303

HISTORY OF PHYSICAL ASTRONOMY.

the question relates to some particular place. Halley, in a paper on thetotal eclipse of the sun which happened at London on the 3rd of May,1715, has remarked that there had not previously occurred a total eclipseof the same body, which was visible in that city, since the 30th of March,1140 a.d. In connexion with this circumstance it is to be borne inmind that the cycle of 323 lunations has respect to the centre of theearth, and not to any point on its surface. Now, in virtue of the diurnalmotion, the position of any point on the earth’s surface relative to the sunand moon, is generally different from the position of the centre of theearth relative to the same bodies. Moreover, since the earth is a body ofconsiderable magnitude, while on the other hand the region obscured bythe moon’s shadow, generally does not exceed 180 miles in diameter, itfollows that only a comparatively narrow zone of the earth’s surface canbe eclipsed during any particular conjunction of the sun and moon. It isclear, therefore, that a total eclipse of the sun may recur regularly at theprescribed time within the cycle, and yet may not be visible at the sameplace of the earth’s surface.

Although a solar eclipse may last several hours, counting from thecommencement to the end of the obscuration, the interval of time duringwhich the sun is completely hidden behind the dark body of the moon isvery limited. The duration is greatest when the moon is in perigee andthe sun in apogee ; for the apparent diameter of the moon being then thegreatest possible, while that of the sun is the least possible, the excess ofthe former over the latter, upon which the totality of the eclipse depends,has then attained its maximum. Now the perigean diameter of the moonis equal to 33' 31", and the apogean diameter of the sun is equal to31' 30". The difference, 2' l", is the arc which the moon in this casedescribes during the totality of the eclipse. It is manifest, therefore,when the rapidity of the moon’s motion, especially in perigee, is takeninto account, that even under the most favourable circumstances the sunwill not continue totalty eclipsed for more than a few minutes.

The duration of a total eclipse of the sun varies, when all other cir-cumstances are the same, with the latitude of the place obscured, beinggreatest at any place under the equator. Du Sejour found from theorythat the utmost possible duration of a total eclipse of the sun is 7 m 58 sunder the equator, and 6 m 10 s in the latitude of Paris *.

The duration of an annular eclipse is greatest when the moon is inapogee, and the sun is in perigee, for the apparent diameter of the sun isthen the greatest, while that of the moon is the least possible, and con-sequently the excess of the former over the latter, upon which the annularappearance depends, is then a maximum. The greatest apparent diameterof the sun is 32' 35", and the least apparent diameter of the moon is29' 22". Hence the difference, 3' 13", is the arc described by the moonwhile the eclipse continues annular. The maximum duration of auannular eclipse exceeds that of a total eclipse for two reasons : first, becausethe excess of the perigean diameter of the sun over the apogean diameterof the moon (S' 13") is greater than the excess of the perigean diameterof the moon over the apogean diameter of the sun (2' 1"); secondly,because when the moon is in apogee her motion over the sun’s disk ismuch slower than when she is in perigee. Du Sejour found by actual

* M6m. Acad, des Sciences, 1777, p. 318.