Notices respecting New Books, 333 



with the same accuracy as that of the other heavenly bodies. In 

 1870 the writer showed that this belief was entirely unfounded, 

 and that the correctness of the tables since 1750 had been secured 

 only by sacrificing the agreement with observations previous to that 

 epoch, so that about 1700 Hansen's tables deviated more widely 



from observations than did those which they superseded 



Altogether it appeared that, notwithstanding the immense improve- 

 ment that Hansen had made in the accuracy of the inequalities of 

 short period, the theory of those of long period was no nearer such 

 a solution as would agree with observation than when it was left 

 by Laplace." 



In consequence of Hansen's tables deviating so widely from ob- 

 servation in 1700, and generally at epochs previous to 1750, "the 

 latter date was fixed upon as the terminal point of the investiga- 

 tion, consisting of the study of the inequalities of long period, 

 partly because it is the epoch at which accurate meridian observa- 

 tions commence, and it is also that which separates the period 

 within which we have readily accessible observations and copious 

 tables of reduction founded on modern data from that during which 

 both these requirements are wanting." 



This investigation, as well as that of the mathematical theory of 

 the inequalities of long period in the moon's mean motion, were 

 made a part of the author's official duty at the Naval Observatory. 

 Difficulties arising in the investigation of inequalities of long period, 

 it was found necessary to leave this part incomplete until the best 

 method of treating the subject could be decided on. In the mean- 

 time the author, in the course of a journey in Europe, obtained 

 several valuable series of observations which he has employed in 

 obtaining his result. He remarks that the material most used has 

 hitherto been least known ; also that the most valuable portion of it 

 is possibly found in the unpublished Paris observations, whereby the 

 moon's mean longitude is determined with astronomical accuracy 

 from 1680 onward. 



The general scope of the work may be gathered from the table of 

 contents, as follows : — § 1. Historical Introduction. § 2. Sum- 

 mary of Data for determining the apparent Secular Acceleration. 

 § 3. Discussion of Narratives of ancient total Eclipses of the Sun. 

 § 4. The Ptolemaic Eclipses of the Moon recorded in the Almagest. 

 § 5. Arabian observations of Eclipses, from Caussin's translation of 

 Ebn Jounis. § 6. Mode of deducing the Errors of the Lunar Ele- 

 ments from observations of Eclipses and Occultations. § 7. Effect 

 of Changes in the Lunar Elements upon the path of the central line 

 of an Eclipse. § 8. Observations of Bullialdus and Gassendus. 

 § 9. Observations of Hevelius. § 10. Observations by Astrono- 

 mers of the Erench School between 1670 and 1750, from Manu- 

 scripts at the Paris and Pulkowa Observatories. § 11. Positions 

 of: the Moon from Hansen's Tables used in comparing the prece- 

 ding observations with theory. § 12. Details of Reduction of the 

 Occultations. § 13. Equations of Condition given by the preceding 



