ELASTICITY OF AIB, 



43 



whole. On depressing the piston, this tenth part is expelled through the tube 

 D. On elevating the piston, the air remaining in the vessel R, which is nine 

 tenths of the original quantity, now expands through the vessel and barrel, and, 

 for the reason already assigned, the barrel will contain a tenth part of this re- 

 maining nine tenths ; that is, it will contain nine hundredth parts of the original 

 quantity. On the second descent of the piston, this nine hundredth parts will 

 be expelled. The nine tenths which remain in the cylinder after the first 

 stroke of the piston, have now lost nine hundredth parts of the whole, and since 

 nine tenths are the same as ninety hundredths, nine hundredths being deducted 

 from that leave a remainder of eighty-one hundredths. 



This, therefore, is the proportion of the original quantity which now remains 

 in the vessel R. When the piston is next raised, this portion will expand as 

 before into the enlarged space, and the tenth part of it will rise into the barrel. 

 But a tenth part of eighty-one hundredths is eighty-one thousandths. Accord- 

 ingly, on the next descent, this eighty-one thousandths will be expelled. The 

 eighty-one hundredths which remain in the vessel R before this diminution, 

 are thus diminished by eighty-one thousandths. This eighty-one hundredths 

 are equivalent to eight hundred and ten thousandths, and therefore the quantity 

 remaining in the vessel R, will be found by subtracting eighthy-one thousandths 

 from eight hundred and ten thousandths. 



The remainder will therefore be seven hundred and twenty-nine thousandths, 

 which will be the proportion of the original quantity of air which remains in the 

 vessel after the third stroke of the piston. It will not be difficult to continue , 

 this reasoning further, and to discover, not only the quantity of air expelled at > 

 each successive stroke, but also the quantity remaining in the vessel R ; and 

 we may without difficulty compute the following table : 



To make this table more intelligible, let us suppose that the vessel, R. con- 

 tains in the first instance, ten million grains of air. The first stroke of tt 

 piston expels a tenth part of this quantity, that is, one million grains, 

 remain in the vessel, R, nine million grains. The tenth part of this n 

 million is expelled by the second stroke, that is nine hundred thousand graj 



