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1907—8.] The Problem of a Spherical Gaseous Nebula. 
geneous, in equilibrium under the influence of mutual gravitation between 
its parts ; and let g be the gravitational attraction on a unit of mass at the 
position P. Let 
gpR=p ( 8 )- 
This means that H is the height to which homogeneous liquid, of uniform 
density p, ideally under the influence of uniform gravity equal to g, must 
stand in a vertical tube to give pressure at its foot equal to p. 
§ 8. The idea expressed by (8) is useful in connection with questions 
connected with internal pressure throughout a spherical liquid mass, 
such as the sun. It is also useful when we are considering pressure and 
temperature in gaseous fluids, such as our terrestrial atmosphere, or the 
outermost parts of the sun ; which may be regarded as practically gaseous 
where the density is anything less than T. 
§ 9. For a perfect gas, (8) divided by p, becomes 
yH = S* (9). 
By this we see, what is interesting to remark, that for the same temperature 
and same gaseous material, the “ height of the homogeneous atmosphere ” is 
the same for the air at the earth’s surface and for the air at any height 
above the surface; and is the same for different barometric pressures. For 
different temperatures, it varies as the absolute temperature. For different 
gases at the same temperature, it is proportional to their specific volumes. 
For different forces of gravity, it is inversely proportional to them. 
§ 10. Even for cosmical reckonings in respect to our present subject, 
and in many and varied terrestrial reckonings, it is convenient to take 
as unit of force the heaviness in mid-latitudes of the unit of mass. The 
unit of mass, for all nations and peoples of the earth, must for general 
convenience be founded on the existing French Metrical System. The unit 
may, according to the particular magnitude or character of substance 
of which the mass or quantity is to be specified, be conveniently taken 
as a milligram, or a gram, or a kilogram, or a metric ton (one thousand 
kilograms), or 10 9 tons. 
§11. The choice of unit force, as mean terrestrial heaviness of unit 
mass, is very convenient for ordinary earthly purposes, but language in 
which it is adopted is, unless properly guarded and tacitly understood, 
always liable to ambiguity as to whether force or quantity of matter is 
meant. Thus if (using for a moment the moribund British Engineering 
reckonings in pounds, inches, etc.) we speak of 73 pounds of lead, there is 
no doubt that we mean quantity of a particular kind of matter ; but if we 
