44 



ELASTICITY OF AIR. 



of air. There now remain in the vessel eight million, one hundred thousand 

 gruins. Of this again a tenth part is expelled by the third stroke, that is, eight 

 hundred and ten thousand grains. The quantity remaining in the receiver will 

 then be seven million, two hundred and ninety thousand grains. The tenth 

 part of this is expelled by the fourth stroke, that is, seven hundred and twenty- 

 nine thousand grains, and there remain in the vessel six million, four hundred 

 and ninety-one thousand grains. The fifth stroke expels a tenth part of this, 

 or six hundred forty-nine thousand, one hundred grains, and there then remain 

 in the vessel five million, eight hundred forty-one thousand, nine hundred grains. 

 A tenth part of this again is expelled by the sixth stroke, that is, five hundred 

 eighty-four thousand, one hundred and ninety grains, and the remainder in the 

 vessel is five million, two hundred and fifty-seven thousand, seven hundred and 

 ten grains. A tenth of this again, or five hundred twenty-five thousand, seven 

 hundred and seventy-one grains, is expelled by the seventh stroke. The fol- 

 lowing table exhibits these results : 



By attending to the numbers in the third column of the above table, it will 

 be perceived that each succeeding number is nine tenths of the preceding one. 

 It follows, therefore, that after each stroke of the piston, the quantity of air 

 which remains in the vessel R, will be nine tenths of the quantity which it 

 contained before the stroke. From a due consideration of this circumstance it 

 will be perceived that, however long the process of rarefaction be continued, 

 the vessel R, can never be completely exhausted of air, for a determinate 

 j quantity being contained in it, nine tenths of this will remain after the first 



> stroke. After the second stroke, nine tenths of this again will remain, and 

 s however long the operation be continued, still a determinate quantity will re- 

 Jllmain after every succeeding stroke of the piston, this quantity being nine tenths 



of what the vessel R contained after the preceding stroke. But, although a 

 perfect exhaustion can never be attained by these means, yet if the instrument 

 now described could be constructed as perfect in practice as it is in theory, 

 there would be no limit whatever to the degree to which the air in the vessel 

 R might be rarefied. Thus, by a determinate and finite number of descents 

 of the piston, it might be reduced in weight to the millionth part of a grain, or 

 even to a quantity millions of times less than this. Still, however small the 

 j quantity which may remain in the vessel R, so long as the elastic force by 



> which i-ie r.irticles repel each other exceeds the weight of the final or ultimate 

 ( parti clee o.f the air, so long that repulsive energy will cause it to expand 

 S thuaipi the tube C, into the cylinder, A, B. 



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