320 



SCIENCE. 



about its axis considered motionless, and an infinite 

 number of paraboloids will be generated, all interlacing 

 throughout the length of the ring. The centre of grav- 

 ity of a paraboloid is two-thirds the distance, from the 

 vertex to the limiting plane. 



Table II. Altitudes of Paraboloids in Miles. 



Distances of 

 Base Below 

 Neptune. 



Altitudes 

 Above 

 Base. 



Altitudes 



Above 

 Neptune. 



Diame'ers of 

 Mass when so 

 Elongated. 



500,000,000 

 400,000,000 

 300,000,000 

 200,000,000 

 100,000,000 

 50,000,000 

 25,000,000 



1,500,000,00c 

 1, 200, OOO, coo 

 900,000,000 

 600,000,000 

 300,000,000 

 150,000,000 

 75,000,000 



1,000,000,000 

 800,000,000 

 600,000,000 

 400,000,000 

 200,000,000 

 100,000,000 

 50,000,000 



7,560,000,000 

 7,160,000,000 

 6,760 000,000 

 6,360,000,000 

 5,900,000,000 

 5,760,000,000 

 5,660,000,000 



No tables of altitudes of hyperbolas or hyperboloids 

 have been inserted) as the distances of their gravitation 

 centres differ so little from parabolic segments, that it 

 was not thought best to fill up the columns of 

 "Science" with useless figures. For those who think 

 the ring could not have been left when sections were 

 parabolic or hyperbolic, we give a table of altitudes of 

 ellipsoids, that is when sections cut to the chord as be- 

 fore, were ellipses. " The centre of gravity of a semi- 

 prolate spheroid of revolution is on its axis of revolution 

 and at a distance from the centre equal to three-six- 

 teenths the major axis of the generating ellipse." — Peck's 

 Calculus, p. 175. 



Therefore Neptune is 3-16 above the conjugate axis, 

 and 13-16 below the vertex of the ancient semi-ellipsoid, 

 all the worse for the theory of ring detachment. Con- 

 sider the ring cut by perpendicular planes descending to 

 the chord, into an infinite number of semi-ellipses. The 

 chord becomes the conjugate ; revolve each curve about 

 its semi-transverse axis regarded as stationary, then the 

 ring will be made up of an infinite number of semi-pro- 

 late spheroids of revolution, each so nearly coincident 

 with the next as to have the surfaces fail to coincide only 

 by infinitesimal space. The table is computed by call- 

 ing the conjugate diameter, the chord of the arc, and the 

 semi-axis major, the line reaching from its centre up to 

 the equator, Neptune being in the centre of gravity of 

 the solids of revolution. 



Table III. Altitudes of Semi-Prolate Spheroids. 



Distances of 

 Conjugate Axes 

 Below Neptune. 



Altitudes 

 Above 

 Base. 



Elevations 



Above 

 Nep'une. 



Diameters of 

 Cosmic Sphere 

 When so 

 Elongated. 



500,000,000 

 400,000,000 

 300,000,000 

 200,000,000 

 100,000,000 

 50,000,000 

 25,000,000 



2,667,000,000 

 2,134,000,000 

 1,600 000,000 

 1,066,000,000 

 533,000,000 

 266,000,000 

 133,000,00c 



2,167,000,000 

 1,734,000,000 

 1,300,000,000 

 866,000,000 

 433,000,000 

 216.500,000 

 108,250,000 



9,804,000,000 

 9,028,000.000 

 8,160,000,000 

 7,292,000,000 

 6,426,000,000 

 5,502,000,000 

 5,778,000,000 



These tables of absurd figures are inserted to show 

 the hypothesis irrational. No such extension cf the mass 

 was possible, and no protuberance could have arisen 

 above the equator able to afford perpendicular sections, 

 hyperbolic, parabolic or elliptic. Nor could the chord 

 become the limiting plane of any parabola, hyperbola or 

 conjugate axis of any ellipse. Yet, the tables are logical 

 deductions from the doctrine of ring detachment, for if 

 the mass depressed at the poles, and elongated at the 

 equator, curvature of radial sections must have assumed 

 all varieties of conies. Since the centres of gravity of all 

 these curves, and solids generated by their revolution are 



known, the figures are correct if the theory is true. It 

 will be shown in a paper on mass, volume and density, 

 that most of these equatorial elevations could not have 

 contained matter enough to form Neptune. 



