30 REPORT — 1859. 



balance. But Laplace showed that they do not : he showed that the increased 

 amount of decrement (when the earth is nearest the sun) overbalances the diminished 

 amount (when the earth is furthest from the sun) ; and, therefore, that the less 

 excentric i6 the earth's orbit, the less does the increased amount of decrement at one 

 part overbalance the diminished amount, at another part, and the less is the total 

 amount of the sun's disturbing force. And, as the sun's disturbing force diminishes 

 the moon's attraction to the earth, that attraction is less and less impaired every 

 century, or becomes practically stronger ; every century the moon is pulled into a 

 rather smaller orbit, and revolves in a rather shorter period. On computing the 

 effect from this cause, it was found to agree well with the effect which Halley and 

 Dunthorne had discovered in observations. The lunar tables thus amended (and 

 with other, but minor improvements) were applied to the computation of other 

 ancient eclipses which require far greater nicety than Ptolemy's lunar eclipses, 

 namely, total eclipses of the sun. The most remarkable of these were the eclipse of 

 Thales (which occurred at a battle), that at Larissa or Nimrud (which led to the 

 capture of that city by the Persians from the Medes), and that of Agathocles (upon 

 a fleet at sea). They are all of great importance in settling the chronology. Dates 

 were thus found for these several eclipses, which are most satisfactory. About this 

 time Mr. Adams announced his discovery, that a part of the sun's disturbing force 

 had been omitted by Laplace. The sun pulls the moon in the direction in which 

 she is going (so as to accelerate her) in some parts of her orbit, and in the opposite 

 direction (so as to retard her) in other parts. Laplace and others supposed that 

 those accelerations and retardations exactly balance. Mr. Adams gave reason for 

 supposing that they do not balance. In this he was subsequently supported by M. 

 Delaunay, a very eminent French mathematician, who, making his calculations in a 

 different way, arrived at the very same figures. But he is opposed by Baron Plana, 

 by the Count de Pontecoulant, and by Prof. Hansen, who all maintain that Laplace's 

 investigations are sensibly correct. And in this state the controversy stands at 

 present*. It is to be remarked, that observations can here give no assistance. The 

 question is purely whether certain algebraical investigations are right or wrong. 

 And it shows that what is commonly called " mathematical evidence " is not so 

 certain as many persons imagine ; and that it ultimately depends on moral evidence. 

 The effect of Mr. Adams's alteration is to diminish Laplace's change of the periodic 

 time by more than one-third part. The computations of the ancient eclipses are 

 very sensibly affected by this. At present we can hardly say how much they are 

 affected : possibly those of Larissa and Agathocles would not be very much disturbed ; 

 but it seems possible that the computed eclipse of Thales might be thrown so near 

 to sunset as to be inapplicable to elucidation of the historic account. This is the 

 most perplexing eclipse, because it does not appear that any other eclipse can possibly 

 apply to the same history. The interest of this subject, it thus appears, is not con- 

 fined to technical astronomy, but extends to other matters of very wide range. And 

 the general question of the theory of the moon's acceleration may properly be indicated 

 as the most important of the subjects of scientific controversy at the present time. 



On the Mid-day Illumination of the Lunar Craters Geminus, Burckhardt, 

 and Bernoulli. By W. R. Birt, F.R.A.S. 



The object of the present communication is to lay before the British Association 

 for the Advancement of Science a few of the features that characterize the lunar sur- 

 face in the neighbourhood of the craters, Burckhardt, Bernoulli, and Geminus, or 

 more particularly on the area between the angular points -. Burckhardt, Bernoulli, 

 a small but bright crater on the southern margin of Messala (B), and a crater on an 

 elevated ridge (a*) under the mid-dny illumination. 



In the first report of the Committee appointed at Belfast to report on the physical 

 character of the moon's surface, the mid-day illumination is alluded to as "making 

 apparent the unequal reflective powers and different colours which characterize the 

 different lunar regions, and the systems of brilliant stripes which are connected with 

 certain lunar forms." 



* See also Mr. Main's elaborate statement in the Monthly Notices of the Eoyal Astrono- 

 mical Society. 



