Ro^jal Society. 217 



Laplace, Damoiseau, Plana, and Hansen ; the principal change made 

 by the latter writers from Laplace's values being in the motion of 

 perigee. 



The method of computation adopted by the author is then ex- 

 plained. He adopts the Greenwich mean motions and Damoiseau's 

 coefficients for progressive change of secular mean motion. He then 

 repeats the calculation with an arbitrary change of longitude of 

 node ; considering that, from the loose nature of the early Green- 

 wich observations, this element is most likely to be in error, and that 

 its errors will produce the greatest effect. 



The author then discusses the account of the eclipse of Agathocles, 

 B.C. 310, August 15. Adopting Alhowareah (under Cape Bon) as 

 his landing-place in Africa, he states his belief that Agathocles sailed 

 northward from Syracuse (a conjecture which he owes in the first 

 instance to J. W. Bosanquet, Esq.), and was not far from the Straits 

 of Messina. On the usual supposition of his sailing to the south, 

 he would be near Cape Passaro. 



On making the calculation with the Greenwich Elements unvaried, 

 it is found that the eclipse would be total on the southern possible 

 place of Agathocles, but not on the northern. The calculation being 

 repeated with an arbitrary change in the place of the node, a gra- 

 phical construction is employed to discover the numerical amount of 

 the changes that must be made to satisfy the four following condi- 

 tions: — 1, the northern edge of the shadow touches the south station ; 

 2, the northern edge touches the north station ; 3, the southern edge 

 touches the south station ; 4, the southern edge touches the north 

 station. If the south station be adopted, the change must lie be- 

 tween those of conditions 1 and 3 ; if the north, the change must 

 lie between those of 2 and 4. The numerical values must be slightly 

 increased for application to a more distant eclipse, as to that of 

 Thales. 



The eclipse of Thales is then considered. There appears to be no 

 reason for connecting, the locality (as Mr. Baily supposed) with the 

 river Halys. The historical circumstances indicate with great pro- 

 bability that two large armies had met ; and the question appears to 

 be, in what part of Asia Minor is it likely that such bodies of troops 

 would be collected. The author adverts to the form and passes of 

 the mountains, and decides that the Median army entered most pro- 

 bably by the pass of Issus, or possibly by that of Melitene, and that 

 the battle-field might be anywhere in the space bounded by Melitene, 

 Issus, Iconium, Sardes, and Ancyra. 



On calculating the eclipses which occurred for many years before 

 and after e.g. 600, it appears that only the eclipse of b.c. 585, May 

 28, answers to the requisite conditions, and that it does so in a most 

 satisfactory way. [This is the date adopted by the principal ancient 

 chronologists ; it would seem that it was first verified, by calculations 

 founded on good elements, by J. R. Hind, Esq. during the prepara- 

 tion of this paper.] The path of the shadow which is most agree- 

 able to the military and geographical circumstances, is one which 

 implies a correction to the Greenwich Elements corresponding to that 



Phil. Mag. S. 4. Vol. 5. No. 31. March 1853. Q 



