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POPULAR SCIENCE REVIEW. 
16*9916) times the daily motion of Mars, 1886"*518, to find by 
how many days on the average the date of the later opposition 
precedes the date of the earlier. We find the average difference 
of date to be about 18^ days. But owing to the considerable 
eccentricity of the orbit of Mars and the consequent variation 
of his daily motion, the difference of date largely exceeds this 
value for oppositions occurring near perihelion, and largely falls 
short of it for oppositions occurring near aphelion. For instance, 
the opposition of 1862 occurred on or about October 5, while 
that of the present year — fifteen years later — occurs on Sep- 
tember 5, thirty days earlier. On the other hand, the opposi- 
tion of 1869 took place on February 13, while that of 1884 will 
occur on or about January 31, about thirteen days earlier. 
In a similar way the closer approach brought about in 
thirty-two years, and the still closer approach brought about in 
forty-seven years, can be dealt with. 
The approach brought about in seventy-nine sidereal years 
is so much nearer that it merits closer attention. We have the 
general relation that seventy-nine sidereal years exceed forty- 
two sidereal periods of Mars by 2*1082 days (or 2*1 days, 
nearly enough for our purpose). And we have for the average 
case, of course, the same daily motions as before ; whence the 
average number of days by which an opposition in any given 
year falls later than one occurring seventy-nine years before is 
equal to 1886"*518 x 2*1 divided by 1661*675 or about 2*4 
days. But when Mars is near perihelion his daily rate of motion 
is about 2286", while the earth in the corresponding part of her 
orbit has a daily rate of about 3470" ; consequently, the daily 
gain of the earth is about 1184" only, with which gain a differ- 
ence of 2*1 times 2286" has to be made up. Hence we have 
for the interval in days between two oppositions occurring near 
perihelion and separated by seventy-nine years 2*1 times 2286 
divided by 1184 or 4*14 days. On the other hand, when Mars 
is near aphelion his daily rate of motion is about 1576", while 
the earth in the corresponding part of her orbit has a daily rate- 
of about 3636", so that the earth’s daily gain is 2060", with 
which gain a difference of 2*1 times 1576" has to be made up. 
Hence we have for the interval in days between two oppositions 
occurring near aphelion and separated by seventy-nine years, 
2*1 times 1576 divided by 2060 or 1*66 days. (The date of 
the later opposition follows the date of the earlier.) 
The approaching opposition is important in two chief respects. 
First, it affords a favourable opportunity for determining the 
sun’s distance : and secondly, it will be possible to study under 
very favourable conditions the southern hemisphere of Mars. 
On the first point it is not necessary to say much here. I 
have already entered somewhat fully into the merits of this par- 
