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once in the zenith of a place upon Jupiter ’s equator in thephase of full moon, would, it is true, he somewhat more thantwice the apparent area of our Moon , hut the intensity of thesunlight which they reflect being about wVth 0 f that which ourMoon receives, their united light would even then be equalonly to about ' x Vth of the average amount which the full moongives to the Earth .
We will next proceed to the discussion of a certain especiallyinteresting class of observations which may be made in con-nection with the Satellites of Jupiter. We refer to theirEclipses, their Occnltations, their Transits, and the Transits oftheir Shadows across the planet’s disc.
In connection with their Eclipses, the first thing to be realizedis, that Jupiter continually casts a huge conical shadow behindit while travelling in its orbit; and that the axis of this shadowalways points directly from the Sun, in the prolongation of thestraight line joining the Sun’s centre with that of Jupiter .We may very easily calculate, by the solution of a simplesum in proportion,* that this conical shadow will extend toabout 54,000,000 miles, before it narrows to a point. This dis-
* Let p and c in Fig. LXXV. be the centres of Jupiter and of the Sun:,tj / and ss' their semi-diameters ; then jj' is approximately equal to Athof ss'. If, therefore, the point of the shadow extend to o, the distancePO will be about T yh of co, or Jth of ci>. The mean value of CP, i.e., ofJupiter ’s distance from the Sun, being about 484,000,000 miles, it follows
that po, or the distance to which the shadow of Jupiter will extend behindit, is about Jth of this, or about 54,000,000 miles.
The above style of calculation is comparatively rough, but, as we haveoften shown in our lectures at Gresiiam College, it may be very usefullyand instructively applied in many similar cases, including some to whichwe shall refer a little farther on.