i68 



NATURE 



[Dec. 26, 1878 



eclipses he admits in this category are eight in number, 

 from that of Thales, B.C. 585, to the eclipse of |ajx_364, 

 described as total at Eoos. Looking for" mention of dis- 

 tinct indications of totality, he has not included such an 

 ecUpse as that of B.C. 763, the record of which"was dis- 

 covered by Sir Henry Rawlinson on one of the Nineveh 

 Tablets in the British Museum, where importance appears 

 to be attached to it by the description being underlined?; 

 hence its presumed totality. The eclipses of the moon 

 recorded by Ptolemy in the Almagest are thoroughly 

 examined, with satisfactory results, except in the case of 

 the echpse of B.C. 383, December 22, where there appears 

 to be a mistake as to its having been really observed at 

 Babylon; and he concludes that during the eight cen- 

 turies preceding the Christian era the mean longitude of 

 the moon in Hansen's Tables requires a correction of 

 about 18'. The Arabian eclipses, solar and lunar, twenty- 

 five in number, between A.D. 829 and 1004 are then com- 

 pared with the Tables. 



In the next two sections Prof. Newcomb supplies a full 

 description of the method adopted for deducing the errors 

 of the lunar elements from the eclipses and occultations, 

 and for determining the effect of changes in the elements 

 upon the path of the central line of an eclipse, adopting, 

 in the latter case, formulas originally given by Bessel. 



In a following portion of the volume, occupying about 

 a hundred pages, are given, mostly as originally recorded, 

 the observations of occultations and ecHpses by Bullialdus 

 and Gassendus, Hevelius, and, as the author terms them, 

 the astronomers of the French School, between 1670 and 

 1750, preserved in the archives at the observatories of 

 Paris and Pulkowa ; it is needless to say that this section 

 possesses a great value, supplying as it does the par- 

 ticulars of so many observations hitherto unpublished. 

 We have then the positions of the moon from Hansen's 

 Tables, used in the comparison of the preceding observa- 

 tions with theoiy, in the calculation of which, and for the 

 numerical work generally. Prof. Newcomb was assisted 

 by a grant from Congress, sufficient to enable him to 

 employ two computers. Certain modifications of the 

 strict form of application of the Tables were considered 

 allowable for the older observations, their degree of 

 accuracy rendering an exact computation of Hansen s 

 Fundamental Argument of no advantage, and he con- 

 siders such modified plan of employing Hansen's Tables, 

 preferable to the use of the older Tables, which might be 

 adopted for the sake of saving labour. A " Tabular 

 exhibit of Reduction of the Occultations," 286 counting 

 immersions and emersions separately, is then given. 

 The equations of condition for the occultations, and a 

 provisional solution follow. 



In the next section the author presents an elaborate 

 discussion of eclipses from 1620 to 1715, which it may be 

 remembered is the last total ecUpse that was methodically 

 observed in this country. In this series is included the 

 eclipse of 1639, ]^^^ i> observed by Gascoigne and 

 Horrox amongst others, and 1706, May 11, which was 

 total in the south of France, but of which Prof. Newcomb 

 takes no other observations into account than those of 

 La Hire, of Paris : the fact, indeed, is that the observa- 

 tions along the belt of totality appear to be strangely and 

 unaccountably discordant, so far at least as regards the 

 beginning and ending of the total phase. The eclipse of 



1715 is very fully discussed, and remarking that by 

 Halley's organisation of a numerous body of observers 

 throughout the path of the moon's shadow across 

 England, valuable observations for determining its limits 

 were procured, the author deduces from them a correc- 

 tion to the motion of the moon' s node, which he finds to 

 be 10" X 7" ( 7" being counted in centuries from 1850), the 

 argument of latitude being diminished by this amount; 

 this result he considers nearly certain with respect to its 

 algebraical sign, but observes that it must be affected by 

 any corrections of Hansen' s value of the moon's parallax. 

 We now reach the main conclusions to which Prof. 

 Newcomb is led, by the laborious and masterly discussion 

 of observations prior to 1750, of which necessarily little 

 beyond an outline has been given here. The theoretical 

 value of the secular acceleration of the moon's mean 

 motion due to the cause discovered by Laplace, has been 

 fixed with accuracy by Prof. Adams and Delaunay : the 

 latter geometer, carrying his approximation to a greater 

 number of terms than had been included by Prof. Adams, 

 assigned 6""i8. 2"-. But this value, as is well known, 

 has not been found to accord with the older observations, 

 and the difference between the theoretical value and that 

 which observation seemed to require, has been generally 

 attributed to a retardation of the earth' s axial rotation ; 

 thus, as Prof, Newcomb remarks, *' the apparent secular 

 acceleration will be made up of two parts — the one a real 

 acceleration, the other an apparent one, due to the 

 change in our measure of time. But further, he says it 

 will be found that the hypothesis of a constant tidal 

 retardation does not account for the observed mean 

 motion of the moon, and either the retardation must be 

 supposed variable, even to becoming at times an accelera- 

 tion, or it must be admitted that her mean motion is 

 affected by changes not hitherto explained. He then 

 proceeds to inquire what deviations of the moon' s mean 

 motion remain unaccounted for, and with this object he 

 first collects into tabular form the individual corrections 

 to Hansen's mean longitudes, derived from the discussion 

 of eclipses and occultations from 162 1 to 1728, with their 

 probable errors, the latter being necessarily somewhat 

 arbitrary, for want of data for their rigorous computation. 

 The older results do not exhibit larger discordances than 

 might be expected. In order to complete the investiga- 

 tion of anomalies in the moon's mean motion unex- 

 plained, it was necessary to have the errors of Hansen's 

 Tables from 1750 to the present epoch, or to 1875, and 

 these were partly obtained from Hansen's paper in the 

 MontJily Notices of the Royal Astronomical Society, and, 

 since 1850, from Part III. of the publications of the 

 American Transit of Venus Commission, where it was 

 shown by Prof. Newcomb that at the epoch i875'o the 

 meridian observations at Greenwich and Washington 

 agreed in indicating a correction to the tabular mean 

 longitude of -9"7. The occultations about the same 

 time giving a correction nearly two seconds less, it is 

 assumed that the true correction at this epoch was -8". 

 Hansen introduced in his tables a term depending on 

 the argument, 8 times the mean motion of Venus winiis 

 13 times the mean motion of the earth, which has not 

 been theoretically explained, and is to be regarded as 

 empirical. This term is therefore removed from the 

 theory, before examining, as Prof. Newcomb proceeds to 



