[ 27 ° ] 
C draw CF, parallel to AD, meeting the atmofphe- 
ricai curve in F. CF is the denfity of the atmo- 
fphere, at an infinite height (by p. 23 1). The pro- 
portion of CF to the denfity at the level of thefeais 
given in any uniform given temperature of the air. 
For the uniform temperature being given, thefubtan- 
gent of the curve DF is given; and confequently, 
the proportion is given, of which the given line 
CA is the logarithm. The diminution of com- 
preffive force is fubjed to a correfponding limit. 
This curious circumftance hath been remarked 
by no one, that I know of, but Dr. brooke 
taylor, whofe writings are too little attended 
to, even among mathematicians, from an opinion 
which prevails of their obfcurity. That confummate 
geometer feems indeed to have thought it im- 
probable, that a finite denfity of the atmofphere, at 
infinite diftances, though the neceflary confequence of 
the theory, fhould actually exiff ; and, for this reafon, 
he would imagine fuch a law of the elaftic force, as 
; fhould render the denfity of the atmofphere, beyond a 
certain height, much greater than in proportion to the 
comprefiive force; and circumfcribe the whole within 
narrow limits And if the theory inferred a great 
denfity at infinite or even at great heights, fuch a den- 
fity as would fenfibly difturb the motions of the pla- 
nets, it would be neceflary to have rccourfe to fome 
fuch hypothefis ; but, as this is not the cafe, I fee no 
fuch neceflity. I know not, for what reafon, mathe*» 
maticians have been afraid to admit the infinitude of 
the atmofphere of the earth ; whether they thought 
it would bear hard upon the Newtonian do&rine 
(w) Method. Increment, prop. a6. Scholium. 
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