91
not far short of the length of the Earth ’s radius; sucha passage through the zenith of a place of observation beingpossible (owing to the inclination of the Moon ’s orbit to theecliptic) in localities situated within about 28£ degrees oflatitude on either side of the Earth ’s equator.
Let c in the above figure—in which, for the sake of simplicity,we may suppose the place of observation to be upon the equatorof the Earth , so that the diagram may be all in one plane—bethe centre of the Earth . Let h and z be the positions of theMoon on rising and when seen in the zenith ; p the observer’sposition. Then cz equals ch, and ph does not fall muchshort of the same value. Consequently pz is less than ph bya distance which is nearly equal to cp, the radius of the Earth .If the Moon were as near to p when in the horizon as when inthe zenith, it would be at h instead of at h, p h being takenequal to pz. The diagram is drawn upon an exaggeratedscale, the real value of cp (and approximately of h Ji) beingabout 4,000 miles, which is about Arth part of cz (or ph), themean length of which is nearly 239,000 miles.
Under such circumstances the Moon will have an apparentdiameter, when in the zenith, which will be about ^th partwider than when it is in the horizon. And if at such a timea total solar eclipse occur, the totality will be prolonged, sincethe great distance of the Sun precludes any corresponding■effect upon its apparent size.
The greatest excess of the Moon ’s apparent diameter when■seen in the horizon over the Sun ’s is about yjth part of either.In that case totality would last while that excess was travellingbetween the observer and the Sun . By suitable calculationsit is found that it might continue for rather more than sixminutes. But if the Moon be overhead, and its apparentdiameter be increased by Aith part, its excess over the Sun ’sdiameter is made about -j-th greater than before (Ajth being■one-fourth of yLth), and the totality may consequently last ]-thlonger than before, and approach a duration of eight minutesinstead of being limited to six.
In such a phenomenon so considerable a prolongation maybe of the utmost importance. And it is worthy of special