[ 2 49 ] 
to the forces by which it is comprefTed. But to this 
condition, a particular law of elafticity is requifite ; 
namely, that the force exerted between every two 
adjacent particles diminifh as the diftance between 
them is increafed; and, adopting this law, die com- 
preffive forces might be proved to be in the propor- 
tion affigned, that of the denlities and abfolute elafti- 
cities jointly, by the fame kind of reafoning as is 
ufed to demonftrate the 23d proportion of the fe- 
cond book of the Principja , which is only the molt 
fimple cafe of the more general theorem now pro- 
pofed. 
Hence it follows, that if any caufes a£l upon the 
atmofphere, to change the degree of its abfolute 
elafticity, provided they a£t in fuch manner, as to 
change it equally at all heights- fo that, though dif- 
ferent at different times, it fhall always, at any one 
time, be the fame at all different heights ; then, the 
denlities in all different parts of the cylindrical 
column, reding perpendicularly upon a given fmall 
part of the earth’s furface, will, at any one time, be 
as the compreffive forces upon each part refpeftivelv. 
But the denfities, in any one part of this column, 
at different times, when the abfolute eladicities are 
different, will not be as the compreffive forces upon 
that part, at fuch different times refpedtively. 
Hence the relation between the decrement of 
deniity, and the increment of height, reduced 
according to the conftrudtion of fedtion iecond, will, 
-at every time, be reprefented, by the decrement of 
the ordinates, and the increment of the afymptote of 
ffome logarithmic curve. But of different curves, 
at different times, or in different dates of the 
abfolute elaflicity ; that is, the length of the fub- 
Vol, LX 1 V. K k tangent 
