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for the reason' lying still farther back, that they mean alike ; and further, that this likeness of meaning is not confined to a group of sign-words having the same primitive, but that it can be traced throughout the whole family of homophonous sign-words.”
“ The Chinese written system is not to be considered as an inven. tion, as M. Callery seems to do, but as a growth, perhaps of several ages, quite similar to the gradual formation of spoken languages in other countries. The law of its growth is to be sought in the spoken language of China which previously existed. It is the greatest of mistakes to suppose the written system to be something quite distinct from and disconnected with the spoken. In order to make out an obvious relation between the numerous and apparently diverse meanings of a Chinese syllabic word, recourse must be had to processes of investigation somewhat new in their kind. The natural relations of ideas to each other must be sought out. Etymology has been too much studied, as the Chinese study anatomy, by mapping out the surface of the body. What we want is that science which shall enable us to trace out a positive relationship between ideas superficially the most remote from each other, as the nerves, and arteries, and veins of the body connect and cause to sympathize parts apparently the least related. These relationships of ideas must be shown to exist metaphysically, and at the same time it must be shown that they are testified to by parallel processes of derivation in various languages, except only the Chinese and a few others, which do not admit of derivation.”
Two hundred and ninety-second Meeting.
March 2, 1847. — MONTHLY MEETING. The PRESIDENT in the chair.
Mr. Andrews presented a dissertation on the Tones of the Siamese Language, by Mr. J. Caswell, American Missionary in Siam, which was referred to the Committee on Publication.
Dr. C. T. Jackson read a paper on the recent discovery, claimed by himself, of the effects of the inhalation of sulphuric ether in producing insensibility to pain.
Two hundred and ninety-third Meeting.
March 16, 1847. — SPECIAL MEETING. The President in the chair.
Professor Peirce communicated to the Academy the following notice of the computations of Mr. Sears C. Walker, who found that a star was missing in the Histoire Céleste Française, observed by Lalande on the 10th of May, 1795, near the path of the planet Neptune, at that date, which may possibly have been this planet.
“Shortly after the arrival of the news of the physical discovery of Neptune at Berlin, on a suggestion by Mr. E. C. Herrick of its probable identity with the Wartman planet of 1831, Mr. Walker engaged in the study of the orbit of the former, and soon concluded that they could not have been the same, and that no set of elements could be found, with a mean distance at all probable, which would represent the four places of Wartman's planet, as published in the Comptes Rendus for 1836.
“ His first examination of the orbit of Neptune led to the presumption that the orbit is nearly circular. Also, the large planets lead by analogy to the same conclusion. The eccentricity of
Jupiter is 0.048
Neptune " < 0.060, conjectured. " With a small eccentricity, it was impossible for the sun's mass at that distance to impress much daily variation of the radius vector. Accordingly, an approximate solution was made from the places observed on the 26th of September, 26th of October, and 21st of November, on the supposition of a constant radius vector. The concluded true sidereal orbital motions n', n, and n", together with the mean daily sidereal motion u, for the radius vector r = the semi-axis major = a, are here given. a First thirty days. Average motion. Last 28 days.
16.7 197 17.90 14.6
17.7 20.3 18.71 16.6 18.8 20.8
19.60 19.4 20.1 21.2
20.56 21.7 21.6 21.6
21.58 24.1 23.4
“The most plausible value of r from this table is that in which (n — n')? + (n — n') is a minimum. This value by the table is 30 nearly, and for this value we have very nearly n = n = n" = M. Hence the orbit comes out nearly a circle, unless we suppose the planet now to present the possible, but still improbable, case of a great eccentricity and true anomaly nearly 90°.
“Accordingly, he selected for the next trial the circular hypothesis, for which two places of the planet sufficed, those of the 26th of September, from the mean of nine European observations, and the 26th of December, from the mean of 33 transits and 11 measures in declination of Neptune (compared with the same two stars used in September) by himself with the Washington equatorial. All the small corrections were taken into account. In this manner he obtained Elements I. in the table below. These elements enabled him to compute an ephemeris of Neptune for the six months following August 1st, 1846, with which he compared one hundred and sixteen nights' works, seventy of the European and forty-six of the Washington Observatory, and derived from them sixteen normal places, which indicated the following corrections of the geocentric longitude computed from Elements I.
“The above places are referred to the mean equinox of January 1st, 1847, and mean obliquity. The planet's place is corrected for stellar, but not for planetary aberration. It is also corrected for planetary parallax. The residual errors, though small, show in the course of six months a sensible deviation of the orbit from a circular form. They show at the same time that if the eccentricity is greater than 0.06, the true anomaly must be nearly +90°, a possible, but, as was said before, an improbable case.
“The next step in the investigation was to make equations of condition of the form, 0 = ax +by+cz + n, in which x is 50 x ur, n = 10 X Av, % = A 2300, a, b, and c are computed coefficients, v the daily increase of 2, and 2300 the heliocentric longitude of Neptune on the 300th day of the year. Finally, n is the equivalent heliocentric value of A a above with sign changed. The number of equations was reduced to nine, by taking for the first the one third of Nos. one and two, above. Then follow the next five unchanged, then the mean of Nos. eight, nine, and ten. No. eleven is rejected, then the mean of Nos. twelve and thirteen. Lastly, the mean of Nos. fourteen, fifteen, and sixteen. The nine conditional equations have then equal weight, and stand thus :
k=Gauss's constant of the earth's velocity. .
u=ka- * = 21".37881. Period = T = 165.97030 tropical years.
“Thus it appeared that Elements II., assuming the eccentricity and perihelion point unknown, and neglecting the daily variation of the radius vector, would give an ephemeris following the planet's path for five months so closely, that the sum of the squares of 9 comparisons of theory with observation was only 4".21. This residual quantity might have been still further reduced by inserting a fourth term of the form du, in which u is the daily increase of r300, and d, a coefficient of the form
d=aart () A t, where a is the former coefficient of x, and ) is the daily variation of 1 for conservation of areas. Since these terms become sensible in the course of a few additional months, it was thought preferable to postpone the research after the final values of e and 7, and by assigning them suitable limits, that of e < 0.06, and to a its corresponding value from the equation, cos. v = 4 , then to compute the locus of Neptune's orbit for these limits for any given date, and search for an observation of a missing star in Neptune's path on the same night in some of the ancient catalogues. The fact that (
n u ) is at this time only 0.28, shows the limit of v <+90°. The following table of limits of v was computed.
ues of o.