on the local arrangement of the celestial bodies in space. 305 
does not require that the stars should be at equal distances 
from each other ; nor is it necessary that all those of the 
same nominal magnitude should be equally distant from us. 
It consists in allotting a certain equal portion of space to every 
star, in consequence of which we may calculate how many 
stars any given extent of space should contain. This defini- 
tion of equal scattering agrees so far with observation, that 
it admits, for instance, Sirius, Arcturus, and Aldebaran to be 
put into the same class, notwithstanding their very different 
lustre will not allow us to suppose them to be at equal dis- 
tances from us ; but its chief advantage will be, that instead 
of the order of magnitudes into which our catalogues have 
arranged the stars, it will give us an order of distances, which 
may be used for ascertaining the local distribution of the 
heavenly bodies in space. 
To explain this arrangement, let a circle be drawn with 
any given radius about the point S fig. t, Plate XV. and 
with 3, 5, 7, 9, &c. times the same radius draw circles, or 
circular arcs, about the same centre. Then if a portion of 
space equal to the solid contents of a sphere, represented by 
the circle S, be allotted to each star, the circles, or circular arcs 
drawn about it will denote spheres containing the stars of 
their own order, and of all the orders belonging to the in- 
cluded spheres, and on the supposition of an equality of scat- 
tering, the number of stars of any given order may be had 
by inspection of the figure, which contains all the numbers 
that are required for the purpose ; for those in front of the 
diagram express the diameters of spherical figures. The first 
row of numbers enclosed between the successive arcs, are the 
cubes of the diameters ; the next column expresses the order 
Rrs 
