t he had been mistaken, and
that what he thought was the effect of parallax was due to some other
cause, perhaps the imperfections of his instrument, perhaps the effect
of heat and cold upon it or upon the atmosphere through which he was
obliged to observe the star, or upon the going of his clock. Thus
things went on until 1837, when Bessel announced that measures with a
heliometer--the most refined instrument that has ever been used in
measurement--showed that a certain star in the constellation Cygnus had
a parallax of one-third of a second. It may be interesting to give an
idea of this quantity. Suppose one's self in a house on top of a
mountain looking out of a window one foot square, at a house on another
mountain one hundred miles away. One is allowed to look at that distant
house through one edge of the pane of glass and then through the
opposite edge; and he has to determine the change in the direction of
the distant house produced by this change of one foot in his own
position. From this he is to estimate how far off the other mountain
is. To do this, one would have to measure just about the amount of
parallax that Bessel found in his star. And yet this star is among the
few nearest to our system. The nearest star of all, Alpha Centauri,
visible only in latitudes south of our middle ones, is perhaps half as
far as Bessel's star, while Sirius and one or two others are nearly at
the same distance. About 100 stars, all told, have had their parallax
measured with a greater or less degree of probability. The work is
going on from year to year, each successive astronomer who takes it up
being able, as a general rule, to avail himself of better instruments
or to use a better method. But, after all, the distances of even some
of the 100 stars carefully measured must still remain quite doubtful.

Let us now return to the idea of dividing the space in which the
universe is situated into concentric spheres drawn at various distances
around our system as a centre. Here we shall take as our standard a
distance 400,000 times that of the sun from the earth. Regarding this
as a unit, we imagine ourselves to measure out in any direction a
distance twice as great as this--then another equal distance, making
one three times as great, and so indefinitely. We then have successive
spheres of which we take the nearer one as the unit. The total space
filled by the second sphere will be 8 times the unit; that of the third
space 27 time