SU 42.1 ... If we put 1, we shall have the elements and the U == differences without the hypothesis of a resisting medium, determined, so that the sum of the squares of the differences ( A3 A. R. cos + A♪2) may be the least possible. This sum is found, for 34 observations = 11405 + 1594950 The mean error of an observed place will be 18".3 in the hypothesis of an ether; and 217.6 without it; which seems to prove the necessity of in troducing a correction, of which the law is not very remote from that which is here supposed. It is only the masses of 24 and g of which the changes could have any material influence, the perturbations of the other planets being too small to require further consideration. For Jupiter Mr. Bouvard finds, from the motions of 1⁄2 1040.5. Mr. Gauss and Mr. Nicolai, from Pallas and Juno 53.9249 and this latter value is confirmed by Vesta and Ceres, of which the elements have lately been corrected. The agreement of the observations of the comet will be still more satisfactory if we employ a mass greater than 0.09, and if we substitute the mass of Nicolai we shall have us For Venus, Mr. Burckhardt has found a diminution of, or f = 0.1125. The observations of the comet would give 0.0583 but if we employ the mass found by Burckhardt, the sum of the squares of the errors is neither increased nor diminished. Without wishing to decide that it is necessary to employ for the comet the mass of 2 such as Mr. Nicolai has found it, the last results have been added in order to prove that the reality of the hypothesis of an ether does not depend on the supposed value of the mass of any of the planets. Dated, Berlin, 7 Feb. 1829. iv. LUNAR OCCULTATIONS of the Principal Fixed Stars, in the months of April, May, and June, 1829, calculated for the Royal Observatory at Greenwich. By THOMAS HENDERSON, Esq. The explanations of the columns are the same as in preceding numbers. Observers are advised to be prepared two or three minutes before the times here stated, the calculations having been performed in an approximate manner only. v. Extract of a Journal of the TIDES, kept at ST. HELENA, by Lieut. JOHNSON, R.N. Communicated by the Rev. FEARON FALLOWs, M.A. [The original Observations are deposited in the Library of the ROYAL SOCIETY.] 1 |