206 



SCIENCE. 



[N. S. Vol. XII. No. 293. 



tempted, under some limitations regarding 

 the motions, by some of the ablest of math- 

 ematicians and physicists, among whom 

 are Lane, Eitter, Gr. W. Hill, George H. 

 Darwin, and Lord Kelvin.* The results 

 reached by all are in substantial agreement, 

 though somewhat different analytical meth- 

 ods were followed. The distribution of 

 density computed by Darwin was used in 

 our computations. 



The present moment of momentum of the 

 whole system, sun, planets and satellites in- 

 cluded, was found to be 22.7666, reckoning 

 the sun as homogeneous, which gives too 

 large results but favors the nebular hy- 

 pothesis. The unit is a convenient arbitrary 

 one. The moment of momentum of the 

 solar nebula when it reached the orbit of 

 Ifeptune and had the angular velocity of 

 Neptune, which would be necessary to sepa- 

 rate the Neptunian ring, was by compu- 

 tation 4848.055.1 These momenta, which 

 should be equal, stand in the ratio of 1 : 213. 

 Furthermore the ratios are different at dif- 

 ferent stages of the evolution ; for example, 

 for the stage just preceding the separation 

 of the earth the ratio of the nebular mo- 

 mentum to the actual momentum was found 

 to be 1 to 1208, and for the stage just before 

 the separation of Mercury, 1 to 754. Larger 



*Laiie, 'On the Theoretical Temperature of the 

 Sun under the Hypothesis of a Gaseous Mass main- 

 taining its Volume hy Internal Heat, and depending 

 on the Laws of Gases as known to Terrestrial Exper- 

 iments.' Am. Jour. Sci., Vol. XLIX., pp. 56-74, 

 1870. 



Eitter, ' Untersuchen iiber die Hohe der Atmo- 

 sphare und die Constitution gasformiges Weltkorper, ' 

 Wiedmami's Annalen, New Series, Vol. LXVI., 1882, 

 p. 166. 



G. W. Hill, 'Annals of Mathematics,' Vol. IV., 

 1888. 



Darwin, ' On the Mechanical Condition of a Swarm 

 of Meteorites, and on the Theories of Cosmogony.' 

 Trans. Phil. Soc, 1888. 



Kelvin, ' On the Origin and Total Amount of the 

 Sun's Heat, ' Popular Lectures and Addresses, 1891. 

 Cmistitution of Matter, pp. 370-429. 



t Paper III., pp. 127-128 and Paper II., p. 64. 



discrepancies would have been found if the 

 Laplacian hypothesis had not been given 

 the benefit of every doubt as to the struc- 

 ture and of all margins in computation. If 

 for example, the sun be assigned an increase 

 of density toward the center, according to 

 Laplace's law, which is probably near the 

 truth, the last two ratios would be 1 to 

 1801, and 1 to 1127, instead of the figures 

 given. 



For a discussion of the question whether 

 these discrepancies can be due to a radical 

 error in the law of density, the reader must 

 be referred to the original paper.* It can 

 only be stated here that the probable 

 variations from the accepted law of density 

 seem rather more likely to increase the dis- 

 crepancies than to diminish them, and 

 further that the discrepancies are so enor- 

 mous that the law must be supposed to 

 quite break down to bring them into har- 

 mony. Furthermore it must break down 

 irregularly, for the figures run 



Neptunian stage 213 



Jovian stage 141 



Terrestrial stage 1208 



Mercurial stage 754 



Present stage 1 



To satisfy the laws of mechanics all these 

 should be unity. 



2. As the foregoing comparison involves 

 the distribution of density in the supposed 

 gaseous nebula, concerning which there is 

 some doubt, it was obviously desirable to find 

 some mode of comparison which should not 

 involve this factor. This was sought in a 

 comparison between the ratios of the plan- 

 etary masses to their parent nebula, and 

 the ratios of the planetary momenta to the 

 nebular momenta. In this case the nebular 

 momenta were obtained by adding together 

 the component planetary momenta which 

 they must have equaled under the laws of 

 mechanics. The momenta of the satellites 

 were reckoned in with their respective 



* Paper II., pp. 65-67. 



