Mr. Ivory on the astronomical refractions. 413 
principles on which it must depend. Conceive a cylinder of 
air extending indefinitely in a vertical direction, and let it be 
divided into equal parts of <a moderate length, so that the 
density of every division may be considered as uniform : 
then, if we abstract from the diminution of gravity and the 
increase of the centrifugal force, which are inconsiderable 
within 200 or 300 miles of the earth’s surface, the weight of 
the air in every portion of the cylinder will be proportional 
to its density. Now, if we admit that the elastic force is 
likewise proportional to the density, as it would be in an 
atmosphere of uniform temperature, it will follow, that the 
weights of the several divisions of the cylinder will vary in 
the same proportion as their elasticities. But in the lowest 
part of the cylinder, the weight of the small quantity of air 
contained in one division, is incomparably less than its elastic 
force, which is an equipoise to the whole atmosphere : and 
the same thing will therefore be true of every portion of the 
cylinder, however high it is placed. Hence an atmosphere 
constituted as we have supposed, must necessarily be infinite 
in its extent. For if it were finite, since there is no pressure 
at the surface, the weight of a volume of air situated there 
would be in equilibrium with its elastic force, whereas it has 
been proved that the former is always an inconsiderable part 
of the latter. 
But in the foregoing reasoning, a cause is neglected which 
diminishes the elasticity of the air as we ascend above the 
earth’s surface, without affecting the force of gravity in any 
degree. In the higher parts of the atmosphere a continually 
increasing degree of cold is found to prevail. Now, the 
effect of cold is to contract all bodies in their dimensions ; 
