5^4 



NATURE 



\pct. 25, 1877 



and Plana, gave a coefficient for the moon's mean motion 

 agreeing with that found from observation by Halley. 



This satisfactory agreement between theory and observation 

 remained uncharged until 1853, when Adams announced ' that 

 he had found a deficiency in Laplace's calculation, arising from 

 the fact that Laplace had considered tlie radial disturbing force 

 only, and had neglected the tangential disturbing force. 



When the fuller computation is made, it is found that the 

 coefficient of Halley's expression is reduced from \o 2 to 6'll, 

 leaving 4 '09 not accounted for, 



Adams' calculations were verified by Delaunay, who found 

 them quite correct, and who had the merit of suggesting the 

 explanation of the 4^09, which form a residual phcnonution. 

 According to Delaunay, this uncompensated portion of Halley's 

 coefficient is to be explained by the retardation of the earth's 

 angular velocity, and consequent increase in the length of the 

 day, caused by the residual tidal current set'ing constantly from 



east to west. This residual current, although excessively small, 

 is a vera causa always acting, and must, in due course of time, 

 produce a sensible effect in lengthening the day. It is easy to 

 show that the effect of the lengthening of the day upon ancient 

 solar eclipses acts in the same direction as the acceleration of the 

 moon's mean motion, viz., it throws the place of observation to 

 the eastward (left) of the calculated place ; for the earth moves 

 from right to left, in the same direction as llie moon, and as its 

 rotation in that direction, from the period of the eclipse, has 

 been greater than that assumed in cur calculation from the present 

 rotation of the earth, it follows that, at the time of the eclipse, 

 all places on the earth's surface must have been absolutely, with 

 reference to a meridian fixed in space, to the westward (right) of 

 their present positions. According to this view, therefore, the 

 displacement eastwards of the places of observation of ancient 

 eclipses, when compared witli the calculated places of observa- 

 tion, is the sum of two displacements— one caused by not allow- 



A 



ing for the aeeeieiation cf I he moon, and the other caused by not 

 allowing for the rdarJation oj the earth. 



Thus, if B represent the true position of the eclipse in space, 

 its calculated place will be A, to the west of i), the interval A B 

 being due to the neglect of the acceleration of the moon's mean 

 motion (with coefficient — 6'ii) in the calculation; and the 

 point exactly below B, on the earth's surface, will have moved 

 on to c, to the east of c, in consequence of the neglect of the 

 retaidation of the earth's rotation in the calculation. 



Let us illustrate the case by one of the most famous solar 

 eclipses on record, that of Agathocles, on August 15, 310 B.C. 

 The accompanying outline map represents the course taken by 

 the expedition of Agathocles from SyracuSb to Carthage. - 

 IJThis eclipse is recorded by Diodorus Siculus, and has been 

 alwajs considered one of the most important in support of 

 Halley's coefficient, lo'2 seconds. 



It has recently, however, been called in question by a high 



authority ; for at the meeting of the American Association for 

 the Advancement of Science (1877), "Prof. Simon Newcomb 

 presented a communication on the secular acceleration of the 

 moon, and its increasing deviation from uniformity through many 

 years. He reviewed tlie existing theory on the subject ; the 

 calculation of Laplace according with Halley's estimate of the 

 acceleration as about 10^ seconds of time, to be multiplied by 

 the square of the centuries for a given period ; also the Adams 

 theory, which reduces the explanation of Laplace to 6 seconds, 

 leaving more than 4 seconds to be otherwise accounted for. In 

 ascribing the surplus acceleration to diminished rotation of the 

 earth, we are dealing with a subject where the evidence should 

 be carefully weighed . Much dependence seemed to be placed 



' Proceedings of the Rcyal Society, vol. vi. p. 321. 



2 The places passed in order by the e.\pediiion of Agathocles alctig the 

 Sicilian coast are described in the fine lines of Virgil : — 

 Sicanio prfetenta sinu jacet insula contra 

 Plemmyrium undosum : nomen dixere priores 



on the record of ancient eclipses. I'rof. Newcomb considered 

 these eclipses separately. 7'he nwst promising of the Greek solar 

 eclipses was that oJ Ai^athocles, tyrant of Syracuse, occurring at the 

 commtncement of his voyag-e to attach Carthage. But tve do not 

 kno-iti on which side of Sicily he sailed : according to whether he 

 was on one or the other side of the coast, the difference of time for 

 that eclipse may he calculated as justifying the 10 seconds or the 6 

 seconds acceleration of the moon. Tlie eclipse known as that of 

 Thales has a record still more open to criticism, because it came 

 to its historian by hearsay, and probably through two or three 

 generations after the lapse of a huncred years, ft seems cuiious 

 that if Tfcales predicted the year {by an estimate of lunar periods) 

 he did not also predict the day. Each of the ancient solar eclipses 

 yielded similar elements of doubt, on careful examination. From 

 the records of lunar eclipses, if all uncertain features be weeded 

 out, the old estimate of acceleration will be reduced one-hall. 

 The Arabian records of lunar eclipses were published at Leydeii 

 in the early part of this century. Tiie work is very 

 rare. Altitudes of sun and moon are constantly given 

 in it. Calculations from these eclipses give the 

 smaller estimate of acceleration. From all the data 

 he has been able to study. Prof. Newcomb con- 

 cludes that the whole amount of acceleration is 

 about S'4 seconds. He hopes to make further 

 estimates from modern records, having had the 

 good fortune to pick up in Paris carefully compiled 

 data of occultations going back to 1680." 



Let us compare this statement of Prof. Newcomb 

 with the original account of Diodorus Siculus. Aga- 

 thocles was blockaded in Syracuse by the Car ha- 

 ginian fleet, and the town was in danger of starvation ; 

 under these circumstances he formed and carried out 

 the daring project of breaking the blockade, and 

 undertaking an expedition by sea against Carthage 

 itself ; which he successfully accomplished. Diodorus 

 says : "But Agathocles, thus overtaken and sur- 

 rounded, hit upon an unexpected chance of escape 

 when night came on ; and on the following day 

 there came to pass so great an eclipse of the sun 

 that night appeared universally, the stars being 

 seen in every direction ; wherefore the people of 

 Agathocles, believing that the Divinity foreshadowed some 

 evil to happen them, were in still greater anxiety of mind 

 than before. When they had voyaged for six days and as 

 many nights, at the dawn of day the fleet of the Carthaginians 

 appeared unexpectedly, not far off. . . . But when Africa came 



, fama est hue Elidis amnem 

 ubter mare ; qui nunc 



nfunditur 1 



Ortygiam. Alphe 



Occultas egisse vi: 



Ore, Arethusa, tuo Siculi 



Jussi numina magna loci veneramur ; et inde 



Exsiipero prsepingue solum stagnantis Helori, 



Hinc altas cautes projectaque saya Pachyni 



Radimus, et fats nurquam conces*a moveri 



Adparet Camarina procul campique Geloi, 



Inmanisque Gela fluvii cngnomine dicta, 



Arduus inde Acragas ostcnt^it ma.xinia looge 



Moenia magnanimum quondam generator tquorum, 



Teque datis linquo veniis, palmosa Selinus ; 



Et vada dura lego saxis Lilybeia cxch, 



Hinc Drepani me portus et inla:tabilis era 



Adcipit. — JEn., Lib. ill., 692-708. 



