it will be found that even with Dr. Brown's more elaborate tables the work can be done in two days. Happily the time taken in computing a number of places does not vary in proportion to the number of places computed. A comparison between the sizes of the tables of Burckhardt, Hansen, and Brown which have been successively used at the Nautical Almanac Office will show how much more numerous are the perturbations contained in this last set of tables than in its predecessors.
I referred a moment ago to the difference between the true position of the Moon and the position deduced from our most accurate tables. In the case of Dr. Brown's tables the principal cause of this discrepancy is that he has adopted too small a value for the secular or progressive acceleration of the Moon's motion. There are at least three causes which produce such an acceleration referred to our standard of time. Of these, the gravitational effect of the diminution in the eccentricity of the earth's orbit, discovered by Laplace, and the gravitational effect of the oblateness of the earth's figure, discovered by Stockwell, can be computed with exactitude, and Dr. Brown has made the proper computations. We know, however, that the total acceleration is greatly in excess of the values which can be computed from gravitational theory, and we know that part or all of this excess must be due to the action of the tides, more especially to the tides in shallow seas, more particularly the Behring Sea. This subject has been recently developed by Major Taylor and Dr. Jeffreys.[1] Unfortunately we are unable to determine from hydrographic observations or theory the amount of accelera-
- ↑ See in particular Dr. Jeffreys's paper, 'Tidal Friction in Shallow Seas', Philosophical Transactions of the Royal Society, A. 221 (1920), 239-64.
