THEORETICAL ASTRONOMY. 107 
bodies is called inertia. It is, moreover, evident, by reference to what 
is said, sec. 46, of the parallelogram of forces, that if the paths of the 
planets, and consequently of the earth, also be ellipses about the sun, two 
forces must combine to their production. The one is the attractive force 
of the sun, varying with the distances; the other a continuous tangential 
force, originating in an impulse. PZ. 10, fig. 2, will show how an elliptical 
orbit for each planet is produced by the co-operation of these two forces. 
We have to remark, finally, that gravitation communicates to all freely 
falling bodies a tendency towards the centre of the earth. 
We will now direct our attention to the orbit of the earth, with the help 
of the figure in pl. 8, representing its motions. By measuring the distances 
of the earth from the sun, at different times of the year, the shape of its 
orbit has been ascertained. These distances, as they were unequal, could 
not, of course, be semi-diameters of a circle, but they corresponded, taken 
together, to the radii vectores of an ellipse ( p/. 10, fig. 2). The mean dis- 
tance of the earth from the sun, is about 95,103,000 (statute) miles; it 
moves in its orbit at the average rate of 165 (Ing. geog.) miles in a 
second; the eccentricity of its orbit amounts to 0,016,784; the least or 
perihelion distance from the sun, to 81,276,000 (Eng. geog.) miles, or 
33,917,997 hours; while the greatest or aphelion distance is 84,052,000 
(King. geog.) miles, or 35,085,379 hours. The straight line connecting the 
perihelion and aphelion, passing through the centre of the sun, is called the 
line of apsides. The inclination of the earth’s orbit to its equator, or the 
so-called obliquity of the ecliptic, amounts to 23° 27’. The velocity of the 
earth is greatest at the perihelion and least at the aphelion. It is further to 
be observed, that the mean distance of the earth from the sun is equal to 
half the major axis of the earth’s orbit, and the line of apsides is itself the 
major axis. There are four noteworthy points in the earth’s orbit; they 
are those which mark the beginning of the four seasons. Two of these 
points are called the solstices—they mark the beginning of winter and sum- 
mer. The straight line ( p/. 8) uniting them, passing through the centre of 
the sun, is called the solstitial colure. ‘The twe other points are the equt- 
noxes, vernal and autumnal, marking the commencement of spring and 
autumn. ‘The straight line connecting these points, passing through the 
centre of the sun, is the eguinoctial colure. It still remains to observe, that 
the axis of the earth being always parallel to the axis of the heavens, may 
also be conceived to coincide with it; for, in consequence of the great dis- 
tance of the fixed stars from our sun, the diameter of the earth’s orbit (of 
more than 190,000,000 [statute] miles), as well as the whole orbit itself, 
would be seen as a mere point at the stars. 
The representation on pl. 8, shows the position of the earth on the first 
day of each of the twelve months of the year, the solar distances corres- 
ponding to these twelve positions, and the shape of the earth’s orbit. The 
horizontal projection has been chosen, in order to represent to the eye the 
increase and diminution of days, and the variation of illumination about the 
pole of the earth. The deeper circle surrounding the pole at a short dis- 
tance, is intended to represent the parallel of latitude of Paris, or the hour 
107 
