[ 4* 6 ] 
I (hall not take up time with a particular recital of 
the alterations I have made, for near four years pail, 
in order to remove fome obstacles, which I imagined 
hindred the effedfs, that the theory I fet out upon 
feemed to promife. It will be lufficient, that I give 
an account of what has appeared to anfwer befl, 
after a great number of different trials; which, tho* 
fhort of what I at firffc expedted, yet as this pump 
performs much better than the common ones, my 
labour may not be thought wholly ufelefs ; and the 
refpedt, which I have to the Society, would ftill have 
prevented me from troubling you or them about it 
at this time, could I have thought of any alteration, 
that promifed materially to improve it. 
The principal caufes of imperfedtion in the com- 
mon pumps arife, firft, from the difficulty in open- 
ing the valves at the bottom of the barrels ; and, 
2dly, from the pifton’s not fitting exadfly, when put 
clofe down to the bottom ; which leaves a lodgement 
for air, that is not got out of the barrel, and proves 
of bad effedt, as I ffiall ffiew in the courfe of this 
paper. 
In regard to the firft of thefe caufes ; the valves of 
air-pumps are commonly made of a bit of thin blad- 
der, ftretch’d over a hole generally much lefs than 
one tenth of an inch diameter ; and to prevent the 
air from repaffing between the bladder and the plate, 
upon which it is fpread, the valve muft always be 
jeept moift with oil or water. 
It is well known, that at each ftroke of the 
pump the air is more and more rarefied, in a certain 
progreffion, which would be fuch, that an equal 
proportion 
