( 2240 ) 
' Aud any two of the three firftjX.b^and a,being given, the o» 
ther is known,and confeqaently the reft alfo. 
For^ if by the incumbent weight of 33 feet depth in water, 
the Air in the tube is compreft into half the Ipace it fill'd be- 
fore then the faid 3 3 feet depth of Water equals the weight or 
preffurc of the incumbent Air on the furface of the Water* 
Now, as the weight or preffureof the Air on the furface of 
the Water, is to the Depth of the Water from the furface 
thereof to the bottom of the Air within the Tube ; fo is the 
Length of the Tube fill'd with Air, to the length thereof filFd 
with Water : That is^ according to the faid Experiments, put- 
ting z for 55, or whatever, at other times or places , (hall be 
found to be the weight or preflTure of the incumbent Air on the 
furface of the Water, (for it is not always the fame exa(iHy ; ) 
z. a : : a f b* a * + ab = CD. 
z 
And therefore a^+ab + za+zb 
— ^ = = 
Wherefore 2_x-a=b. 
z+ a 
And 7:b*t2zb4:z* + 4zx: + b— z . 
. 
And therefore a and b being given,x is known to be the firfl 
equation ; And a and x being given^J is known by the fecond ; 
And b and x being giveq^^ is known by the third. 
The Horizontaf Hne BFBAF is fiibftituted for GABEFb, 
when the Clofe end of the Tube is not even with the furface of 
the Water, to avoid the breach cC = bB = ^^b*in the length 
of the Tube. 
JSIote, 
That the Perpendicular immerfion of the Tube or Cylinder, 
fpoken of in the faid TranfaBions'^.y:^^ is not to beunderflood 
of the Depth of the bottom or open end in the water , but of 
the Depth of the Air within the Tube or Cylinder from the 
furfaceof the water;, r/;^. FC5 notFD^ 
