C 418 ] 
this valve, in the conttruction made ufe of in this 
pump ; and as the bladder is fattened in four places 
inftead of two, I have made the breadth of the hexa- 
gons three tenths of an inch ; fo that the furface of 
each of them is more than nine times greater than 
common. But as the circumference of each hole is 
more than three times greater than common, and as 
the force, that holds down the valve, arifing from 
cohetton, is, in the firtt moment of the air’s exerting 
its force, proportionable to the circumference of the 
hole; the valve over any of thefe holes will be 
raifed with three times more eafe than common. 
But as the railing of the valve over the center-hole 
is aflifted on all fides by thole placed round it; 
and as they all together contribute as much to raife 
the bladder over the center-hole, as the air imme- 
diately adting under it ; upon this account the valve 
will be raifed with double the eafe, that we have be- 
fore fuppofed, or with a fixth part of the force com- 
monly necettary. 
It is not material to confider the force of the co~ 
hetton, after the firtt inttant: For, after the bladder 
begins to rife, it expofes a greater furface to the air 
underneath, which makes it move more eafily. I 
have not brought into this account the force, that 
keeps down the valve, that arifes from the weight of 
the bladder, and the refill ance from its being 
ttretch’d ; for I look upon thefe as fmall, in compa- 
rifon of the other. 
I was not however contented with this conttrudHon 
of the valves, till I had tried what effedt would be 
produced, when they were opened by the motion of 
the winch, independent of the fpring of die air: 
4 And 
