1882.J 4UJ [Chase. 



248. Harmonies of Central Condensation. 



The superficial intersections of d^, in the foregoing note, describe circles 

 about the poles, which have diametrical arcs of 5° 10' 40", which differs 

 by only 2' from the inclination of the Moon's orbit. If we take 1 X^X'^X'h 

 the product of the first four phyllotactic numbers, as a divisor of Earth's 

 diameter, calling the quotient a, we have the following approximate 

 accordances : 



The coefficients of nodal division in the radius which is nearest the Moon, 

 (4, 11), are the- second and fourth of the secondary phyllotactic numbers. 

 The coefficients in the remote radius, (8, 7), are the third phyllotactic 

 numbers in the primary and secondary series, or the artiad and perissad 

 divisors (Notes 201-2,). It may be interesting to inquire whether the 

 frequency and locality of earthquakes are affected by these nodal influences. 



. 249. Pendulum Estimate of Earth" s Oblateness. 



The ratio of Earth's equatorial semi-diameter to its theoretical equatorial 

 l^endulum, or the corresponding ratio of v^^ to v^^, (square of limiting 

 orbital velocity to square of equatorial rotation-velocity), represents a cen- 

 trifugal force which would tend to produce oblateness in a liquid globe, to 

 maintain oblateness in a solidified globe, or to exert a constant pressure for 

 restoring oblateness, should it be temporarily disturbed in any way. 

 From the estimate of the theoretical pendulum in Note 246 we get 



3962.8 : 1.142,882 : :1 : 288.40 

 Bessels' estimate was 298.1528; Clarke's two estimates 291.36, 293.76; 

 Listing's (1878, cited by Newcomb and Holden, p. 202), 288.5. This ac- 

 cordance furnishes additional reasons tor believing that Eartli's rotation 

 and Moon's mean distance are as invariable as planetary major axes. 



250. Oscillatory Relations of Venus. 



The masses of Venus and Earth are more nearly alike than those of 

 Jupiter and Saturn. This is perhaps owing to their comparatively central 

 position in the belt of greatest condensation. The reasonable expectation 

 that their mutual actions and reactions should be rhythmical is strength- 

 ened by many harmonic relations, among which are the following : 



1. If we divide Venus's mean locus of subsidence (mean aphelion) by 

 the product of the first four phyllotactic numbers, 1x2x3x5 = 30, 



