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as the dots show, about the beginning of May 1881, and thenext early in December 1882.
Fig . XXVIII. in like manner shows the apparent path ofMars , in 1877, 1878, and 1879; the average interval betweenits nearest approaches to the Earth , or (very nearly) betweenits being twice seen in succession in opposition to the Sun,being about 780 days.
We may remark in passing that the interval between twonear approaches of Jupiter, or Saturn, to the Earth , differs butlittle from a year, as may be seen by a reference to Fig . XXV..,
Earth
Fig. XXVI I.—Apparent path of Venus, as seen f from the Earth , frcm February 1681 to
February 1883.
it being for the former 399, and for the latter 378 days; whilefor Uranus or Neptune the excess over 305 days is still less.
Now it cannot be denied that these apparent paths areso complicated in their forms and periods of description, thatthe ancient astronomers and geometricians may have oftenbeen almost tempted to give them up in despair as inexplic-able. And yet there is one additional peculiarity which theymust have especially felt they were bound to explain ;—onewhich is involved in all the above diagrams, although forsimplicity’s sake we have only distinctly indicated it in