SCIENCE. 



351 



Fowne's Chemistry, p. 137. Thence one cubic mile of 

 hydrogen weighs over five (5) trillion grains, or 777 mil- 

 lion pounds. And as the ring was of such density as to 

 require one cubic mile to contain 157 grains of matter, 

 the Neptunian mass was thirty-four(34) billion times less 

 dense than hydrogen. 



The volume of the sphere, radius three (3) billion 

 miles, whence Neptune was detached, the ring being seg- 

 mental, was * it R 3 = 1 13 octillion cubic miles. But the 

 ring was in volume nine octillion cubic miles, nearly 

 the entire mass ! 



What unheard of convulsion took place to disrupt the 

 mass and cause it to part with its bulk ! What in- 

 conceivable power was displayed if the dogma is true, 

 yet all the force present was gentle centrifugal tendency 

 caused by slow rotations of 3.36 miles per second ! 



The mass of the first world is ^ nioo of the solar sys- 

 tem, but -fe the volume was required to make it. The 

 volume of a sphere bounded by the orbit of Neptune is 

 y e K D 3 =c)o* octillion cubic miles, and as it contained 4 

 nonillion pounds of gas, each cubic mile held 44 pounds, 

 — 17,500,000 times less in density than the lightest body 

 on eaith, the mass being homogeneous. But it was not 

 since the centre must have been compressed. 



The density of the segmental ring was 34 billion times 

 less than hydrogen, therefore, the sphere was old when it 

 cast away its first world, having had time to acquire in- 

 ternal density, greater than peripheral, in the proportion 

 of 17 millions to 34 billions. All along we have been 

 quoting Helmholtz, where he says : — " It required several 

 cubic miles to weigh a single grain," — not having made 

 calculation, but now we do not see how he arrived at 

 these results, as one cubic mile, by following the prin- 

 ciple of centre of gravity, is found to have contained 157 

 grains. 



He probably alluded to the mass when expanded 

 larger; but if extended to half the distance of the stars, 

 a thousand cubic miles might have been required to con- 

 tain one grain of matter. And we feel that we are tra- 

 versing solid ground, in basing these deductions on the 

 doctrine of the centre of Gravity. The volume of a 

 cylindric ring to form Neptune must have been the same 

 as the segmental, the density being nearly equal. The 

 diameter of a section of a cylindric ring whose length 

 was equal to that of Neptune's orbit, in order to have 

 the required volume, was 822,000,000 miles. Since the 

 planet coalesced in its centre of gravity, which was its 

 geometrical centre, the material of the ring extended 

 41 1,000,000 miles above, and the same distance below 

 the orbit. This added 822,000,000 miles to the equator- 

 ial diameter of the mass, retarded its assumed rotation, 

 and prevented detachment of any particle of matter. The 

 disrupting force had to be applied, not where Neptune 

 revolves, but 411,000,000 below, at a point where force 

 was weakest, and resistance strongest. And then such a 

 ring was subjected to lateral pressure, and could not be 

 severed on that account. 



The ring made up of an infinite number of solids gen- 

 erated by revolution of circular segments about their 

 chords, to have the same volume as segmental and cylin- 

 dric, was in radial diameter 380,000,000, and in diam- 

 eter north and south 2,090,000,000 miles. If this form of 

 ring was discarded the break took place 190,000,000 be- 

 low the orbit, and along a line more than two billion 

 miles long. Rotation was slower than the orbital veloc- 

 ity of Neptune, and the separation was again required to 

 be made where the force to cause it was in minimum, 

 and its opposing powers, gravity and cohesion, at a max- 

 imum. We reassert that in no possible case could the 

 Neptunian matter have been detached from the primeval 

 mass when it was a sphere. 



Neither could it have been separated when sections of 

 the protuberance were parabolic ; thus a chord, or limiting 



* Ninety Octilliun. 



plane, the base of a parabolic segment, in order to cut 

 out a ring in volume sufficient to contain the Neptunian 

 gas, was in length 634,000,000, in altitude 1,250,000,000, 

 the vertex extending 750,000,000 above, and base de- 

 scending 500,000,000 miles below, the orbit, in order that 

 Neptune might condense in its centre of gravity. This 

 would make the equatorial diameter of the mass 7,060,- 

 000,000 miles a physical impossibility, for rotation would 

 have come to a dead rest ages before such elongation. 

 Consider the curvature of sections semi-elliptical and 

 results are still more absurd. Since the mass was un- 

 able to part with rings whose sections were hyperbolic, 

 parabolic or semi-elliptic, we dismiss as untenable all 

 varieties of such ring-shaped masses. 



Now conceive the mass a sphere again and at rest ; 

 let rotary motion be imparled, and should the velocity 

 become sufficient, the equatorial regions will become a 

 swelling tide. But when a protuberance elevated motion 

 waned, and the equator subsided. When at greatest 

 altitude the whole mass was an ablate spheriod. There- 

 fore, we lay down this proposition which must have ob- 

 tained if the Hypothesis of ring displacement is true. If 

 the equatorially expanding mass parted with a ring, it 

 did so at the first opportunity. 



And such fullness of time was when a segment of an 

 ellipse could be cut away large enough to have Neptune 

 in its centre of gravity. When the mass was an ablate 

 spheroid, sections cut by passing planes through the entire 

 mass, at right angles to the equator, bisecting the poles, 

 would all be plain curves — ellipses. And a segment 

 severed from the equator to make Neptune, was a seg- 

 ment of an ellipse, whose centre of gravity coincided with 

 that planet's present track. The dimensions of this ring 

 were, height, 319,000,000, and chord 2,350,000,000 miles, 

 to have volume sufficient, to contain gas enough to 

 solidify into the most remote member of the solar system. 

 The axes of the ellipse whence this segment was cut were 

 transverse, 5,800,000,000, and conjugate, 5,400,000,000, 

 the diameter of the mass when spherical being 5,560,- 

 000,000 miles. Therefore, we say that during all muta- 

 tion in form of the primordial cosmical mass, admitting 

 the hypothesis true, its equatorial diameter was never 

 augmented more than 240,000,000 miles, as is seen in 

 these dimensions. 



Mathematical instruments of delicacy are required to 

 measure such small deviation from a sphere. Yet.it was 

 able to discard a ring having a volume of nine octillion 

 cubic miles. Basing conclusions on the sure foundation 

 of the principle of the centre of gravity, we assert that the 

 mass never detached rings whose sections were of any 

 form of curvature known to geometry. Then none were 

 cast off, since every department of celestial mechanics is 

 known to be subject to rigid mathematical laws. 



The theory of cosmic evolution, which holds that 

 planets were formed of masses detached from an aeri- 

 form sphere belongs in that list of delusions which re- 

 tarded the early progress of astronomy — the "Geocen- 

 tric System," the " Firmament," and " Music of the 

 Spheres." 



New Windsor, III., July 10, 1881. 



CORRESPONDENCE. 



[The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. No notice is taken of anonymous communi- 

 cations.} 



To the Editor of " Science ": — 



Dr. J. J. Mason in his second rejoinder to the critic- 

 ism made by a reviewer in Science, leaves his un- 

 known critic to the contemplation of the latter's clause. 

 "Notwithstanding the construction which Dr. J. J. 

 Mason now desires to see placed on his words," and 

 does him "the justice" of supposing that the critic 