Is it ct edible that the primeval mass ever detached 

 rings or any other shaped portions ? From the altitudes 

 of these conoids it is seen that to cast off the Neptunian 

 material the rupture in every case took place at depths 

 of hundreds of millions of miles, where cohesion was 

 greatest and rotary velocity least ! In all these compu- 

 tations the abandoned masses were considered as homo- 

 geneous, as difference in density in a gas of such exces- 

 sive rarity cannot enter as a factor at depths of a few 

 hundred million miles. It may be said that cohesion 

 in a gas so rare, was not a factor. Granted, then 

 rotation was not, since a ball of gas of such tenuity as 

 to have no cohesion, could not possibly be set in revolu- 

 tion. The equatorial edge of the mass could not have 

 become angular, for sections cut to the base would be 

 triangles, whose centres of gravity are two-thirds the 

 distance from the angle to the base, and nowhere near 

 where Neptune exists. Neither could sections have been 

 cissoidal, conchoidal, cycloidal or sectoral, nor of any 

 other similar curvature known to geometry. The surface 

 was not irregular; loose masses did not float above the 

 periphery ; the matter was all of the same specific grav- 

 ity, hence buoyancy did not obtain on a mass of dissoci- 

 ated atoms. The mass existed in a void, else external 

 matter by friction would have induced currents from east 

 to west. No modes of energy save rotary force, existed 

 to detach a ring, no internal repulsion, as that had van- 

 ished in dissociation. The dogma is beset on all sides 

 with difficulties. When the mass was spherical, matter 

 enough to form Neptune was unable to leave the equator ; 

 when elongated, segments of enormous depth had to be 

 left by the shrinking mass, to afford material sufficient to 

 condense into the oldest planet; and the break occurred 

 where it was most difficult to be made, and where the 

 power necessary to make it was the least. 



Not only the most complex, but the simplest laws of 

 nature dispute the Nebular Hypothesis. Even primary 

 schools have text books wherein laws are laid down that 

 subvert it ! Primers of natural philosophy teach that if 

 a revolving sphere diminishes in diameter, its velocity of 

 rotation becomes accelerated, and the same primers 

 teach that if the diameter increases the velocity dimin- 

 ishes. Therefore, if the primeval gaseous sphere ever 

 revolved, said rotation caused the equatorial diameter to 

 increase in length ; but as soon as lengthened the 

 velocity of rotation diminished and the mass again be- 

 came a sphere, the oscillation always remaining within 

 small limits. The diameter of the mass when spherical 

 was 5,560,000,000 miles ; can it be believed that rotation 

 so far gained mastery over retardation as to allow the 

 mass to attain diameters ranging between 6,000,000,000 

 and 7,000,000,000 miles to detach parabolic segments; 

 and between 6,000,000,000 and 9,000,000,000 miles to 

 abandon semi-prolate spheroidal sections to make up a 

 ring? We are unable to conceive that valid argument 

 can be made in favor of the detachment of matter in any 

 form or volume from the mass. This theory, opposed by 

 every known law of nature has actually been entertained 

 by eminent physicists, geometers and astronomers, fully 

 conversant with these same laws that destroy the doctrine; 

 a thing long noted by psychologists, wherein delusions 

 hold sway over fine nrnds with greater tenacity than 

 ideas known to be true. 



Seismology in Japan. — The labors of the Seismological 

 Society of Japan have established the fact that there is a 

 chronic center of disturbance within a radius of a few miles 

 from Yokohama. We are glad we do not reside in the said 

 Yokohama ; at the same time, we congratulate the society 

 on the success attending its researches. 



