C 105 ] 
and each fpace anfwering to an Incko? Quickftlver grows 
greater and greater, fb that the Atmoffhere inuft be extend- 
ed to a much greater hight. Now upon thele principles, 
to determine the hight ot the Mercury at any affigned hight 
in the Air^ and e contra having tlie hight of the Mercury giv- 
en, to find the hight of the place where the Barometer ftands, 
are Problems not more difficult than Curious ; and which 
I thus refolve. 
The expanfions of the Air being Reciprocally as the 
bights of the Mercury ^ it is evident^ that by the help of tiie 
Curve of the HyferhoU and its Afympotes the faid expanfions 
may be expounded to any given hight of the Mercpiry: For 
by the 6 ^jth prop, lib, 2« Come, Mydorgiij the Reftangles AS 
CE^ AKGE5 ALDE, &c. ( in fig. 5 ) aix alwais equal, 
and confequently the fides CB^ GK^LD, &c. are recipro- 
cally as the fides, AB/ AK, AL, &g. If then the lines AB, 
AK5 AL, be fuppofed equal to the bights of the Mercury^ or 
the preiTures of the Atmofphere^ the lines CB, KG, LD, 
anfwering thereto, will be as the Expanfions of the Air un- 
der thofe prefllires, or the bulks that the fame quantity of 
Air will occupy ; which Expanfions being taken infinitely 
many, and infinitely little, ( according to the method of 
Indivifibles ) their fumme will give the (paces of Air be- 
tween the feveral hights of the Barometer \ that is to fay the 
fumme of all the lines between CB and KG, or the AreA C 
BKG, will be proportioned to the diftance or fpace inter- 
cepted between the Levels of two places in the Air^ where 
the Mercury would ftand at the hights reprefented by the lines 
AB, AK ; fo then the fpaces of Air anfwering to equal parts 
of Mercury in the Barometer, are as the Areas CBKG, GKL 
D, DLFM, &c, Thefe Areas again are, by the Denion^ 
flrration of Gregory of St. Vincent\ proportionate to the Loga- 
rithms of the numbers expreifing the Kationesdi AKto AB, 
ofAL to AK, of AM to AL, 8^:c. So then by the common 
Table of Logarithms, the hight of any place in the Atmof- 
pherej having any affigned hight of the Mm^^ry^ maymoft 
