MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
51 
homogeneous, the whole mass of matter would form a spherical nebula of literally 
infinite extent, and would therefore be in neutral equilibrium. The introduction of 
even the smallest irregularities into this structure is equivalent to the application oi 
an external field of force. This, as has already been seen, will destroy the spherical 
symmetry, and it can easily be seen that the motion from spherical symmetry is such 
as to lead to a concentration of matter about points of maximum density. 
It appears, therefore, that the configuration which will naturally he assumed by an 
infinite mass of matter in the gaseous or meteoritic state consists of a number of 
nebulae (i.e ., clusters round points of maximum density). We may either suppose 
the outer regions of these nebulae to overlap, each nebula satisfying the gas-equations 
by being of infinite extent, or we may suppose the nebulae to be distinct and of finite 
size, the interstices being filled by meteorites or other matter, which by continual 
bombardment upon the surfaces of the nebulae supply the pressure which is required 
at these surfaces by the equations of equilibrium. 
§ 48. What, we may inquire, will determine the linear scale upon which these 
nebulae are formed ? Three quantities only can be concerned : y the gravitational 
constant, p the mean density, and XT the mean elasticity. Now these quantities 
can combine in only one way so as to form a length, namely, through the expression 
XT 
VP 
> 
of which the dimensions will be readily verified to be unity in length, and zero in 
mass and time. We conclude, then, that the distance between adjacent nebulae will 
be comparable with the above expression. 
Now the value of y is 65 X 10 -9 , and if we assume the primitive temperature 
to be comparable with 1000° (absolute) we may take XT = 10 9 (corresponding 
accurately to an absolute temperature of 350° for air, 2800° for hydrogen). If we 
take the sun’s diameter as a temporary unit of length, the earth’s orbit is (roughly) 
of diameter 200. If we suppose the fixed stars to be at an average parallactic 
distance of 0'5" apart, measured with respect to the earth’s orbit, we find for their 
mean distance apart, about 4 X 10 7 sun’s radii. The density of the sun being, 
in C.G.S. units, roughly equal to unity, we may, to the best of our knowledge, 
suppose the mean density of the primitive distribution of matter to be about 
(4 X 10 7 )~ 3 , or say 10~ 23 . Substituting these values for y, XT and p, we find as the 
scale of length a quantity of the order ot 10 19 ’ 5 centims. The distance which 
corresponds to a parallax of CB5" would be about I0 18 ' 6 centims. It will therefore be 
seen that we are dealing with distances which are of the astronomical order of 
magnitude. 
