Part 20 (2/2)

And so on, indefinitely

Nohat is a cube? It is no more difficult It is a number multiplied twice by itself

For instance: 2 ain by 2 equals 8 So 8 is the cube of 2 3 3 3 = 27; 27 is the cube of 3, and so on

Now let us take an example that will show the simplicity and precision of the formula enunciated above Let us choose a planet, no iant of the worlds He is the Lord of our planetary group This colossal star is five times (precisely, 52) as far from us as the Sun

Multiply this number twice by itself 52 52 52 = 140

On the other hand, the revolution of Jupiter takes almost twelve years (1185) This number multiplied by itself also equals 140 The square of the number 1185 is equal to the cube of the nuulates all the heavenly bodies

Thus, to find the distance of a planet, it is sufficient to observe the tiiven nu it into itself The result of the operation gives simultaneously the cube of the number that represents the distance

To express this distance in kilometers (or miles), it is sufficient to multiply it by 149,000,000 (in miles 93,000,000), the key to the syste, then, could be less complicated than the definition of these methods A few moments of attention reveal to us in their majestic simplicity the immutable laws that preside over the immense harmony of the Heavens

But we must not confine ourselves to our own solar province We have yet to speak of the stars that reign in infinite space far beyond our radiant Sun

Strange and audacious as it hts, to rise on the wings of genius to these distant suns, and to plumb the depths of the abyss that separates us frodoulation And the distance that separates us fro the distances of the stars

The Earth, spinning round the Sun at a distance of 149,000,000 kilometers (93,000,000 miles), describes a circumference, or rather an ellipse, of 936,000,000 kilometers (580,320,000 miles), which it travels over in a year The distance of any point of the terrestrial orbit from the diametrically opposite point which it passes six months later is 298,000,000 kilometers (184,760,000 miles), _ie_, the diameter of thisobt This immense distance (in comparison with those hich we are fale of which the apex is a star

The difficulty in exactthe little luminous point persistently for a whole year, to see if this star is stationary, or if it describes ain perspective the annual revolution of the Earth

If it remains fixed, it is lost in such depths of space that it is ie the distance, and our 298,000,000 kilo in view of such an abyss If, on the contrary, it is displaced, it will in the year describe a minute ellipse, which is only the reflection, the perspective in miniature, of the revolution of our planet round the Sun

The annual parallax of a star is the angle under which one would see the radius, or half-diameter, of the terrestrial orbit from it This radius of 149,000,000 kilometers (93,000,000 miles) is indeed, as previously observed, the unit, the le is of course smaller in proportion as the star is more distant, and the apparent motion of the star diminishes in the same proportion But the stars are all so distant that their annual displacement of perspective is almost imperceptible, and very exact instruments are required for its detection

[Illustration: FIG 84--Small apparent ellipses described by the stars as a result of the annual displacement of the Earth]

The researches of the astronomers have proved that there is not one star for which the parallax is equal to that of another The le, and the extraordinary difficulties experienced inthe distance of the stars, will be appreciated from the fact that the value of a second is so s with it could be covered by a spider's thread

A second of arc corresponds to the size of an object at a distance of 206,265 times its diameter; to a millimeter seen at 206 meters'

distance; to a hair, 1/10 of a millimeter in thickness, at 20 meters'

distance (more invisible to the naked eye) And yet this value is in excess of those actually obtained In fact:--the apparent displacement of the nearest star is calculated at 75/100 of a second (075”), _ie_, from this star, [alpha] of Centaur, the half-diameter of the terrestrial orbit is reduced to this infinitesiht line seen from the front be reduced until it appear to subtend no le of 075”, it th As the radius of the terrestrial orbit is 149,000,000 kilometers (93,000,000 miles), the distance which separates [alpha] of Centaur from our world must therefore = 41,000,000,000,000 kilometers (25,000,000,000,000 miles) And that is the nearest star We saw in Chapter II that it shi+nes in the southern hemisphere The next, and one that can be seen in our latitudes, is 61 of Cygnus, which floats in the Heavens 68,000,000,000,000 kilometers (42,000,000,000,000 nitude, was the first of which the distance was determined (by Bessel, 1837-1840)

All the rest are much more remote, and the procession is extended to infinity

We can not conceive directly of such distances, and in order to iain measure space by time