RECENT ADVANCES IN SCIENCE 177 



importance, but continues to maintain its position as one of 

 the most readable of the philosophic reviews. 



The philosophical congress at Oxford in the latter half of 

 September comes, unfortunately, too late to be referred to in 

 the present notice. 



ASTBONOMY. By H. Spencer-Jones, M.A., B.Sc, Royal Observatory, 

 Greenwich. 



Brown's " Tables of the Motion of the Moon."^ — No record of the 

 progress of astronomy would be complete which omitted a 

 reference to the publication of the new Tables of the Motion 

 of the Moon, with the preparation of which Prof. Brown has 

 been occupied during the past thirty years, and the value of 

 which is attested by the honours conferred upon him by the 

 Royal Society, the Royal Astronomical Society, Cambridge 

 University, the Paris Academy of Sciences, and the Astro- 

 nomical Society of the Pacific. 



To a first approximation the " theory " of the motion of 

 the Moon is a particular case of the problem of three bodies, 

 complicated by the fact that neither the Earth nor the Moon is 

 spherical ; but, further, the attractions of the planets Mercury, 

 Venus, Mars, Jupiter, and Saturn have to be taken into account. 

 Differential equations expressing the laws of motion and the 

 law of gravitation are formed and solved for the longitude, 

 latitude, and parallax in terms of a single variable quantity — 

 the time. The results are expressed as the sum of many hun- 

 dreds of periodic terms, each of which has portions which come 

 from several different parts of the calculations. Prof. Brown 

 has stated that in this work " the number of figures written 

 mounted to four or five millions, not counting algebraic 

 symbols or the figures which passed through the mind while 

 doing the calculations. ... In the final results, about 1,500 

 terms were left which seemed large enough to be recorded as 

 having an effect to be included when obtaining the position of 

 the Moon at any time." 



To calculate the values of these 1,500 terms every time the 

 position of the Moon was required would prove an enormous 

 task : hence the need for the construction of tables which 

 perform the separate calculations once for all time. The num- 



* Tables of the Motion of the Moon. By E. W. Brown, Professor of 

 Mathematics in Yale University, with the assistance of H. B. Hedrick, Chief 

 Computer. [Vol. i. Sections I and II, pp. xiv + 140 + 39. Vol. ii. Section 



III, pp. 223. Vol. iii, Sections IV, V, and VI, pp. 99 + 56 + 102. 

 Section I, Explanation of the Tables ; Section II, Tables of the Arguments 

 and Mean Longitudes ; Section III, Tables of the True Longitude ; Section 



IV, Tables of the Latitude ; Section V, Tables of the Parallax ; Section 

 VI, Tables of the Planetary and other Perturbations and Auxiliary Tables.] 

 (New Haven : Yale University Press, 1919.) 



