that in a purely accidental 

 arrangement of the letters, the faultless one would be as likely to take 

 place as any other. It would be no more absurd to inquire whether the 

 jiiusic of an orchestra might not be accidental, than to make a like inquiry 

 as to the rhythm of atoms and waves and spheres. When mathematical 

 tests confirm the probability that special forms of harmony are due to 

 special laws, as in phyllotactic, thermodynamic and fundamental atomici- 

 ties, they are useful ; but when they fail to give any reason for obvious ac- 

 cordances, as in Schuster's first examination of spectral lines (Note 141), 

 they are utterly worthless unless they awaken further inquiries which lead 

 to satisfactory results, as in Schuster's final conclusions. 



345. Centre of Daioning Condensation in the Terrestrial Belt. 



The intrinsic probability that the major axis of the ]Moon's orbit is in- 

 variable, is greatly enhanced by the following proportion : 



?*3 : (3 : :^i?3 : X3 



Substituting the several known values, we have : 7'3 = Earth's equa- 

 torial semi-diameter = 3962.8 miles; ^3= Laplace's terrestrial limit = 



/86164.1\3 



\'50^^^3~6/ ''3' -^.1 == ^l^oon's semi-axis major = 60.2778 ?'3; Z3 = limit of 



incipient belt-condensation = iJg ?3 -^ r^ = 1,578,217 miles. The oscillatory 

 value of Sun's mass (Note 23, etc.,) gives, for the ratio of Earth's subsi- 

 dence from the centre of the belt of greatest condensation, Z, -~ p^=i 

 1,578,217 -T- 92,785,700 = .0170093, and for the dawning central locus of 

 the belt of greatest condensation, 1.0170093 ^3. The arithmetical mean 

 between Stockwell's estimates of Mercury's secular perihelion and the 

 secular aphelion of Mars is (.2974008 + 1.736478) --- 2 = 1.0169394^3. 

 The diflerence between tli# two estimates is less than ■^\^ of one per cent 



* See Note 252. 



