24 
POPULAR SCIENCE REVIEW. 
points respectiveh'. Of the absolute dimensions of the two 
orbits, it will be sufficient to say that the greatest and least 
distances of the earth from the sun are respectively 93,190,000 
and 90,110,000 miles, the greatest and least distances of Mars 
152,670,000 and 126,620,000 miles. 
Mars takes 686*979 days in completing one circuit around 
the sun ; thus it is easily calculated that the mean interval be- 
tween successive oppositions is 779*836 days. Owing, however, 
to the great eccentricity of Mars’ orbit, and the consequent 
considerable variation in the rate of his motion around the sun, 
the successive synodical revolutions of the two planets vary in 
length, being greater or less according as opposition occurs 
near perihelion or near aphelion respectively. The positions of 
the oppositions from 1856 to 1871, marked in fig. 1, will be 
sufficient to indicate this. The line of opposition travels round 
in the order of the signs. After travelling twice round the 
zodiac, the line falls very nearly in the position it had at 
starting, such double revolution occupying thirty- three years, in 
the course of which Mars has been fifteen times in opposition. 
It will be obvious, from a moment’s inspection of fig. 1, that 
the appearance presented by Mars, when in opposition near M,* 
must be very different to that presented when he is in opposition 
near M' : the distance of Mars in the former case being less 
than his distance in the latter case in the proportion of about 
19 to 37 ; or, in miles, the former distance is 34,140,000, the 
latter 61,860,000 miles. Hence arise variations in the magni- 
tude of the disc presented by the planet; and since Mars in 
perihelion is more brilliantly illuminated than when in aphelion, 
his apparent brightness is yet further increased. By the first 
cause his brightness is increased as the squares of the numbers 
37 and 19, and by the second as the squares of the numbers 41 
and 34 ; or, on the whole, his brightness, when in opposition in 
perihelion, is about five times as great as his brightness at oppo- 
sition in aphelion. So bright does he appear, when the first 
conditions are nearly approximated to, that his appearance has 
caused alarm to the uneducated. Theoretically, indeed, he 
ought to appear brighter at such times than Jupiter himself at 
his brightest, since the disc of Mars, smaller than that of 
Jupiter in the ratio of 24 to 49, is more brilliantly illuminated 
in the greater ratio of 472 to 126, so that Mars should appear 
brighter than Jupiter in the ratio of about 5 to 3. Jupiter, 
* Owing to the eccentricity of the earth’s orbit, and the circumstance that 
the perihelia of the two orbits have different positions, M is not absolutely 
the point of Mars’ orbit which lies nearest to the earth’s orbit. The point 
of nearest approach Recedes M by a small arc, which (were it worth while) 
it would he easy to calculate. 
