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THE PLANET VENUS.

But if the surface observed is sufficiently distant to have novisible area (as in the case of Venus when viewed by the nakedeye), so that the brightness of the object is estimated simplyby the whole amount of light received from it, then its apparentbrightness will be the greater the nearer it is to the observer.

In regard, therefore, to naked-eye observations of Venus , itslight and its apparent brilliancy would be greatest when theplanet is at its nearest approach to the Earth ; and least, whenit is at its farthest departure from it; were it not that its phase(or the ratio which the illuminated portion bears to the wholearea of the disc which is turned towards us) changes from timeto time.

Before, however, we begin to take this change of phaseinto consideration, we must remember that each degree ofphase corresponds to a certain distance from the Earth .We must therefore, in the first place, calculate what amountof light we should receive from the planet, not only at itsgreatest or least distances from the Earth , but at any inter-mediate distance, supposing that its whole disc remained illu-minated; and then, in the second place, estimate how muchthe corresponding phase still further alters the amount of lightwhich reaches us.

Now apart from any change of phase, the total amount oflight which we receive must vary, according to a certain well-known law of optics, inversely as the square of the distance of theplanet from us. But the apparent area of its disc, as seen bymeans of a telescope, varies according to exactly the same law.*We may therefore take the apparent size of the telescopic disc ofVenus at any given time to represent the total amount of lightthat an observer watching it, without the aid of a telescope, wouldreceive from it; so that the whole areas of the first and fifthcircles in Fig . XLVI.,which are drawn to represent the compara-tive sizes of the disc, seen with the same telescopic power, when

* For instance, if Yenus were to recede, at any given date, to twice thedistance from the Earth at which it was at a previous date, the apparentarea of its disc, seen by a telescope, would be reduced to one-fourth of itsprevious size, inasmuch as that area varies as the square of the apparent■diameter, which would he reduced by one-half.